 Ciao, Alessandra. Ciao, buongiorno e buon merede. So, welcome back everybody. So, Atish cannot be here. I think he will join telematically later. Ok, welcome to the third lecture of Professor Alessandra Bonanno. And she's now going to talk about constraints on gravity and modified theory of gravity. So please if you can share your slides. Great. I leave the floor to Alessandra for her third lecture. Thank you. Ok, good afternoon. I'm very glad to be here again. So, I wanted to have just a short connection with the previous lecture where I was showing you these slides that summarized the questions in physics, industrial physics that we are addressing with gravitational field observations. And today I wanted to focus the lecture on how we can use the gravitational waves to probe gravity in the highly dynamical strong field regime. However, before doing that I wanted to spend the first ten minutes also telling you something that I couldn't cover last week, which is basically how we are, what are we learning about the formation scenario for the compact object binaries that we are observing. I merely discussed on Thursday and Friday so-called exceptional events, but we have not discussed how we are seeing the entire population. So I wanted to actually spend just the first ten minutes on that. So this is the outline of my presentation of my lecture today. So, as I said, I will first discuss some of the astrophysical properties of the binary system seen as a population. And then we are going to see the test, the theoretical diagnostic test of general relativity, which the observation of LIGO and VIRGO have enabled in the last few years. In particolar, the test of so-called gravitational wave generation, where the conservative and dissipative dynamics is intertwined, the test on the gravitational wave propagation. What can we say about the object that forms after merger and gravitational wave polarizations. We will see, not surprisingly, that so far the binary neutron stars and neutron sub-black hole binaries that LIGO and VIRGO have observed are consistent for the inspired stage with general relativity, and the same is true for binary black holes, including goals for the merger and the ring down. Now, through the lecture, I will also point out in a few occasions the fact that so far this test, at least from the point from the side of the LIGO and VIRGO collaboration have been done as student diagnostic test. And so what are the prospects of theory specific tests of general relativity, and this we will see in a few times. Ok, so, again, this is the overall plot that describes the binary black holes. This is the mass in solar masses that have been observed by LIGO and VIRGO, so you can see a variety in the distribution of masses of the black holes, and also the neutron star that are here in orange, the binary neutron star and the neutron star black holes. Ok, so, a few words about, again, if we look now at the overall distribution, what can we learn about it. So, first let me reintroduce the parameters on which the binary depends, the mass ratio, the total mass, the spins, intrinsic rotation that the neutron star or the black hole carry. And there is a combination of the spin that was alluding last time on Friday that is best measured, which is the projection of the spin weighted by the masses along the direction perpendicular to the orbital plane. Now, when we put together the events, for example, the second catalog, which is not the latest one, the latest one is the third, but this is the first six months of the most recent run, which is called O3, the third run. So, if you put together the posterior distributions, now I don't pretend that you can appreciate all the details here, but these are the order, I think, of 24 sources. These are the so-called violin plots, the posterior distributions for the mass or the primary, the secondary mass ratio, the sky effective and the distance. I just want to give you the, you can see immediately that there is a certain variety. The total masses of this binary are typically larger than the first catalog, which was covering the first two runs of Lyko and Virgo. Moreover, three, for example, binaries had a mass quite low, between 2.5 and 5 solar masses. Remember the first detection of gravitational waves, the masses were around 30 solar masses. And also, last week, I was pointing out that there will be one particular event with very large masses. In particular, the primary mass is above the mass, where we think black holes from the collapse of stars should not be there. And actually, the first six months of the run had overall three binaries, with component masses larger than this value, which is the beginning of the gap, the so-called supernova mass gap, the instability supernova mass gap. So, it was not just an accident that we found, that Lyko and Virgo found, one event there. Moreover, people are also interested to understand whether the spin of the black holes or the neutron stars are different from zero. And at 90% credibility, time sources had this high effect, this combination to be positive, which is possible if the spins, at least one of the spin of the two black holes is also positive. Another question we are interested in is the projection of the spin on the orbital plane, because that will give us information about precession. If the spin are precessing, are not aligned with the orbital angular momentum, they produce some precessional cycles, and in principle they could be measured. And so this parameter is denoted kip, and here the posterior distribution is plotted for some events contrasted with the prior, which is on the right. And you can see some mild sign of precession in the sense that the posterior distribution is slightly different with respect to the prior. And last week I was in particular telling you about this actually effect of the precession for the very large binary black hole 1905-21. Okay, so now this was just the first six months of the last run. Now if you add the second six months of the last run, which ends basically all the binary black holes of binary, compact binary observed by Lyko and Virgo. These are the new events. This is again the mass ratio, and this is the total mass. And I want to highlight just a couple of them. The 20th of February 2020, Lyko and Virgo measured observed another very high mass binary, which was very far from us, a six gigaparsec. You can see here the total mass being around 200 solar masses. Another binary I want to highlight is this one, which had a mass ratio around 33. This is really quite an unusual event, in fact the largest mass ratio that we have seen, which poses also some challenges from the point of view of the modeling. So that's quite interesting. And finally, I talked also about last week, we had the first neutron star black hole that was discovered, which is actually the position distribution is represented here. Now an interesting quantity that astrophysicists are interested in is basically to compute the mass spectrum, for example, for the primary mass in the binary. And now what you can do with that is that you can actually try to use it to in fact maybe discriminate between population, different population of compact objects. I'm listed here the main channels to form binary systems. I don't have the time to go into the details. I just want to highlight a couple of them. The binary could be from what we say isolated binary channel could be coming from, which is basically a binary originally composed of stars that then go to supernova collapse and form black holes to neutron stars. And another big main scenario is dynamical interactions in global cluster, young cellar clusters, where the compact objects, black hole and neutron stars could form the binary