 Okay, good afternoon everybody. First I would like to thank the organizers for the very interesting school and also the opportunity of this talk. So as you see on the screen, I divided my talk into three main parts. First I would talk about the inflationary models involving non-ability engaged fields. Then I would focus on transfer fluctuations during inflation in the presence of the gauge fields and eventually I will present leptogenesis scenario based on inflationary models involving non-ability engaged fields and finally I will finish by conclusion the first two parts are actually based in this course. So we are proud that our current measurements of CMD and large scale structure are in great agreement with the concept of inflation and moreover inflation provide a plausible physical mechanism for explaining the origin of the large scale structure. But you know, despite the observational successes of the inflation paradigm, the nature of the inflationary pack is still poorly understood and we hope that the next generation of experiments actually answered some fundamental questions about the mechanism behind inflation. So in fact the scalar field's lower models, although they are the simplest possible models of inflation, maybe not the whole story of the physics behind inflation. So yeah, maybe this new physics involves some new fields and in addition to the inflow of the fields. And on the other hand, the field theories are the widely accepted framework for building particle physics models and beyond standard models. So in view of this ever-present, every energy scales of non-ability engaged fields then that's a natural question to ask what is the role of engaged fields during inflation and in the physics of inflation. So in order to actually answer this question, first I would answer these two questions but of course I don't have enough time to answer them, I just briefly go through them. The first one is how to preserve the spatial isotropy in the presence of the gauge fields. Because if I have a vector field, of course it would break the isotropy of the space. So this is the first question, the second question is actually how to break the conformal invariance. If I have conformal invariance in my system then the vector fields will dilute and they cannot actually make sizeable contribution in the physics. I would briefly talk about the first question but there are some models already in the market that answer the second one and actually in the concepts of non-ability engaged fields it's actually have been non-engaged inflation model and common natural model. So before that I just want to mention that I'm interested in Einstein GR gravity minimally coupled fields in four dimension and we do respect gauge symmetry. So I'm not talking about vector inflation models. For simplicity I will set the non-ability engaged group to be SU2 but the idea is quite general so you can use any kinds of non-ability engaged fields. If I start from this general Lagrangian so GR gravity and this term which is actually involves some scalar fields and some non-ability engaged fields then fortunately in the presence of the non-ability engaged fields it's possible to have an isotopic and homogeneous solution which is this one this is where scalars are quite trivial but for the gauge field we have this solution so I can set the gauge field in the temporal gauge and then the solution for the spatial part would be this one. This is the scale factor and the Psi is a somehow effective scale field which is proportional to delta. For later actually for what I would tell you later note that the Psi is not an actual scalar but it's a pseudo scalar and then when I would talk about the tensor perturbation we will see that the pseudo scalar would lead to some parity at interactions in the tensor perturbation action. So because I don't want to talk about any specific model let's consider this general actions there are some scalar fields and some gauge field interactions here and in this setup if you study the tensor you study the cosmic perturbations there are some interesting features for this model first of all there is a non-zero scalar anisotropic inertia so the body potential would not be zero in this model. For this we had this talk about the lensing effect and actually it is common to consider that any deviation from this equality is associated with modified models of inflation but in presence of I mean interaction time that are coming from any fields but scalar fields would lead to this scalar anisotropic tensor and then this system has a sizable tensor to scalar ratio and there are some parity odd interaction in the tensor perturbation which leads to chiral gravitational waves and also the systems generally violate the lifespan and then we have the violation of the consistent relation in our system. I only have I mean actually from these things the most robust features are from the tensor perturbation so let me focus on the tensor perturbation the second part of my talk so if you perturb your metric around the FRW you would have this term which are the famous gravitational wave terms and I'm only considering the tensor perturbations and then here if you have just a scalar field this delta phi is just a scalar term so it won't have any tensor perturbations but here we have a gauge field as well and it has some tensor fluctuations for itself and because of this tensor fluctuation it contribute to the tensor parts of the anisotropic stress and it modified the field equation of the gravitational waves like this so let me just intuitively tell you what are the effects of this new charge as I told you before this term that there are some parity odd terms and there are also another interaction I just keep these two bonds because of this parity odd interaction then I cannot actually diagonalize my system in terms of plus and cross polarizations of the gravitational wave but I need to use that I need to write the system in