 Pnežite občasno. Vse je zelo za državnje energije z Flippo Bernizi. OK, zato sem... ...zato sem... ...zato sem zelo. Zato sem zelo, da bomo, da pošličimo... ...završnje potenšel... ...zamega. V nekaj del, da boš vse... kaj je zelo, da se je zelo usuallya, da je to nekaj del, zelo da se je innočno, zelo da se je innočno, da se je, da se je, da se je innočno, zelo se je innočno na strah, na strah, nekaj del, nekaj del, v verbe se vse koristite. So I wrote down this expression, which allows you to compute the effective action. In fact, I would like to consider the simplest case, where I considered the ground field, which is a space and time independent. So it's constant. In mi je tako več, da je devetno odpočen, da pospeš vzelo, eto po jedno ljub, OK? Je to tko složene, da zašliš vzelo vzelo, da vzelo 3 ljubi, je to vzelo, da mosti naša efektivnu atípina jutro je vzela sa pohajnjenj da je zelo pasbačeno. Faktivne aspetivne strane v otej ljube, ki je tačnja, zato, ki se pričem osega je za posluto vse z naprečenje in na kodrå ni še. tudi, da je tudi vse kratilje. Faj, i, vsega vsega vsega, 4, minus 1,5 phi, kratilj, in tudi minus v5 phi, phi 0, phi kratilj. I to me nekaj nekaj nekaj zelo skupil in početno. V fronu... Ja, ker je... ... in, nekaj, da, da. In odlišaj mi, da je menej, da se kaj mi je vzelo, mu square, faj 0, način način, tako, ok. Tako, to je intergačne intergačne. Tako, v prinsipulnih, ne znam, kaj je zelo. Ne znam, da je kvalifikacija. To je intergačne. To je zelo, da je intergačne. In ti je soluzija. Tako, da je zelo kvalifikacija, to ne znam. If you have questions about the solution, we can discuss them together, either in the discussion, or you can come to me. Ok. We will take a little time. So the result that you find is that the, let's say that the one loop effective action is equal to the integral in dx4 minus an effective potential, and since I'm considering a constant phi zero field here, I can neglect the kinetic term, but otherwise I would find the kinetic term. And the effective potential is given by the bare effective potential, which contains the bare value of the cosmological constant, the mass and the coupling. And then I have this expression, which consists in an integral on a four momentum. So this phi is a four momentum. You have a phi zero. So it's a four dimensional integral. And well, as you can see, this integral goes like a p cubed dp, and it's quartically divergent. So it will go as, if you put a cutoff to this integral, it will go like the cutoff to the power four. So there is a trick to, clearly you have to regulate this integral in the UV. There is a trick to compute this integral, which is the following. So this would be the V1 loop. If you take the third derivative of this V1 loop with respect to the parameter mu squared, you find an integral that is convergent. So if you compute the first derivative is not convergent, the second derivative is not convergent, but at the third derivative it is convergent. So you can do the integral, and I give you the result. The integral is very easy. You can do it by weak rotation, for instance. And this is given by 1 over 32 pi squared mu squared. So now I can take this result and integrate it with respect to mu squared three times. So I can find my effective potential. And this will be given by an integration constant A, a second integration constant B times mu squared, and the third integration constant C times mu to the fourth plus something, plus a function of mu squared. So, clearly these integration constants are infinite in principle, because we knew that, we know that our integral was quartically divergent. We can put them together with the initial, with the bare potential. And this at the end, I write here the final result, will give me a renormalized value for the cosmological constant plus a renormalized value for the mass plus some renormalized value for the quartic coupling to the fourth, and then the last term, which depends logarithmically with mu squared, p squared. And this is called the Kolemann-Weimberg potential, where Weinberg is Eric Weinberg. And so our initial focus was the cosmological constant, which should be given by the initial bare value plus some constant, which in principle is infinite, if we integrate over all scales, plus B mu squared, sorry, plus B mu squared, plus C mu to the fourth. And then I can write down that we have them in a note all the other renormalized values, for instance, the mass squared, et cetera. But what we would like to focus on is this result. Well, yeah, you can put some scale. Anyway, you have all these constants, but yes, if you want, I can put some scale here, plus B mu to m squared. So this scale is the reference scale, but anyway, you can always remove it and solve it in one of these constants. Okay, so, yeah, so we see that the, so basically what we measure, okay, is not this bare value, but that is the renormalized value. And it seems that this renormalized value receives contributions from all scales, even from the UV. And in particular, it is dominated by the UV because typically these constants, if we had put a UV cutoff to this integral, it would go like this cutoff to the power four because we said that the integral was practically divergent. So what do we learn from this? If you compare, so as we said, the renormalized value is equal to the bare plus this one loop contribution, which seems to be of the order of the cutoff to the four. Now, the measure value is of the order of three times ten to the minus three electron volt to the fourth. So it must be of the order of H zero. Today, mass bank squared or eight pi, sorry, H zero over eight pi g. Okay. And what is this cutoff here? Well, it's a bit up to a choice, but so we know the standard model very well up to the tev, so tev to the fourth, but we also know that the standard model is not the end of