by dynamical capture. And so they have not always been together if you want, but they come so close to each other that they are captured in a bound orbit. And primordial black holes that do not come from the core collapse of stars, but large fluctuation in the early universe. And people have been interested also to see if there are subpopulation in all this, you know, 90 binary system that we have discovered if there is a subpopulation of primordial black holes. Now, one way of discriminating between these scenarios is to look at quantities like the distribution of masses, but also the eccentricity, the spin magnitude, the spin precession. Because, for example, you would expect precession if the two compact objects are dynamical, you form the binary through dynamical capture because you can imagine the spins are originally randomly oriented and then when the binary comes together they still have memory of a generic direction of the spin in space. And while with this scenario here, isolated binary channel, you generally tend to have spin which are aligned with the orbital angular momentum. The spin magnitude also can have an impact in the primordial black holes because we expect at least in some scenarios that the spin are basically negligible for primordial black hole population. It is true that at the moment we are not able to extract in detail this information. So it is difficult to actually disentangle one scenario from the other. I think in the future with many more events this will be possible. Now, what I wanted to show you is that now if you take all the parameters that you have extracted, so you have all this population of tens of events, you do an inference study, and then you can try to fit this population for the mass of the primary. You can try to extract the spectrum of the binary black hole primary mass by fitting all the population with a function that in the first approximation you may think this could be just a simple power law. With an abrupt cut off because of super low apparent stability you would expect that basically there is a cut off with a mass larger than 50, 45, 50, 60 solar masses that you don't see anymore black holes at least up to, you know, something like 120 solar masses. This is the results of the study done by the Lagoon Vico collaboration. There are different models, I'm not going to describe them. But what came out is that actually there is a strong statistical preference for a mass distribution model which is not a simple power law with an abrupt cut off. In fact, there are some features in the spectrum around 35 masses, solar masses 18 and 10, which are not completely understood. Perhaps this one comes from the beginning of a possible mass gap, but the mass gap, as I said, is not an abrupt cut off. The 10 solar masses here, while there is a lack of binary black holes at mass in this range, so at some point you have a peak and this could be explained with the population, the isolated binary population, for example models. But the 18 solar mass peak here, for what I understand is not really understood, what's the reason. So I'm sure there will be many studies in the future about that. And the other important question you can ask is to look at the larger rate, for example of binary black holes on this population as a function of the redshift, also that you can reconstruct. And this is plotted here at a 95% credible level, and you see also here the star formation rate as a function of the redshift. And the merger rate follows, as expected, the star formation rate. We cannot say at the moment whether we can see a peak in the merger rate, the star formation generally has a peak around between I think 1.5 and 2 in redshift. Ok, now finally considering all the binary black holes and the binary neutron star only two binary black holes in particular that we have discovered but with the binary neutron cell black hole. You can also estimate the so-called stochastic or a background of astrophysical background of these objects from the merger rate. And this is just the forecast taken again from Eligo paper of the energy in the background, the stochastic background due to the sources that you can see here. And when you take the total you get basically this upper bound here and I wanted just to highlight that this is the last run that was done. So in order to detect this background astrophysical background of made of all the binary, the signal from binary system that we cannot resolve individually. And we will need to go to not even beyond the four or four will start as I was saying last week at the end of this year. O5, sometime in 2025-2026, there might be the possibility of reaching this level here. Ok, so with that I finish this first part and now I want to dedicate the next 45 minutes to the test of general relativity that has been done in the last couple of years. So, first of all, let me emphasize again that the regime that gravitational wave detectors are probing is different from the one that you can use to probe general relativity in the solar system with the experiment gravity. In this case, you are looking at the galactic center eventurize on telescope because in this case you are looking at a stationary black hole and and an object that go around or in this case also affect you to the equation these etc. For binary pulsars, you are in the strong field by the velocity is still low. And so here is really strong highly dynamic a regime as we are used to say. Io credo che molte persone hanno il loro plotto di favorito per contrastare questi risultati e ho preso uno dei rapporti dei dettagli di determinazione. Questa è la carbatura, che scala come l'inverse di km qui. Per solo un obiettivo, questo sarà il massimo dell'obiettivo. E qui hai il potenziale. E ci sono molti punti che rappresentano i risultati nel sistema solare, i pulsati doppi, etc. E non voglio parlare del fatto che se sei in un sistema binari, l'ultimo sarà la separazione. Questo può essere tradito anche come la velocità in il binario, l'ultimo. E se stai in questa direzione e sei in velocità di alta velocità, e qui hai i dettagli di base di grado, questo è in spazio. Questo è l'esperimento di gravità, con i flasciati osservati sui Stati Sagittarius. E l'eventorizontelescope, in realtà, il Messia 87, l'immagine, è andato qui, perché la carbatura è più piccola, perché il blacolo è più grande in massima con il rispetto di uno all'interno della nostra galaxia. Quindi questo sarà essenzialmente dove l'eventorizontelescope sarà se la nostra blacola, la centrala della nostra galaxia, sarà mescata. Ora, come se consideri i complettori di coppato di obiettivi che sono più piccoli insieme, quindi, effettivamente, bene, se la complettoria del massimo è più piccola, la carbatura è più grande. È per questo che, con il detecto di grado, la carbatura è più grande che per eventi che vedrete con l'IASA, per esempio. Excepto le minari di massimistra, dove potete avere un obiettivo più piccolo. Quindi questo arriva anche in questa zona qui. Ora, cosa voglio dire è che se hai due cittadini in un motore in bollito, come ho detto, il V² è questo e il Mvrl, e la carbatura, in realtà, è la frequenza di la minari, e puoi compruire per mettere i numeri qui. E quindi questo significa, insomma, se hai sorsi che migliorano in cittadini, la carbatura, la carbatura sarà più alta. E questo è il caso di Mvrl, per esempio, o a massimistra con piccoli cittadini. Ora, un altro cosa che voglio dire che potete tornare più tardi, è che l'orbitale periodo, quando i due cittadini andano per l'ultima volta, migliorano molto rapidamente, per esempio, con un ordine di magnitudine da 30 a 130. Quindi la faccia della formazione, migliorano molto, molto velocemente. Questo è diverso da, per esempio, cosa hai fatto