 Can you just tell me, sorry, okay, and how it goes, okay, so and so the first I would like convince you that the universe exists in the universe we have the turbulence as well and everywhere there is a turbulence so this is a nice picture by Van Gogh, this is a credit paper by in Cosmos and Culture in 2015 how the Van Gogh's turbulent mind captured the basic laws of the turbulence and it shows the turbulence in each media it is in air in the fluid and everywhere so of course when we speak about the turbulence the first association it is about the flying here in Trieste to this conference and probably if someone took the fly from Munich knows that there is a usual turbulence and you have to fasten the belts and when you go more in the space we know that the cosmic turbulence it is almost everywhere magnetized and plays a very important role when we are describing the physical processes on the Sun in the galaxies in interstellar and in the cluster medium so now I would like tell you that the turbulence might be presented in the universe and in fact in the very early stages so here it is a brief history of our universe so usually everyone will be convinced that here we have in this realization epoch and galaxy formation of course everyone is convinced that there is a turbulence but I will talk about the turbulence which exists much earlier here before any kind of even during the cosmological phase transition when there was no any regular matter so the outline of my talk based on this one will be following I will talk about the origin of the magneto hydrodynamical turbulence and I will review the primordial magnetic fields and also the cosmological velocity fields I will talk about the evolution of the turbulence magneto hydrodynamic turbulence and I will describe the amplification as a decay I will also talk about scaling laws and these simulations that we have done are three-dimensional compressible and I will talk about very briefly about the signatures so about the cosmic magnetic fields and primordial magnetic fields the first idea comes by Enrico Fermi in 49 in the fissure of letters papers in which he tried to explain the origin of the cosmic radiation so but today there are some precise measurements that can indicate that magnetic fields exist not only in Sun in the galaxies and clusters but most probably the magnetic fields exist in the voids where we do not have matter so here it is a big question from where these magnetic fields can come so this is a paper by Neronoff and Walk published in science in 2010 and they have used Fermi observation of the blaster spectra and based on this observation in fact that they do not observe TV range and TV range of the blaster spectra that it is expected to be seen they concluded that probably when the blaster ultra high-energy photons are propagating they are going to the long large-scale correlated magnetic field and the producing of the cascade between the electron and protons is interrupted because positrons and electrons are diluted in the different way of the sign difference electric charge difference so here's is this region here it is a lower bound it is not detection of the primordial magnetic fields but it is just a lower bounds and in fact very it will be very hard through the astrophysical mechanism explains the existence of the magnetic fields correlated to 10 megaparsecs for example with the same feeling factors so from where the magnetic fields can come there is a different scenarios in fact the magnetic field can be originated in any epochs of the early universe and the first idea comes by Hoyle it was even not paper it was a conference talk never published when he said this magnetic fields can be generated in the early epoch so there is a different mechanism it might be inflation it might be a cosmological phase transition it might be defects cosmological defects topological defects supersymmetry but for me it's more natural assumes that the magnetic fields are generated as a during inflationary epoch of the phase transition so both these scenarios have advantages and disadvantages so I quote just the pioneering work it for example you search for the magnetogenesis mechanism you will find more than 300 different papers so I cannot cite all of them I just cited the pioneering work so by inflation the magnetic field generation through the supercharge coupling to the inflat on field was described by Turner and Vidro in 88 and Barat Ratra in 92 and in this case the magnetic fields might have an extremely large correlation lens it may agree well with the lower bounds as well can be constrained well and in agreement for the upper bounds as well but the inflationary magnetic field generation has some difficulties because we do have the back reaction so the magnetic field presence might spoil the inflationary stage as well and also sometimes we have to pay quite big price in fact we should assume that some kind of the symmetries have been broken during the cosmological phase transition the first papers appears in 91 by Tommy Wachaspati and this this mechanism is usually called biogenesis based mechanism in which he considers cosmological first-order phase transition when the phase transition buffs are colliding each other and since we have almost perfect conductor in the early universe the magnetic fields are generated through these bubble collisions so in this case the magnetic fields correlation lens is now limited because we have the causality so correlation lens cannot be larger than the Hubble horizon at the moment of the magnetic field generation and actually it is a very small but on the other hand we have quite natural mechanism of the generation of the magnetic fields now if somehow cosmological observation will detect the magnetic fields and will be claimed that these magnetic fields are primordial origin we can reconstruct the conditions during the early universe epochs so in fact if we just measure the magnetic fields today in the galaxies and we will know that these fields comes from the amplification of the primordial seed we can just go back and test what was the physics at the moment of the moment of the generation for example at the energy scales which will be never be reached in the lab for example if it is inflationary generated magnetic fields that it will be