the story. So there must be new physics behind the tev, so we could go even higher with the scale. And, well, the maximum scale that you can imagine would be something like m plank to the fourth because we know at least that, well, at the plank, clearly something happens at least to gravity. So, now, we have something, if we take as value the plank scale, we see that the cosmological constant is, the observer cosmological constant is about 10 to the minus 119 value times this one loop term. So there must be an enormous cancellations between these two terms to give you the observed one. So the fact that we observe, the fact that we see that there are contributions to the cosmological constant that are practically divergent is just an artifact of the fact that we don't know the UV theory. So we cannot compute all our theory up to, well, we cannot make this integral, this four-dimensional integral from zero to infinity. So at some point that we have to regulate it, we can decide to regulate it by putting the cutoff. But, of course, ideally we would like to have some completion, I don't know, some spectrum, some new particles in order to fully make this integral. However, we observe that whatever there is in this integral, it will affect very strongly the observed value of the cosmological constant. So the tiny change in our theory will affect very strongly the value of the cosmological constant. And this is something that you don't see in other places of the standard model apart from maybe the Higgs mass. So you don't see that the mass of the electron is usually affected by the UV, for instance. So this is called the cosmological constant problem, or it's one of the aspects of the cosmological constant problem. So it's a fine-tuning problem. It's a bit like the cosmological problems of inflation. It's not that there is an inconsistency, you measure something that is consistent with your theory. It's a fine-tuning. You see that there is a problem. On the other hand, well, you cannot compute really the cosmological constant. You can only measure it. But if we try to use a fettific theory argument to estimate it, we see that we get something completely different from what we would expect. There is a question from Zoom. Just a clarification. Do we take lambda cutoff as m-plank to get these 10 to the 119? Yes. If you take the tab, you get something, of course, less, but still 10 to the minus 58. There is a discrepancy, which is quite large. So the fine-tuning problem is why the bare value is much, much smaller than the correction to it coming from quantum fluctuations. OK. No, in fact, no, even if you tune this at one loop, and then you compute the two loops, you see the same quartic, yes, quartic divergent. So it doesn't get better. In fact, it's the same, yeah, there is the same problem at each order, at each loop order. Yeah, 119. So here I put the plank mass. So maybe let me write it more. So I can take the plank mass to the fourth. This is about 2 times 10 to the 18 jev to the fourth. And this is about 10 to the 119, what I observe, which is this value. OK. Anyway, it's not so. OK, so maybe just an extra comment. So yesterday I gave you an example of the effect of quantum fluctuations of the electron and positrons in the hydrogen atom. I said, OK, if you consider the exchange of of proton, the interaction between a proton and the electron, and we know that the so-called lamb shift is due to loops of the electrons and positrons and that they contribute to the spectrum of the hydrogen atom, so to the energy of the hydrogen atom by the equivalence principle, they gravitate, so they also couple to gravity. These are very tiny effects, but there are larger effects. For instance, we know that similar things happen to the nuclei of elements. The mass of the nuclei of elements is also corrected by these loops. And for instance, a typical example is that if you take aluminium and platinum, the corrections by their electrostatic energy in the case of aluminium is of order 10 to the minus 3 and in the case of platinum is of the order of 3 times to the minus 3. So you say, well, these are tiny corrections. Well, but they should induce similar corrections to they should induce a violation in the equivalence principle if these loops did not gravitate at the order of 10 to the minus 3. And however we know that the equivalence principle has been checked up to something like 10 to the minus 15. And so these loops gravitate are there, so they would contribute to the cosmological constant. So we have one cosmological constant problem which is why is the cosmological constant the observed cosmological constant not huge. So why is not is not of the order of a lambda cut-off. And this is called the old wait, it's a question of momentum but the old cosmological constant problem. Sometimes. And this is the most important problem in a way it's the more difficult to solve. Then there are other problems for instance we can say why is the cosmological constant small but not totally zero. But not zero. And then another one is why is the cosmological constant of order of a romantic exactly now today. And this can be seen as a new cosmological constant problem. While this distinction is not so sharp but the historically people at some point cosmology has started to say well before the observation of the acceleration has started to say well I suppose that probably the cosmological constant is zero so let's put this problem it's too difficult to solve let's put it beside zero this is the old cosmological constant problem but then after 98 clearly there was a new problem which was to explain why why there is zero value and the small value but the real problem is the one that I explained before so it's the old one. Questions? Small but not zero. Sorry. Why it is so tiny if you want it should be huge. Because at some point people