con la minari Pulsar, dove la variazione in periodi orbitali è piccola, molto piccola, ma, ovviamente, è usata per testare o generalizzare, ma se stiamo facendo la seconda derivata di l'orbitale periodo, sarà sicuramente ineggibile per la minari Pulsar. Quindi questo non è il caso per cosa il migliorano in periodo può vedere. Ok, ora andiamo al testo. Quindi, sto riferendo qui a questo pezzo più recenti, che il migliorano in periodo di migliorazione ha fatto sull'alchivio l'ultimo dicembre, per la seconda parte del terzo riferimento, c'erano 14 nuove minari di Pulsar, un'ultima minari di Pulsar, ma questi risultati sono anche aggiornati in un modo cumulativo, perché potete aggiungere eventi, così che i tuoi bambini diventano migliorati, per il numero di minari di Pulsar e minari di Pulsar che sono osservati precedenti. Ora, potete vedere qui che non hai, come ho detto, un numero di eventi negli eventi, e il risultato è che questo testo di generatività non è fatto sull'interno della popolazione, ma solo per i signori di gravitazione, che hanno un riferimento di Pulsar meno di 10 a minus 3 per l'anno, solo per essere più confidenti sull'alchivio. I signori sono più forti e sono più confidenti di il loro origine. Ok, ora, per imparare a voi, questa è la tabula del paper che illustrava tutti questi eventi, il XIV e il XIV, non potete vedere, sei andando a leggere qui, questi suggerono i parametri, il massimo, la distanza, il riferimento di gravitazione, che potete vedere qui, e ora questi sono i testi che sono perfetti, e questi sono tutti testi nulli, quindi testi teoriagnostici, e uno è assurdo che in genera relatività è rappresentata da un sistema quasi circolari circolari, e l'altro è l'indegnazione. E questa indegnazione lo assurgo di essere piccola, ok? Quali sono questi test? Ci sono i test residuali, che vi explico in un momento, i test consistenti che, in spirale, mescolano, seguono il tipo di segno che vi aspettano in genera relatività, i parametri, i test parametri di generazione o gravitazione di gravitazione, i test sulle strutture multipli sui obgetti compatibili durante il spirale, il riferimento dispensato modificato in alternativi teoriogenerativi, per esempio, se hai una gravitazione di massimo, se hai una gravitazione di massimo, i test della remnant, se la remnant è un col bianco bianco, o qualcosa di altro, o neutro star, ecos che potrebbe essere prodotto se non hai un orizzone o una superficie che è solo assorbente e polarizzazione. Ora, per tutti questi test, i modelli di riferimento che sono usati sono in due famiglie che avevo descrivendo l'ultimo freddo, quindi sono un fenomeno, un fenomenologico, ed effettivamente uno di questi riferimento, quindi non sono andati a discutere loro più oggi, ma questi sono i riferoni che saranno usati, dependendo del test. Ok, andiamo ad iniziare dal test di riferimento. Questo è importante per, in realtà, è un test importante per capire se la nostra assumptione che genera l'attività va a essere violata, che la violazione va a essere piccola, è importante. Quindi, cosa ha fatto? La questione che si chiede è sono i riferoni, quindi le remnanti di riferimento consistenti con il noio nel dettaglio. Quindi, uno studia in cui uno, basicamente, sottratti per le data la possibilità maximale del templo GR, quindi hai una analisi visionale con il templo GR, si guarda al best fit e poi si sottratti e si guarda, basicamente, alla recidua. E questo è fatto per ogni evento una seconda per il tempo del triggere del evento. E ora hai compunto questa recidua, hai guardato la recidua, hai basicamente guardato quanto il signo alla raccoglione c'è in la recidua e, infatti, hai compunto il limitato di 90% di l'attività sull'attività del SNR, sull'attività del SNR e cosa vuoi è che questa quantità deve essere, basicamente, deve essere non molto differente da... deve essere consistente con il noise del dettaglio. E questo è il triggere della recidua SNR per gli eventi differenti come funzione del SNR del templo GR che è usato per quel particolare evento. E quello che hai ad ottenere da questo triggere l'ultimo che voglio dire è che c'è l'absenzio delle correlazioni tra il 90% di l'attività credibile sullo SNR che compunto da la recidua e il SNR due al templo GR. E questo basicamente ti permette di concludere che che i signori sono consistenti con il templo GR. Quindi è una buona assenzione per assumere che, you know, il templo GR fa una buona assenzione per il signore. Ci potrebbe essere un belato di small deviations. Che è quello che stiamo avanti. So, let me go now the first test I want to describe. This is called the Inspiramurgering Down Consistency Test was done from the very first paper of test of general relativity with the Laguan Vico collaboration, the first event Gravitation away 150914. And in fact what you do is that you basically try to understand whether there is consistency in the spiral and post-inspiral part of the signal. Now it's a bit arbitrary to decide where the post-inspiral starts. So what is done is that you take the mass and the spin of the remnant and you compute the innermost settular orbit as your point of transition between inspire and post-inspire. And I just indicated it here for this particular example. Then you compute the final mass of the object that forms after merger from the parameters, the masses and the spin of the spiral part and you do the same just looking just basically using the data up to this point and then you do it from this point on this will be the mass or the spin from the post-inspiral part and then you compute these two quantities that if there is consistency have to be zero otherwise there will be evaluation. And for this test you can imagine you have to be you have to have enough signal to noise ratio in the spiral and the merger so you cannot use all the events and also you really have to have some you know in spiral part that is not negligible for this test so you also have a bound on the total mass of the binary and so only these events were used in this latest study by Lago and Virgo this is the signal to noise ratio and the results is the following for these two quantities now these are the possible distribution that if they encompass zero means the test is good for generativity generativity is here zero then you can basically compute also the possible distribution that are here in gray combining the likelihood of all the events assuming that if there is a deviation this is going to be the same for all the events and this is basically the result of the gray area and by the way the color here just means the total mass of the binary so the color difference because i mean you can have again test that depending on how much is the total mass you are more having you know for low total mass means you are more of the spiral larger total mass means you are more of the of the merger in doubt now this way of combining the events it's too it's non conservative perché you are assuming that if there is a deviation from a generativity that's the same for all the events but that deviation may depend on the parameters of the binary so a hierarchical combined method has been introduced since i think a year or not in the analysis of the live and view data and so what you do here is that you don't assume that all the deviation parameter are going to be the same the non-gr parameters as i wrote here are drawn from a common gaussian distribution which has a certain mean and the standard deviation and the mean and the standard deviation are inferred from the data so now when you do this test you also basically include also these other two parameters and these parameters are then inferred from the data they have to for gr this parameter will be you know mu zero and sigma zero so if you do that