like near the Planck scales and also we can see the cosmological phase transition directly so in fact reconstruct the physical conditions in the universe when the universe was younger than one second so what we know and what we don't know so we measure the magnetic field in galaxies we measure the magnetic fields in the clusters we know its amplitudes we know the shape almost and we know the correlation lens but we don't know where and how these magnetic fields were generated and we don't know what were the initial conditions there are the two options one it is so called astrophysical and other one is a cosmological so there is a still debates and there is no definitive answer and only the observation of the universe at high redshift so in the past can tell us what was this magnetogenesis mechanism so here it is a numerical three-dimensional cosmological mhd simulation by Dohert et al in 2008 when he considered different initial conditions when the magnetic field generated through cosmology or generated through the astrophysical mechanism for example Birmann battery so as you see if you go to the high redshift the picture will be completely different so now I will go to the phase transition because as I mentioned it is one of the mostly natural mechanism to generate magnetic fields so in fact the physics laws are everywhere the same it can be in the kitchen when the water is boiling or in the universe when the phase transition bubbles are presented and collide each other so here it is showing this bubble nucleation and in fact the magnetic fields can be generated on the merger of these two bubbles so the most important quantity which we also care on it is the magnetic helicity in the context of the universe it will reflect the basic parity symmetry or mirror symmetry breaking and is there are several attempt to connect the primordial magnetic helicity with the barogenesis and elliptogenesis and later on I will talk also about the chiral magnetic effect so this chiral magnetic effect originally was proposed by AT by Wilinkin in which he connects a symmetry between left and right-handed fermions with amplification of the seed magnetic fields in the early universe and we as a paper by Boyarsky, Rucharsky and Shapochnikov in 2012 in which they applied this mechanism chiral magnetic effect to the early universe condition claiming that we will have some possibility to generate helical magnetic fields in the early universe and recently the papers was accepted and will appear very soon in astrophysical journal letters but it is available online so we studied turbulent cascade magnetic inverse cascade in the early universe coming from the chiral magnetic effect so how do we describe the turbulence it does not matter it is in the as I mentioned in our home or it is the galaxies the fundamental laws are the same everywhere so now as I said and promised there is a two different conditions in the universe you might have first generation of the magnetic field and after the magnetic field through the image the processes will generate the velocity field or it might be vice versa you have the bubble collisions the bubble collisions produce the turbulence the turbulence is a kinetically dominant and through the image this stuff again you are getting the generation of the magnetic fields so here it is in 2010 papers in which we adjusted the pencil code by Axel Ronderberg to describe the evolution of the image due to the turbulence in the universe so as I also left sorry it's not very very well looked here I don't know because of the resolution so the solid lines are the magnetically dominant case the dashed lines small one is a generated velocity field here the situation is opposite we assumed that there is no magnetic field initially but we have some velocity motions and then you can see that we do have subdominant case but in fact on the large scales velocity field and magnetic fields gets in the in in equi partition so here it is also in the interesting case and on my knowledge it was first numerical simulations in which we assumed that we are ejecting the magnetic field so one k-mode is a primordial plasma and see what will be happens with the magnetic field so you can see this one k-mode here but very soon wishing 20 turnover times at the turnover times the spectrum starts to be redistributed and we see this development of this spectrum the most interestingly independently what kind of the initial conditions you use you always get in k-4 spectrum as a large scales bachelor spectrum we never can get Kazantsev we cannot get the white noise never because this is the result of the divergence free of the magnetic fields it can be shown mathematically that solenoidal field as a magnetic field it is if it is cut it in some scales in means that the correlation lens is limited you always can have only the bachelor spectrum for the energy and the dashed lines again it is a kinetic velocity fields and here it is a snapshot so here it is a movie I will try to play the movie okay so it doesn't work the movie now unfortunately but I will skip it will show this movie how the small correlation lens starts to be increasing during the time and the magnetic fields energy is decaying so as I said the magnetic fields can be generated during the inflation but what will be happens with this magnetic field when it goes through the expansion of the universe so here it is two cases when we assume the rotational and irrotational forcing again you definitely see when it is longitudinal forcing you are getting from the magnetic field this acoustic modes which are just acoustic modes in the fluid nothing else again it is a snapshot so the solid lines again is a magnetic fields I am sorry for the quality of the pictures I don't know why it happens and the inflation generated magnetic fields as every perturbation during inflation must have the scale invariant spectrum so it means it is generated with the same power in all scales and the spectral shape it is k minus one but here it is the scale of the cosmological phase transition so when the magnetic field starts to interact inside the horizon with the turbulence I mean to the fluid inside the horizon only because outside the horizon there is no any kind of the coupling it generates a velocity field here so in fact the magnetic