said there must be some reason why it is zero. But then we observed that there is some value why it is so small. But it's not clear why it should be exactly it should have exactly this value now it could have dominated the universe much before or it could be really much smaller so these two are a bit related in a sense. Well but matter is not a constant it gets diluted with time so the cosmological constant remains the same with the expansion of the universe while matter, you remember we saw that raw matter goes like one over a cube while raw lambda goes like a constant so raw matter does something like that while raw lambda does something like that why we are here why do we live here? There is a tricky question from Zoom. Is the entropic principle currently the most accepted principle or are there viable mechanisms proposed to generate these small cc generically that the coincidence problem? Sorry, say the last part. Ok, let's do the following let me go on and not let put aside the philosophical a bit more philosophical questions for the discussion and let me go on. I will talk a bit about an entropic explanation of the cosmological constant at the end of the lecture I would like to try to to advance so otherwise we will stop there. So I would like before the end to do two things, yes? We discuss about that but next time, ok, when I will talk about the dynamic of that energy exactly. Let's talk about that next time and you can re-ask the question again. So I would like to do two things before the end one is to go back to the calculation of the growth of density perturbation in the dark matter field when there is a cosmological constant ok, you have seen this with a seam a little bit and the second thing is to discuss the Weimberg anthropic argument to the cosmological constant. Let's try to do this. So first of all I think you have seen so let's see the growth of delta in lambda CDM. So let me define delta like that so we have some energy density which is perturbed of the dark matter and then I have a background value which is denoted with a bar and then I have a perturbation. So this is the density contrast of the dark matter if you want. I think with a seam you have seen that this density contrast satisfies in a lambda CDM universe this equation maybe you haven't written it like that but in a cleaner order delta satisfies this equation. Do you remember something? And in fact there are two solutions to this equation that we can write so there is a growing mode that we can write like that and I think this was an exercise that you had to do so there is a growing mode which is proportional to h and then there is an integral in the a, the scale factor over a h cube and then there is a decay mode which doesn't interest as much but I write it here it goes like h and you can check that if you plug this here and you use the Freeman equation in fact you can do that as an exercise it satisfies this equation. Very good, so let me see let me look at this solution which is the growing one and let's try to consider several cases for instance we could look at this solution at early time let me go there early time is much smaller than a0 so I can do the calculation so we have c plus remember that I can write h0 as the function of a like that so this should go like 1 over a to the third plus a constant component which comes from the cosmological constant so and here if I remove the square I can use this expression but now at early times at early times I can simply use that h is h0, or megamet 0 with 3 alpha I plug this expression in here and I make the integral and let me write down the solution so I find 2 5 c plus over h0 squared a squared megamet 0 so I find a solution that grows like the scale factor this I think you know and I also find sort of normalization ok, so at early times we are in matter domination but when we enter into the cosmological constant dominated phase so at late times so let's say when the scale factor is larger than a given value we have seen yesterday that we have computed a redshift at which the energy starts dominating this would correspond to the same redshift while in this case the Hubble would be given by h0 and then omega lambda 0 to the 1 alpha I can plug it here, I can solve the integral and I find something very different than the result before so I will have a lower bound to the integral I integrate between a lambda and a given a and I find something like that which shows me that at late time the density fluctuations approach a constant instead of going so in matter dominance they go in fact I can show here I can look at the growing mode of delta divided by the scale factor as a function of the scale factor and if I had a universe without a cosmological constant which sometimes is called Einstein's Descent Universe so only dominated by matter then this would be then delta would go always like a however in our universe well at early times it goes like a and then it decays and at some point delta becomes a constant so by the way this equation is very general it is also it is also valid when when dark energy is not a cosmological constant and it is always valid as long as the dark energy does not cluster we will see that a bit later very good so we have learned that the onset of lambda domination not only affects the background evolution and therefore that has been measured with the supernova but it also affects the growth of perturbations and this of course is something that last etcetera surveys are going to constrain and are going to look at now I will turn to a to a slightly different use of this of the fact that the structures are slowed down by the energy to tell you about a way of bounding or putting an upper bound to the cosmological constant so that is the following if the cosmological constant had been much larger then what we observe today clearly from this argument