so if you use now the hierarchical combined methods and you also put together all the events cumulative so this is only the first catalog the second catalog the third catalog in a cumulative way you can see that the posterior distribution for example for the mass of the remnant becomes narrow as you narrow it as you should be the case because you are adding more events and you can see here for the spin and these are the bounds at 90% level if you were using the hierarchical combined method or if you were using the joining the posterior which is less conservative okay so now let me go to another test which is done by the library and we go collaboration which concern is called parametri test of the generation of gravitational waves i was saying at the very beginning that you have we have this compact object going very fastly at the very end the orbital period is changing so we can probe the post Newtonian parameters in the phase and also higher order parameters in the merger in down by decomposing the waveform in frequency domain in an amplitude and in the phase the amplitude is not very important here we focus on the phase and the phase in frequency domain besides some irrelevant terms here constant and linear enough can be written as a post Newtonian expansion and this coefficient here are computed in general relativity I will show you in a moment what they are but you can add corrections okay here and how do you get this coefficient well on Friday I was telling you that the phase of the gravitational waveform is computed from the binding energy the luminosity I wrote here at reading border and then through the balance equation you can compute the phase and then you go in the frequency domain and you have it in the frequency domain now I want to actually also highlight one thing that these two quantities and their deviations you know they mix the conservative and dissipative part this is important to keep in mind when we do for example relate to other experiments that are also putting bounds on this position and parameter because some of them are only looking at the conservative part of the dynamic although binary pulse are also the dissipative as you will see in a moment later now to be more quantitative I want in full glory to show you what is this post Newtonian phase in general relativity computed in post Newtonian so I wrote here SPA just mean stationary phase approximation this is for quasi circular orbit all the test I'm going to describe are for quasi circular orbit so this term here is the leading order term B to the minus phi nu is just the symmetric mass ratio then at minus 1 pn order you start seeing here a term which actually should not be there in gr it's for example in France-Dicke in the Jordan Fields-Brand-Dicke theory this would give rise to dipolar radiation this term at 1 pn you have a genuine post Newtonian general relativity term which is this one but you can have a term that is there if the graviton has a mass which induce a 1 pn correction that depends on the Compton wavelength of the gravitational associated to the graviton and also the distance of the binary to the source so we will come back to this later at 1.5 post Newton order you have spin orbit terms that are in this coefficient beta at 2 pn you have a spin-spin term that are in this coefficient sigma and at 5 pn you can have tidal effects I alluded to them in the lectures of last week they are there for neutron stars because lambda is different from 0 in neutron stars they depend on the equation of state of neutron star on the radius of the neutron star etc now one important piece of information is that when you look at low post Newtonian terms the leading board minus 1 pn 1 pn they dominate at low frequency V here depends on the frequency the high post Newtonian terms are going to important as you can imagine close to measure at high frequency now I also wanted to show you the waveform how it is modified when you add these deviation parameters I was alluded to and I want to give you this example sorry here so this is a signal like one of the signal that were discovered during the second run I had a mass ratio 9 this was the binary with a positive companion if you add 50% of valuation at 1 pn and you align a parameterized waveform where you have this deviation with a non parameterized waveform at 20 hertz you start seeing as you see the deviation as you move towards merger however with these methods when we add one parameter and then we look for it with the data we at some point we go back to the waveform in general relativity we apply this only to the inspirer and so if I take now this and I align the two waveform at merger they are going to be the same so the last part is the same but we are looking at this region of the inspirer where we are adding this extra parameter so what are the results okay so we add this extra parameter at each post Newtonian order each time varying the post Newtonian order and we do a vision analysis together with all the other 15 parameters on which the binary depends and then we plot here the posterior distribution after marginalizing on all the other parameters for for example the minus 1 pn the 0 pn etc etc and for the phenomenological model we can have also parameters that describe the merger in downs that are tuned to numerical relativity but then they can be you can add a deviation to them and the different colors okay correspond to the different models because we want to understand the systematics that's why we use different models and whether it's empty or full it's where you use join the different events combining the likelihood just multiply the likelihood or you use the southern method of the eratical combined method so all the posterior here this is the second catalog in Compasero so this means GR is not violated so then you can turn it in a bound on these parameters and I want to highlight first of all the scalar sorry the dipole emission the minus 1 pn this is a test of the strong equivalence principle this is for the binary black holes and you can look here at the binary neutron star we'll come back to this in a few slides because this is important and these are the different post-neutronian parameters and you can see the single event and then with a triangle when you combine the events all together and the color here represent again the total mass or the chip mass of the binary so red means you are having a system that are more massive and not surprisingly you can put constraints on more on the mergers in down parameters and when you have more access to the inspirer you can put constraints on the post-neutronian parameters now this was the second catalog and I should say I forgot I wrote here you can also use these results to put some constraints on a specific theory of gravity alternative to generativity and we'll have actually a slide in a moment also about that but let's go to the most recent catalogs now you can add the 15 events that were discovered during the last six months of the third run and these are again the posterior distributions and when you put now these results together again if you use the hierarchically combined methods you will get a posterior on the mean and the standard deviation parameter of the underlying distribution because this is the method as I said in which you don't assume that the deviation parameter is the same for all the events and the results you get by using this hierarchical method is now the following so this is again adding all the events including the second catalog up to the third for the post-neutronian parameters and I want to highlight this point here for the dipole emission which is a factor of two better than the previous results due to the neutral sublacol so the neutral sublacol it's a