fields initial magnetic fields is a good possibility to generate the vector mode which usually is absent in the standard cosmology so another another possibility it is during the inflation to generate helical magnetic fields it means that you globally globally violate the parity symmetry during the early stage of the universe in this case as a situation is the following so you do not have inverse cascade this is a very important and we have published this one in 2015 or 16 in the PRL or 17 sorry 17 January because usually when we are talking about the helical magnetic fields everyone say okay we do have inverse cascade in the case of inflation generated magnetic fields you cannot have the inverse cascade because you don't have the room more room to transfer energy on the large scales but on the small scales when the magnetic field starts to interact with the fluids velocity field you are getting amplification of the velocity fields you see so the magnetic fields is decay on small scale while on the large scales it's unchanged which is physically very well understandable the same it is for the redistribution of the magnetic field structure so we know because of the converse servers convert conservation of the helicity the fractional helicity is growing for the partially helical magnetic fields in this case this growth is a very very slow almost frozen and here it is this PRL papers here we show the spectra and compensate spectra and here we do have three different case of the turbulence here it is non magnetic in means it is just the hydro turbulence and we have the conservation of the luciansky integral here it is magnetically dominant but helical case and we see definitely the regular inverse cascade which corresponds to the conversation a conservation of the magnetic helicity and in the middle we see non helical case but definitely we see the I will not call it his inverse cascade but we called it it inverse transfer because you have still not like the situation is a hydro case this is a moving on the left the peak is a moving and the growth of the correlation lands it is not too third scaling but 0.5 and the physical explanation of this one it is some question but phenomenologically we can say because the magnetic field independently what was the initial condition always develop k4 spectrum here the velocity fields has a k2 so in some very large scales the velocity field which was in in equipartition in the medium scale with a magnetic field starts to feed the magnetic field so this inverse transfer non helical inverse transfer is due to the feeding of magnetic fields by the velocity field so this is also here in interesting results because still we did not know the why the velocity fields develop this plateau here there is no any peak so and this is it was a really high resolution numerical simulation so this is this another PRL paper in which we try to explain that these dashed lines it corresponds to the velocity field and on the very large scales it starts to like feed and push the magnetic field peaks on the left making the mimics of the inverse transfer it it was for the non helical case but situation will be completely different when we are doing that magnetically field is subdominant so the kinetic energy is dominant so then we do not observe observe any kind of the inverse transfer so this inverse transfer non helical inverse transfer it is just a consequence of the magnetically dominant case the same happens if initially we have in partition between the magnetic field and kinetic field so and the last stuff it is this recent paper about the turbulent magnetic cascade in the early universe so we have here such some kind of the schematic description we get in K-2 spectrum it is three-dimensional of course and here it is a saturation and here it is dumping scales so through this kind of the magnetic carol effect you can get magnetic fields helical magnetic fields in the early universe which will be correlated on the Hubble scales at the moment of the magnetic field generation so here it is very briefly some effects first it is the Big Bang nuclear synthesis so if you have the magnetic field in the early universe or turbulence in the early universe then it will contributes to the relativistic energy density and so you can constrain the amplitude of the magnetic field or velocity field through the Big Bang nuclear synthesis bound then no more than 10 percent can be added to the relativistic component so another effects are based that through the Einstein equation magnetic field generated all kind of the perturbation so here it is the Einstein equation here it is geometry here it is energy momentum so you can have three different kind of the perturbations color mode which is in other sense slow and fast magnetosonic ways you can have vorticity perturbations which is vector modes in cosmological context and in the mhd context it is just the Alvin waves and you have the gravitational waves which does not have any analogy in the regular mhd so you can just do the linear theory of the initial perturbation and see how the magnetic field modifies matter power spectrum so you see this additional stuff so this gives you possibility to constrain the primordial magnetic field through the large-scale structure you can also constrain the magnetic field through the cosmic microwave background induced fluctuation for example vorticity constrained or faraday rotation effect so here it is a paper by polar bear and Planck in which they constrain the primordial magnetic fields but they completely neglected neglected the role of the magnetic field and here it is a puzzle which is that maybe something to be seen more deeply by the turbulence community so the point is that one of the most important puzzles found by Planck collaboration in 2015 it was that e-polarization which is a gradient light and curl polarization BB are different by twice while the theory of the dust polarization in magneto side medium predicts you that it should be just equal each other so there was a paper by Campbell Hirata and Kaminkovsky in which they considered the magneto side slow fast and alvin waves trying to explain this one and after the conclusion of their paper which is here is the same okay mhd turbulence fails to explain this kind of the anomalies and might