you see that structure would have not formed and therefore without structure you cannot form planets in life so in principle you can put an upper bound to the possible value of the cosmological constant that would give origin to life and that could be observed so this is not sometimes the un-topic arguments are a bit fishy because when you start assuming that a certain constant of nature is different from what it is observed, there are many effects that can change the advantage of this argument and the robustness of it is that it only changes the cosmological evolution of structures, it doesn't change the laws of life or biology it's not like changing the mass of the electron a little bit, it only affects the possibility of creating a structure but the rest is exactly the same you see the difference between this un-topic argument and other un-topic arguments so this is why I think it's much more robust let me let me explain you this and in order to do it, I would like to connect this growth of linear fluctuations that we have seen, in particular the growing solution to the solution that you find with the spherical collapse model because Weinberg used the spherical collapse model to study the effect of the cosmological constant on the growth of the structures so are you acquainted with the spherical collapse? Netherlands, okay so what is the spherical collapse you can find it in the Pibos book of 1980 so the idea is the following we have a flat universe described by the standard Friedman equation so 8 pi g over 3 so it's an homogeneous universe and it's flat, so there is no curvature and now let me make a hole in it and put inside this hole a curved universe so a bowl whose radius you can show that the radius is described by a Friedman equation with a different density than the one of the outside universe and with curvature and this can be used to study structures so you are assuming a spherical symmetry so you lose something it's not as generic as this equation on the other hand this equation is linear while this is fully non-linear so it gives you something at the full non-linear level although you lose because you have to assume some symmetry so let's find this spherical and the basic idea is the following so what I haven't told you is that if you go back in time we are assuming that raw matter of the over density here goes to the value to the homogeneous value of the universe flat universe and also that this happens when the radius of this over density touches becomes equal to the scale factor of the universe outside so at the early time this becomes has the same energy density as the flat universe outside but the difference is that here there is a small curvature so in principle this ball here can collapse at the beginning it will be attached to the expansion of the universe outside but then it will feel the effect of the curvature so it will start expanding a bit less than the universe outside and then at some point if the curvature is sufficiently large it will start to collapse and of course when I say if it is sufficiently large with respect to water well it depends on the amount of dark energy that there is in this picture and by the way I forgot to say that here I will have a cosmological constant ok very good well first of all I want to connect this linear growth to the curvature so I want to connect this constant to k there ok and in order to do that I can do the following I can define so I already defined delta now I can also define the perturbation to the scale factor so I just defined this alpha which disguise the perturbation to the scale factor of the order density which we hope that can collapse ok good if I plug this here and I linearize now let me so I want to be in the linear gym so I plug this here and I linearize and I use this equation to eliminate the homogeneous terms then I find this equation h dot delta plus k a squared so you see how I got I take this, I plug it here I expand a cleaner order in delta and in alpha and then I will have some terms that depend on a dot squared et cetera but the right hand side and the left hand side because of this equation and I am left with an equation describing only linear perturbations then I need another equation relating alpha to delta to find a differential equation in delta and this relation is very simple I did here is the fact that cube or matter is constant why is that? I guess that you said the conservation right? the matter mass is conserved inside this ball ok if you write this equation using this you find this a cleaner order one plus delta equal constant and if I derive it so this and this is a constant so I can remove it and I take one derivative I find that delta is equal to 3 alpha dot then I can plug this alpha dot here and I find an equation for delta dot ok while it's just a constant a cube times rho matter bar is just a constant because it's also the matter outside is conserved so I find an equation which is delta dot over h minus h dot over h squared delta is equal to 2 third h squared k over h squared and well is not difficult to see that this this is a derivative of delta dot no sorry delta over h right? times h ok and then I replace the derivative respect to time with the derivative respect to the scale factor and at the end I find this expression but with the c I can identify this c plus with k with the closure ok now let me put this together let me put this and let's consider the early I removed the solution but we saw that at early time in metadominance the solution was delta plus equal to 2 fifth c plus but now I can replace it with this so it becomes a 3 fifth h0 squared omega met 0 a times h0 and I can rewrite this denominator like this 9 fifth 8 pi g o m a squared I just use the fact that the denominator goes like goes like 1 over 8 to the cube so you see that once you take 1 over 8 to the cube