very as many many cycles because of the mass ratio e quindi hai una testa più forte di una termina di minus 1 pn e ancora qui è il star neutro e questi sono tutti i black holes che potete vedere tra il secondo e il terzo catalog non c'è molta difesa ok quindi ora voglio dire qualcosa ah ok scusate, scusate anche in questo modo quindi una cosa per mantenere in mind è che tutti questi test assumono che la deviationa del genere di l'attività ora c'è una teoria alternativa di generatività che predicta alcuni effetti non perturbati vicini a merda come per esempio la scolarizzazione dinamica e per questo caso questo test non può essere usato anche per i black holes quindi comunque questo è solo un commento ora vediamo più a la star neutro la star neutro era un signo molto lungo quindi è perché possiamo mettere il più lungo test specialmente a la frequenza low per l'emissione di dipole quindi questi erano i blocchi di viola per questo evento e questo è il flaccio questo è la deviatione se avete dipole determinato se avete l'emissione di dipole e quindi la bonda è la cosa di l'ordero di 10 per i minus 5 che è anche rappresentata in questo blocchio qui ora se prendete i pulsari di bilano i pulsari di bilano sono molto sensibili per la dissipazione delle effetti dissipativi e la bonda è un po' di ordano di magnitudine che cosa puoi fare con l'Ido e l'Ivo e ma ovviamente ancora la questione quello che avevo detto prima questo test anche per la star neutro è una cosa per ottenere anche attenzione se non sono delle effetti perturbativi che non potrebbero scegliere una frequenza che non potrebbero scegliere in realtà con con questo metodo perché questo metodo assurda che hai una small deviatione da generatività ora se volete tornare questo bond questo è un test teoreognostico ok non ho specificato alcune teoreogeneratività ora se volete tornare in una bond per una teoria specifica vorrei prendere un esempio che è Giordan Fils Franz Dicker che io credo molti di voi sono famigliati questo è abbastanza constrainti io vorrei dire quindi ho preso qui l'instant in realtà l'instant frame c'è il parametro brasdicker che potete anche tradurre in termini di un altro parametro che è chiamato alfanot e cosa puoi far è che puoi usare l'evento di una star neutro per constrainti ora omega brasdicko alfanot ma ora è un punto importante che se usate aggiungere il parametro brasdicker come ho detto fino a ora e faccio il parametro brasdicker e avete un priori che è uniforme su questo parametro brasdicker puoi ottenere un certo risultato ma se sei specificato dall'inizio la teoria specifica teoreogeneratività che vuoi testare poi potete samplare direttamente alfanot e di un priori uniforme su questo parametro e infortunatamente perché anche il risultato silenzio non è molto grande per queste sorgizioni siamo ancora dominati dal priori in questo calcolazione quindi solo perché voglio brevemente di questo quindi in questa teoria la teoria 5-2 coefficiente nella fase è proporzionale per la differenza tra la città colorata dei due star neutro quindi in analisi in cui hai a prendere in account anche la questione di stato dei due star neutro dei maschi perché la città colorata dipende di loro e quando si fa questo fosse fatto da Noah Sennet in questa preparazione hai la distribuzione di posizioni per il parametro alfanot nel caso in cui si fa questa teoria mnostica teoria specifica e ci sono alcune differenze che sono più piccole che la differenza due per esempio la questione di stato che hai usato e perfettamente questa è la città che si può mettere e ora quando compare con la città colorata hai un po' di ordine di magnitudine che è meglio con la città colorata e infatti ho rimanato con Cassini l'omega drastica che corrisponde a questo valore che in realtà ora la città colorata è anche meglio che questa è l'ordine di 40.000 quindi ovviamente è la prima volta che questo può essere fatto con le gravitazioni gravitazioni in la città colorata dinamica ma questo ci ha dato un'idea anche per questo particolare test della emissione di dipole come questi risultati compare con cosa è disponibile oggi con altri esperimenti ma con le gravitazioni i quali si può fare meglio lo vedete in un momento quindi qui non posso resistere a mostrare i risultati con la città colorata che erano in realtà sono avvenuti l'ultimo dicembre questo si è stata per 16 anni ora e nel piatto nel piatto hanno un'interessante piatto dove si muove esattamente questo parametro di deviazione che ho mostrato in prima volta come funzione del post-neutonio ordine e questo è il risultato più recenti ma questo non è l'emissione di dipole ma l'effetto di livello l'effetto del quadro per la deviazione e potete vedere che il passato doppio fa meglio che la neutro star neutro star e il blacol binary in LIGO ma perché è meglio? perché cioè le persone hanno osservato questo sistema per 16 anni e il sistema ha fatto praticamente 60.000 orbitali e quindi questo corrisponde a molti molti cicoli quindi sono hanno un'occurità migliore ovviamente e ora mi voglio dire che ovviamente ok 0.5 pn non è non là in generale relatività quindi anche questo è molto interessante che il pulsato binary può fare comparabile con LIGO ma come si vede beyond 0.5 pn potete vedere che il pulsato doppio non può accedere il mesuramento che possiamo fare su con l'observazione di gravitazione sullo grado o anche in spazio e il riso è perché la velocità del pulsato doppio è ancora più bassa che quello che potete avere con le gravitazioni con LIGO e Virgo che provano i due obgetti per l'ultima volta dove la velocità diventa vicino all'attività di spazio dovrei avere ora questo passaggio prima so mi voglio comunque cercare che per ok la radiazione o anche il quadrupole live in gorde se consideriamo il futuro e come possiamo fare in futuro con la prossima generazione di LIGO i detettori solo aumenta la sensitività ma anche per l'esplorazione l'esplorazione l'esplorazione o anche l'esplorazione dipende di il black hole il tipo di stagione neutro puoi vedere che possiamo constrere per esempio l'emissione di Darpol abbastanza bene e anche meglio se fai questo multiman band gravitazione con l'astronomia dove vediamo l'evento prima in lisa e poi i detettori sullo grado e c'è un studio che ha fatto recentemente per vedere come l'esplorazione neutro evoluziona solo una progettione con i detettori future sullo grado e in spazio ok quindi ora facciamo cambiare il tema puoi anche testare la presenza di puoi testare se l'esplorazione quadrupol sui obiettivi compatibili nel binario è l'esplorazione generativa per i black holes quindi l'esplorazione neutro quadrupol momento come ho scritto il degree di blackness dell'obiettivo che è due per l'esplorazione e questa quantità è imprintata è una di le termini nella spazio post-intenziale basically è imprintata in una forma gravitazione schematicamente questo esplorazione neutro quadrupol momento può essere scritto in un modo seguente dipende di l'esplorazione neutro e il mass cube e la coefficient capa è una per i black holes ma può riuscire tra i 2 e i 14 per la spazio neutro per le spazioni neutro 10, 150 per riuscire a riuscire a spazio post-intenziale può essere anche negativo per le spazioni gravate quindi ora puoi fare questo test con la data di LIGO LIGO e Viggo hanno fatto questo test e ora il solo parametro quindi in una spazio hai due capano dependendo di una per ogni obiettivo nell'esplorazione di questo esplorazione è stata assurda che la diviazione da il giard value è uguale per le due spazioni quindi solo un parametro è stato vari che è questa combinazione e questo è il risultato della distribuzione di posteriori per gli eventi e questo è il risultato quando puoi mettere tutti gli eventi di tutti gli eventi fino a ora anche il catalogo