terms of right hand at the left-handed polarization circular polarization and because the contribution of these two terms are different for the different polarization of gravitational wave then the evolution of the right-handed and left-handed polarization would be different and in order to be more precise here for example we have this right-handed and left-handed solutions for a specific model of inflation involving gauge fields and if I zoom in on these super horizon scales here you can see the right-handed and left-handed polarizations are different after horizon crossing and for instance in this specific setup the right-handed polarization gets some kinds of enhancement and it leads to parity odd correlations of EB and TB to be non-zero in this setup and okay so I'm sorry but and then let me just emphasize that in this system the right so the right-handed and left-handed polarization are not equal to each other anymore and inflationary models involving non-abiliang gauge fields generate intrinsic chiral gravitational waves so this leads me to the third part of my talk which is which I'm gonna talk about the leptogenesis scenario based in this models as you know our observable universe is highly matter dominated so I mean as far as we see our universe is made of matter and there are no I mean there are no that much anti-matter in our universe and we can formulate this actually to this asymmetry by this area parameter which is of the order 10 to minus 10 so for something like more than 50 years this asymmetry between matter and anti-matter with a simple is a mystery for physics and of course we expect that big bang generate matter and anti-matter with the same race so near a standard model of particle physics nor general relativity cannot give us any answer why this is the case that we actually observe this asymmetry and so we need a dynamical approach that starting from in totally symmetric initial condition gives us this asymmetry which is called barrier genesis but within the particle physics setup it's easier to generate it first in the left hand sector and then transform it to the barrier sector the so-called leptogenesis but the standard approach of leptogenesis is to is actually to modify the standard model by adding some massive right-handed neutrinos which after that decay generates some initial leptogen asymmetry so in the standard setup we need to actually some physics beyond standard model and they usually happen after inflation in the era because the source of parity violation in this system systems are not active during inflation so they usually happen after inflation but then there is this nice scenario of gravity to leptogenesis by Alexander Peskin and Chef Diabere they actually proposed a scenario of leptogenesis which is actually happening during inflation and within the between the standard model of particle physics so they know they don't add any kinds of right-handed neutrinos and the scenario so the idea is that using chiral gravitational waves and by means of gravitational anomaly in the standard model they find a net leptome number density so so here the point is that after talking about all this remember that inflationary models involving non-avilion gauge field generate intrinsic chiral gravitational waves so I don't okay I don't need to add any anything in this setup to generate chiral gravitational wave is for free so let us use this present to make some so the gravitational anomaly in the standard models actually gave us these anomaly in leptome number than the leptome number current in terms of this parity odd interaction of gravity gravitational part the so-called gravitational chair and Simon interaction and as far as the number of the the difference between right-handed and left-handed leptomes are different which is different in the standard model then that would give non if you can actually generate a non-zero r r tilde r then you can find a non-zero net net leptome number but the point is that if you start from a gr with and just write these gravitational waves with any interaction then for the it would be zero because there is no source of parity in your setup but here okay so so here I write this net leptome number in terms of this integral and as you see it's proportional to the difference of right-handed and left-handed polarizations which yeah so again in the inflationary models with non-avilion gauge field this term is automatically non-zero so it leads to net leptome number and let me just show you briefly this is right-handed and left-handed polarization of gravitational waves and as you see there is this different I mean there is a the sign of the right-handed left-handed polarizations are different so they are slightly different with each other and then this leads to a net lump number I summarize it here and as you see it's proportional to this psi which was the source of parity violation in our system so let me summarize here so I told you that it's possible to have inflationary models involving non-ability engaged fields and they respect the isotropy and homogeneity of the FRW background and then the presence of non-ability engaged fields during inflation leads to the following robust prediction that can leads to sizable transfer to scalar ratio which is almost impossible for inflationary models with only scalar fields and then we have intrinsic hydro-gravitational waves and parity-odd correlations which has interesting observational consequences and then the system generally violates the lifespan so with a small supply and field value we can have sizable transfer to scalar ratio and we also have the violation of the consistency relation and then at the end I present a leptogen... I showed that it's possible to make leptogenesis scenarios based on using inflationary models involving non-ability engaged fields which are leptogenesis scenarios during inflation and without any extensions of the standard model of particle physics and thank you.