times a squared you get a factor of a and then the rest is just using Freeman equation and the definition of omega and then since I am working metadominance so at very early times I can also replace this a here by r ok so I will have and let me write this equation like this so I have a numerical factor here containing g but anyway I have a constant we said that this is constant is constant always and this is the beginning and also when we enter in the non-linear and this is a represents the size of the initial perturbations and it will be a parameter in our study so now look at this equation here I cancelled the curvature but I put it back here this right hand side contains both Rho matter and Rho lambda and in principle Rho matter initially dominates so we have a decelerating phase and Rho lambda could dominate before the universe collapse or if it is small enough then it never dominates and the universe collapses so if you look at this so this goes like 1 over A cubed and this is constant in A and let me write this equation in fact like that squared ok just multiply both sides so this equation here has a minimum as a function of R ok so it initially it decreases and then it has a minimum and then it goes again now clearly the collapse of this over density happens when R dot is equal to zero this is when R is when the velocity of when the rate change of R is zero because the density is expanding then R dot is zero and then it collapses so to have a collapse I need the curvature to be much larger than this quantity at the minimum of 8 pi g over 3 Rho lambda squared at the minimum so the minimum is very easy to compute I can just take the derivative of this with respect to R because this is going like 1 over R cubed so I have to take the minimum of this I will find something Rho m the minimum it goes like 1 over R cubed but there is an R squared here so we find minus Rho m and then this is constant and I have a R squared here so I will find plus 2 Rho lambda so the minimum is almost done give me one minute then let's have a coffee no, I thought I only had one OK, very good then I will take all the philosophical questions that you want at the end OK, so we have these conditions at the minimum I just found the minimum if you want me to go over this calculation a bit more slowly but I think you see it so Rho matter goes like 1 over R cubed times R, so this must be proportional to minus Rho m and this is plus 2 because of R squared and this at the minimum in a strange way but which is useful which is the following so R squared now I write it like that OK and here I use that Rho matter is equal to 2 lambda 3 so I write this as 3 lambda 3 and here I use that Rho lambda is equal to 1 alpha Rho matter so I find this 3 alpha Rho matter inside OK so at the end I find that kappa is larger than 8 pi g Rho squared Rho lambda 1 third and 1 over 2 2 third then I connect the curvature to the initial conditions to the initial size of the perturbations by using this equation so I plug kappa from this equation here and after some simplification I get the following 5 ninth delta 3 Rho m is larger than Rho lambda 1 third 1 over 2 2 third you see this R squared Rho m to the 2 third goes away with this term here and so you get this final condition that I can write is the following 500 over 729 delta Rho matter larger than delta lambda now we can use we can rewrite this equation by expressing this quantity at the onset of structural formation so as we said that this quantity I have computed this quantity in the linear regime in metodominance it parameterizes the size of the initial perturbations I can write it at the onset of structural formation when delta becomes over there 1 so when delta is over there 1 729 Rho matter today 1 plus z cube this must be larger than Rho lambda and if you put here this is the right shift of structural formation structural formation if you put here z around 5 then I get something like that today that omega lambda Rho lambda cannot be well if you want you can also write it like that today Rho omega matter cannot be much larger than 200 which is not which is not exactly what you observe so it is off by two orders of magnitude but with respect to 120 orders of magnitude it is an improvement and notice that this bound was derived by Weimberg in 97 so exactly before the discovery of acceleration and the measurement of omega lambda and by the way it is a bound that could be improved for instance we can say this is enough to produce a structure but what if we want to produce also life so we want to give time to produce planets and things like that and then it goes down easily to over 1 or 2 orders of magnitude so it gets closer to the observe value of the cosmological constant so the message is that of course we don't know what the cosmological constant is and we cannot explain the cosmological constant problem but a possible explanation is that if we lived in a sort of universe where the cosmological constant can assume different values in different locations then we would be forced to live in a place where it has to be smaller much smaller than than what we saw at the beginning much smaller than mass Planck to the fourth and this could be a way of explaining this so I think I can stop here and I think I can get the questions that I stopped before so the vulnerable and traffic principle can you move so that I can read them but I can also read it too now first of all do you have questions on this plus part and then we can go back to on the calculation if there was a part too fast I have a question I have a question but it's not about calculation so you said something about dark energy cluster what does it mean maybe I made a mistake I wanted to say dark matter clustering but you were saying that this equation that you derived for linear perturbation is very general and you don't have dark energy