previso e, insomma, se usate la combinazione iracica in blu e aggiungere multipliando solo la possibilità in grado e questo è il valore ottenuto da l'analisi combinazione iracica quindi è inizio a diventare you know interessante cioè puoi vedere cioè che l'aero è abbastanza grande devo dire ora questo è un test e in futuro puoi provare che gli obiettivi non you know le carbo in generatività per guardare altre cose sono i titoli della formabilità che è zero per black holes in gr non zero in alternativi teori tidal heating i black holes che possono absorvere gravitazioni questo è il tidal heating quindi con il futuro future runs con un alto ratio sigurato questo può essere you know provato e in futuro se pensiamo di Lisa questa misura sarà solo esquisita e voglio mostrare te uno plot forgetting about these three plots here because now I don't have the time to explain the quadruple moment the deviation from the quadruple moment that you can get with Lisa using the so-called extreme maceration spirals with different populations from for the Henry's and also different models for them it will be of the order of 10 to the minus four 10 to the minus three so this will be really amazing you will we will be able to map the spacetime the multiple structure of the spacetime around the compact object with really very high precision so now let me go to another important test that was done by and then we go collaboration which concern now the remnant the object that forms after merger now in general relativity if to black holes merger should be the final object should be a car black hole and there should be characterized the gravitational waves by quasi normal modes and if we believe in a no air conjecture then the frequency decay time for an astrophysical black hole depending only on the mass and the spin so to disprove this conjecture you can observe more than one quasi normal mode compute the mass and the spin and see whether they are consistent with each other now this is not yet possible because we don't have events which have such a large signal to noise ratio in the merger in down to be able to extract more than one quasi normal mode but some work can be done for the dominant mode so there are two methods one use a superposition of damsino soids so I have a question here to show you that the polarization during the ring down can be decomposed in modes in spheroidal decomposed in spheroidal harmonics so you have here a dam part that this is tau okay that depends on the L and M and also the overtone and then you have a frequency of the mode that also depend on L, M and N so one test that was done was the hypothesis was to assume that the dominant mode the frequency indicator where the values of GR but the first overtone was basically a deviation from GR with some deviation coefficient as you can see here so this test was done with the analysis called Kyring and this is the result if you consider only the second catalog and then cumulative the third catalog for this deviation of the first overtone zero again is GR and you can see the bound with the hierarchical method actually the decay time is not very informative from this analysis now the other method that is used by the hierarchical collaboration was actually something that we developed here so we use not the superposition of quasi normal mode but we parameterize and is paramersuring down a waveform model where now the frequency and the decay time depends also on deviation parameter so we have the full waveform for example in example here if you change by 10% the frequency decay time you see you know the difference between the parameterize and the GR value so you can do again you can use this model against the data and these are the results for the fractional variation of the frequency and the decay time for many events that you cannot see here this is emphasizing two events 150914 the very first one and the event which was very interesting was very similar to the first one ever detected but had even a larger signal to noise ratio and in fact it gives the best bound on the dominant frequency and decay time of deviation parameter until now actually and the gray are just obtained you know putting together all the events and these are basically the bounds that we obtain with this analysis now I will skip a moment this so what thing I wanted to say is that now okay so you have a measurement of the deviation of the dominant frequency normal mode what can you do with that okay how can you turn in some specific theory of generatility that's not so easy I want to give you just one example however what can you extract from it in this paper people have tried to describe extract basically the quasi normal mode in a for a dark object in which you replace your eyes on a with a membrane with some you know physical properties including viscosity and they use bulk of theorem outside the black hole so this is just non spinning and they computed the equation for the perturbation and extracted the actual polar quasi normal mode from it that depends now on the viscosity and the deviation from your eyes on epsilon now you can take these bounds on the deviation parameters okay you assume I mean this is a bit qualitative but give an idea of what what you actually can do for the axial perturbations you assume that you can basically measure the deviation on the level of 10-15% so for the real part of omega as a function of the viscosity and the deviation from the your eyes on they excluded some region which are here and here and then you add the for the imaginary part the constraint that come from the measurement and you end up at the end with only this region that is not ruled out and this is the region close to the viscosity of a black hole actually which is 1 over 16 pi and basically tells you that epsilon so that you are you are putting a constraint on the compactness at the level of 10% now it will be very interesting to extend this result to the spinning case because this result this analysis together with many others in the literature suffered from one program when you try to go back to understand you know what does it mean in terms of a specific theory of general relativity is that unfortunately in a a relative theory of general relativity that we know today people have not been able to compute the quasi normal modes for spinning objects because in the spinning case you cannot at least it's very difficult to disentangue the angular part from the radial part as the opposite is in the case of gravity in the case of general relativity have been studied in the small spin approximation but in the full case this is not available and this is important because if you want to turn this bounds on again some theory specific you need to have you need to know what are the quasi normal modes in the case in which you have rotation because the final object that form after merge is supposed to be spinning actually okay so now I wanted just to touch on a couple of other things I think I have two slides if I remember correctly so what are the other important analysis that was done by the Lyman vivo collaboration which is also related with what I was just saying it's in order to probe the object that form after merge you can look for signature of the presence of not an horizon but a kind of surface which can also be reflected which is somewhere this place with respect to the horizon and this is just a picture taken from this paper when you have a surface that can be also reflected not just absorbing like for a black hole then you can have modes that are trapped in this you know region here and they go back and forth and then they can come out from the potential it's got this potential on Friday actually in form of echoes and so the most analysis is done by the