be related to the large-scale physics but first I guess that Lazarian recently published a paper was a student I don't remember the name of the student in which they said this is a very toy model description of the turbulence and much more detailed it turbulence description might be done so with Axel Brandenburg and my student who are proposing to do the more realistic description of the mhd turbulence inter cluster turbulence and see if the dust polarization can be agreed with current observational stuff second it is polarization of the cosmic microwave background be mode of the polarization as I said if you have the magnetic field you get the vorticity if you get the vorticity then you will have the mode of the polarization and also if the magnetic field by some chance is helical then you will have parity odd cross correlation in the cosmic microwave background radiation and also another effect it is the faraday rotation so in 2008 W Mac collaboration considered the constraint but they forgotten about the magnetic field just considering the Lorentz symmetry violation because in the case of the Lorentz symmetry violation you also have the CMB birefrigian it is completely the same as a faraday rotation but it is not the same way frequency dependent so recently the polar bear and plan published the paper to constraining the not only the Lorentz symmetry violation but the magnetic field accounting for the limit of the rotation angle measurements I mean measurements not measurements I mean the upper bounds but again this kind of the stuff was completely neglecting that before cosmic microwave background fluctuations formed and today the magnetic field has been evolved it is not like stay frozen it's the case it interacts with the fluids and so on so what we are proposing we are proposing to reconsider plank stuff and do the and do the computation of the CMB fluctuations accounting for the magnetic field evolution here it is the most important so everyone is excited that we detected the gravitational waves predicted hundred years ago but the fact that one of the possible signals the gravitational waves might be the turbulence and it might be as well that hydro or magnetized so again the pioneering work it is by Kamikowski Kosovsky Turner in 94 and they consider the bubble collisions follow up turbulence and if the turbulence is there due to the symmetry breaking you are generating the gravitational wave signals so here it is a story which is a was like amazing one I have a collaborator Griggo go goberidze Giga goberidze he is working on the turbulence in Iroacoustic turbulence and he worked on the sound wave generations through the turbulence and so on and he told me oh you are working on the gravitational wave generation why we don't just use a very well known light hill Iroacoustic approximation and compute the gravitational wave through the same formulas as it was done previously so we have done and here unfortunately I don't know what happens with the pf files but here you can see the small dashed lines it is for Mach one one and solid lines it is done through the Iroacoustic approximation by light hill 72 and as a strong numerical simulation does not show in fact any different only for the Mach one number one which is unrealistic for the universe turbulence so after this we said why should we just do so hard computation while this formalism is already ready and it is completely analytical so we have done using these formulas to computing what will be is that not only the signal of the gravitational wave and shown that the signal will be most probably detectable by laser interferometer space antenna and Lisa included this one is a white paper and it is a one so it is a possibility to detect the gravitational wave from phase transition and if you detect from phase transition you can be also know something new about the phase transition and conditions there and we also computed what will be the polarization degree of such gravitational waves but here it is a story everything is fine here but Iroacoustic approximation by light hill gives you possibility to consider the short duration of the turbulence but in reality the turbulence does not stop after the phase transition ends it's decays and comes even on the slower altitude but may become today so here it is a gravitational wave equation these terms in all previous study has been neglecting so it was neglected the universe is expanding because it was said okay the turbulence duration is short comparable to the history of the universe time so now we decided to do the new model in the pencil code and maybe you know the pencil code was just written for the turbulence in the sun magnetosper not for the context of the universe but now we do have the model gravitational model so this is a working progress so Axel with Axel Arthur and two student at Colorado at Carnegie Mellon and here I come to my conclusions the universe is a perfect conductor so it is amazing that you can apply all the turbulence laws to the universe and describe the early stage of the universe expansion that turbulence experience decay during the expansion of the universe so when you are computing what will be the predicted magnetic fields coming from the early universe or what will be the velocity field coming from this universe or what will be the correlation lands you should definitely account for the for the evolution of the and decay of the turbulence in fact the presence of the primordial magneto hydrodynamic turbulence will be a very good close-up explanation for the observed magnetic fields in galaxies and clusters and also may be in voids if confirmed and this primordial turbulence has different signatures which can be tested through current observation and finally I would like thanks the conference organizers I would like thank also the associate program ICTP high energy cosmology section and my collaborators which are here Alex Ibojarski Axel Brandenburg they are in alphabetical order Leonardo Campanelli Rudurer, George Fronich, Griegel Guberidze, Artur Kosovski, Natan Klorin, Leonhard Kislinger, Barat Ratra, Igor Rogachevski, Alek Rucharski, Jennifer Schrober, Trevor Stevens, Aleksandr Tevzadze and Tommy Vachespati and also I would like to thank the three students which are involved in these projects thank you