cluster I guess dark matter is clustering in that equation I said that and I don't deny it so in fact if you want to do it as an exercise you can use the spherical collapse instead of using the first the first Freeman equation you can use the second one to derive very easily this equation so it's really one line of calculation however this equation is much more general in fact it's even relativistic so it's even valid if delta is in commoving age this equation is exact and yes so as long as dark energy does not cluster at least in most cases this equation would be correct it would be changed only if dark energy cluster like for instance in KS and so on these kind of things when the speed of the fluctuations of dark energy is very small but if you have a quintessence field with relativistic speed of sound then this field cannot cluster in most cases and this equation would be correct you would change raw matter because the quintessence would behave differently than the cosmological constant but this still would describe well the growth so this means in that if there is clustering we have a multi component fluid yes, yes maybe we say something tomorrow about that but yes we could have dark energy clustering like the matter if the speed of fluctuations of this component is not relativistic other questions except anthropic principle so do you want me to look at this there is only one it's about anthropic principle is the anthropic principle currently the most accepted principle or other viable mechanism proposed to generate this small cc and solve the coincidence problem are there other alternative solutions well so that I know there are attempts to solve the cosmological constant problems they are very interesting for instance Paolo has worked on similar attempts which imply the attempts which imply the relaxation of the cosmological constant in a very early phase of the universe but at the moment I cannot say that there is an established way of solving the cosmological constant problem so it remains an open issue I don't say that the anthropic principle is the most accepted and probably also this anthropic explanation of the smallest of the cosmological constant problem is probably not accepted by everybody it depends a bit on the taste in general when you hear anthropic you are a bit scared because you would like to explain things from first principle and not give up to some other anthropic explanation but there are many things in nature that we wanted to explain with first principle but we didn't manage to for instance the distance between the planets and the sun or between earth and the sun thanks I have a question regarding the calculation we used the fact that when we are at the minimum value of r the derivative with respect to time is zero so then we have the inequality and we want to evaluate the right hand side at the minimum value of r which we can do by just taking the derivative with respect to r and we would obtain that r is like r r rho m over 2 rho lambda to the 1 1 3 something like that for the minimum? for the minimum value of r when rho m is equal to 2 rho lambda that's what I'm confused about so if I look for we want to evaluate at the minimum value of r because that's right should I evaluate it at the minimum? so what is the minimum value of r? of r itself in terms of rhos I don't care so I want to evaluate at the minimum as a function of r so what var is here is the scale factor of the inside of the region inside the universe or if you want of the over density and I want to look at the minimum as a function of r so I take the derivative with respect to r because this thing depends only on r I take the derivative with respect to r I find the minimum it is when rho m is equal to 2 rho lambda but that's what confuses me so we look at the minimum as a function of r but we got rid of the time derivative how? because that's the minimum with respect to time because this is the time where the universe collapses which is not the same as the time where it has a minimum it has to collapse before reaching the minimum because if it reaches the minimum it means that rho lambda so I don't want it but in terms of time derivative it was actually expanding and then collapsing so this over spherical bubble starts expanding a bit slower than the outside and then if rho lambda is not big enough it collapses while if rho lambda is larger than this it keeps expanding forever so it was actually the maximum value with respect to time of r and there we got the time derivative zero and then we took the minimum with respect to r that's what clarifies so whenever we did that calculation for one loop contribution to the vacuum value we did it for a scalar fight with a force theory but in fact we have some complications like QCD vacuum which is also non-trivial is there a possibility that there is going to be some cancellation because of that? the non impossibility for a cancellation is super symmetry because as I said maybe at some point you would expect a similar contribution but with a negative sign with an opposite sign as the one that we found from fermions and the supersymmetry if supersymmetry is realized you have an exact cancellation between fermions and bosons but supersymmetry is not symmetry of nature at least not well, yeah not realize maybe it is but in some spontaneously broken way so we don't still this cancellation has to be shown so it's not clear that there is such a cancellation but yeah so what I showed is just a part of the possible calculation but we cannot do the calculation anyway because we don't know the content of the description up to the UV so we cannot really do it but if we had a full UV completion of our theories then we could do it and we could compute the cosmological constant ok, so next time I will do dynamical dark energy and I will start modifying gravity thank you