Lyman vivo collaboration looking for these echoes these echoes are characterized by some parameters you know the amplitude of the echo when start the first echo after merge the periodicity of the echoes etc and morphology-dependent approach was used using the train of decaying sine Gaussian as wavelets with some parameters which are basically the parameter I illustrated here in this plot e no statistical significant evidence for echo was found ok so now before I conclude tests of gravitational wave propagation have been done I alluded to this one I think on Friday or only even the first lecture I want to talk about another test that is done by the Lyman vivo collaboration which is looking at modification of the dispersal relation in general relativity gravitational waves are non dispersed in the sense that they satisfy this relation now you can add a term this was suggested many years ago by cliff wheel which will be there for example if you have a mass in gravity theory or theory that violates Florence invariance and then I told you at some point in the middle of my talk that if you have for example a massive gravity theory you can have a modification of the phase so massive gravity here will be alpha equal to zero basically and in this case yes I'm done the mass is related to this parameter ok if you put alpha equal to zero and this turns out to be a new parameter in the phase at 1 p.m. post Newtonian order this is what I mentioned some slides ago and now you can do a Bayesian analysis again adding this parameter actually you can do for each value of alpha and just one second and this is the result of the posterior distributions I thought you see only on alpha equal to zero but you can have also for different value of alpha these are the value in plots again that encompass zero which is the value of gr and then you can turn it in a bound and again just looking at alpha equal to zero this is the improvement of the bound which is the bound of the mass of the gravity which improved by factor 1.4 with respect to the previous catalog and is 2.5 better than the bound on the fifth port from the solar system so this is good so I skip this slide you can ask and I want to go to the end because it's time so well try to explain the gravitational waves are christian astronomical messengers which is very important to do this test of general relativity or gravity although there is some contamination also astrophysically alluded last week also gravitational lensing so like when we have already probed started to probe the strong field gravity and highly dynamical regime setting interesting bounds in a so far unexplored territory e I want to stress the fact that the natural of the compact objects at the multiple moments the presence of a photon orbit or light ring your eyes on it etc all this information is imprinted in the waveform not just in the remnant you know it's in each merger inspire a merger in down you can find signature of this effect of what these quantities are and now until now the light of the collaboration has done a variety of teoreal mastic test for inspire a merger in a waveform it will be important to do theory specific test but for that we need to basically do all the work I mentioned to you last Friday to build a waveform model inspire a merger in down in alternative your general relativity and this is not trivial some of this theory also don't have a well post in it's a value problem so they have to be tackled as an effective theory etc but we need to do that you know going more into the future and finally the future is very bright and yeah finally I want you also to say that it's quite interesting also to connect the different experiments that are happening right now even more into the future including binary forces of gravity the length horizon of the telescope so again I want to thank my group and the work was also represented in this presentation and again the legomaterial that I showed is also based and supported by NSF and by other agency and also on the side of Virgo European gravitational observatory etc and so all my colleagues of the library collaboration thank you very much and I stop here sorry to take a few more minutes I think I went a bit over thank you thank you very much thank you for this inspiring set of lectures any question here from the audience hi I have two unrelated questions so since you mentioned effective field theory I was wondering about the leading term in the effective field theory as to whether gravitational waves can tell us about the value of the cosmological constant in 20 degree of precision now or in the future ah yeah well about the cosmological constant so I was I think in my first lecture I gave I showed that binary system are standard sirens so you can do a cosmology with them you can for example actually there was a measurement of the angle parameter eh with the coincident event of the gravitational wave 17 zero 17 now because that event was a 14 megaparsec the only quantity that you can measure there is the able parameter but in the future we are going to see them at much larger redshift so if you start going to large redshift then you can probe with a gravitational wave not just the able parameter you can probe omega matter omega lambda etc so this will be possible in the future I think mainly with Lisa and the gravitational wave detectors of the third generation on the ground so let's say starting from the next decade so yeah that's possible but not right now and my second question is or whether we can observe some super radiance with the present or future gravitational wave detectors and sorry super ah you do you want to know what how can we measure super radiance and whether we can do it at all with the gravitational wave detectors and okay so actually that's something that I didn't I think I didn't discuss at all yes I didn't discuss at all in these three lectures even today which was maybe also a bit overlapping so you might know that people actually starting from work of being Arvanitaki has been pointed out that if you have very low light ultralight particles having mass in you know 10 to the minus 15, 16 electron volts this particle if they exist they could form because of super radiance phenomena they could form bosons clouds around black holes and these clouds could because the cloud rotate and they could produce gravitational waves like monochromatic signals so they are a bit like the continuous waves from neutron stars isolated neutron stars but now this is different these are black holes which have clouds of this form by this ultralight particles and so people have looked at the projection for seeing these signals either a single event or forming a stochastic background like an astrophysical background and there are papers in the literature again you can even today you can put some bound in fact I should say also they like a real gravitational put some bounds but so yeah this is possible this could be maybe not so direct but it's a phenomenon that is a consequence of super radiance thank you very much okay I should have actually mentioned that today but sorry actually I if there are no questions I have well there is a question there so let's start with that Hello Alessandro I am Gips Can you keep your microphone closer is it? Can you hear me? Yeah Okay I am Gips from QLS Okay you talk a lot about the to improve the performance of the detector I wish you know if machine learning could play a role on this process Yes I think machine learning of course is a technique that now several people working in this field are actually employing and until now it has not been used you know for our like for LEGO Virgo detections or parameter destinations but people have applied for some particular cases some binary with a certain mass spin etc because the fact is that you have also trained so first of all you have to train your your metal so for that you have to use the waveforms so the waveforms still have to be produced and they have to be accurate because otherwise so the answer to you is that there are many examples now of groups that are starting to use these techniques they have not as I said being adopted by the LEGO Virgo collaboration but I think this is I think it's very good to take the best also of this method and try to you know combine with what the way in which we have done this until now which you know it was much filtering I have another question she's I don't know if like the detection of gravitational could tell us something about string theory good question she's mine so I mean maybe I can turn it so what prediction from string theory we won't test okay so I think yeah well there are people who are you know proposing that in order to resolve or try to understand the so-called black hole parallel information problem you could have you know modifications at the level of the horizon of a black hole which is quite macroscopic actually because you would expect that generally the detection of the string theory come from the plank scale which is you know maybe inside a black hole close to this in reality but but there are some examples these are not theories I would say are more models where one trying to modify in order to address the problem of the black hole information paradox you know the maybe you don't have anymore in horizon etc and people have used that to motivate the kind of work I was showing where you put a surface which is reflective so there could be a link there but I think we need to have more a connection between the prediction of string theory and you know really something that we can and probe in a considerate way where it's not just a mooder but maybe here we can have a different some comments from you maybe I'm talking with our host Atisha you you raise your hand to ask a question or maybe no, no, no maybe this was the question no, no, this is not the question no I think it would be I mean okay so thanks a lot first of all Alessandro for really wonderful talks and yeah, I had a question I think it would be great if you could use it for testing string theory but I think string yeah some of these corrections are in more in quantum regime so I'm not sure if it will actually be possible to test it yeah, yeah I had a one sort of sort of technical question and one more than the question so one thing I want to ask is that this effective one body formalism which you developed seems to be on some in some ways considering how non linear the system is it's a bit of a surprise why it works so well so can you comment upon that yeah well that's a tough question it's the question of where are the non linearities okay and well first of all I mean I would say the following the higher order post Newtonian terms are important toward the end so it's not that you know if you were using just one post Newtonian order or even not one you know the leading order you will not get a very good accuracy so the high post Newtonian terms are important however what's happening is that the solution of the signal close to the merger as you go to the merger which is an attractor is not wild is not complex is like that the dissipation is so strong at the very end that you basically very quickly you know I have the two bodies just merging with each other and also there is a kind of redshift effect because you know from the observer at infinity as if you think about you are observer at infinity and you have the body that goes around and then merges into the black hole the gravitational wave frequency associated to the orbital motion is actually redshifted from the point of view of the observer at infinity and so you know I mean yeah it's not a high frequency stage or and also the dissipation very quickly you dissipate the quasi normal mode the space time vibrates and so the transition between the phase in which you get the radiation from the object going around and then when it merge and you know you form the final object is so quick so dissipative that yeah you you are not seeing any wildness so so electricity or you know um but the non-linearities are there I mean in the sense you do need higher order corrections yes in post 20 I don't know if I answer your question because this is no I think yeah no I think no okay I mean yes thank you I also had one more general question about the prospects I mean since there are young people in the audience like like Lisa and this Tian Chen I mean they are supposed to come online like 20 30 or so I mean do you know can you say something about the prospects of it I mean where they how yeah where do they stand how they are in terms of yeah so I had something at the end of my first lecture and but I can say again so first of all there are two important things so the space going to space with Lisa and well the Chinese would like to have also at the same time even to the tech course but we don't know you know if that will really happen but for Lisa this is mission that is you know funded and will take place I think the launch is 20 36 at the moment it's a big it's a mission from Lisa with a big participation from NASA and it is going to see sources that are complementary to what l'aigo in virgo in Kagura can see these are supermassive black holes at the center of the galaxy emerging I mentioned the extremist facial binaries more object around the very big black hole white dwarf in our galaxy etc so it's a very rich the scientific case and then the facilities the next facility is on the ground not yet funded but there is cosmic explorer in the US and Einstein telescope in Europe stile the site is not decided whether it will be in Italy or in in the Netherlands or in some other place in Germany so and these are detectors on the ground but the new facility Einstein telescope is underground and is going to see basically black holes up to when the first star forms up to redshift 10 if they are already there we are going to see them so this is also very interesting is broadening the bandwidth going more at low frequency up to 1 amp I also mentioned in my first lecture I mean for the young people here even why you have 2050 program of ESA for the period 2035 2050 it could be also very good for gravitational waves because they selected a team where gravitational waves could be part of it's not yet decided but so I mean for young people the future is very bright so it's a new field and it will last for centuries actually okay so I think we can conclude and let's thank Alessandra once again yeah thank you very much actually to you for inviting me here and so sorry that I could not be there it will be very different experience okay now so before we leave the floor to Atisha for an announcement yeah yeah thanks no so first of all I want to say I really want to thank Alessandra for agreeing to give these lectures even remotely and really very clear and wonderful organized lectures it's really an exciting field and I'm actually happy to announce also that on 9th of February we'll have Virgo and Ago coming and giving a joint colloquium at ICTP so we are really into gravitational wave excitement professor Stavros Katsanevas who's the director of Ago and professor Giancarlo Cella the data analysis coordinator of Virgo they will come together and give a joint colloquium so Alessandra Alessandra you're also invited I'm sure you have you know about it but we will send you an invitation in any case I think it fits very well with your talk so let's thank Alessandra one more and then I have another announcement to make once again thank you again, thank you very much