arXiv subjects

Leonardo Senatore

Publications and source records attributed to Leonardo Senatore.

At least 91 records · Page 5Linked to original sources

arXiv2013

On Loops in Inflation II: IR Effects in Single Clock Inflation

In single clock models of inflation the coupling between modes of very different scales does not have any significant dynamical effect during inflation. It leads to interesting projection effects. Larger and smaller modes change the relation between the scale a mode of interest will appear in the post-inflationary universe and will also change the time of horizon crossing of that mode. We argue that there are no infrared projection effects in physical questions, that there are no effects from modes of longer wavelength than the one of interest. These potential effects cancel when computing fluctuations as a function of physically measurable scales. Modes on scales smaller than the one of interest change the mapping between horizon crossing time and scale. The correction to the mapping computed in the absence of fluctuations is enhanced by a factor N_e, the number of e-folds of inflation between horizon crossing and reheating. The new mapping is stochastic in nature but its variance is not enhanced by N_e.

hep-th↗

arXiv2013

Anomalous Dimensions and Non-Gaussianity

We analyze the signatures of inflationary models that are coupled to strongly interacting field theories, a basic class of multifield models also motivated by their role in providing dynamically small scales. Near the squeezed limit of the bispectrum, we find a simple scaling behavior determined by operator dimensions, which are constrained by the appropriate unitarity bounds. Specifically, we analyze two simple and calculable classes of examples: conformal field theories (CFTs), and large-N CFTs deformed by relevant time-dependent double-trace operators. Together these two classes of examples exhibit a wide range of scalings and shapes of the bispectrum, including nearly equilateral, orthogonal and local non-Gaussianity in different regimes. Along the way, we compare and contrast the shape and amplitude with previous results on weakly coupled fields coupled to inflation. This signature provides a precision test for strongly coupled sectors coupled to inflation via irrelevant operators suppressed by a high mass scale up to 1000 times the inflationary Hubble scale.

hep-th↗

arXiv2012

The constancy of ζin single-clock Inflation at all loops

Studying loop corrections to inflationary perturbations, with particular emphasis on infrared factors, is important to understand the consistency of the inflationary theory, its predictivity and to establish the existence of the slow-roll eternal inflation phenomena and its recently found volume bound. In this paper we show that ζ-correlators are time-independent at large distances at all-loop level in single clock inflation. We write the n-th order correlators of \dotζ as the time-integral of Green's functions times the correlators of local sources that are function of the lower order fluctuations. The Green's functions are such that only non-vanishing correlators of the sources at late times can lead to non-vanishing correlators for \dotζ at long distances. When the sources are connected by high wavenumber modes, the correlator is peaked at short distances, and these diagrams cannot lead to a time-dependence by simple diff. invariance arguments. When the sources are connected by long wavenumber modes one can use similar arguments once the constancy of ζ at lower orders was established. Therefore the conservation of ζ at a given order follows from the conservation of ζ at the lower orders. Since at tree-level ζ is constant, this implies constancy at all-loops by induction.

hep-th↗

arXiv2012

The Effective Field Theory of Cosmological Large Scale Structures

Large scale structure surveys will likely become the next leading cosmological probe. In our universe, matter perturbations are large on short distances and small at long scales, i.e. strongly coupled in the UV and weakly coupled in the IR. To make precise analytical predictions on large scales, we develop an effective field theory formulated in terms of an IR effective fluid characterized by several parameters, such as speed of sound and viscosity. These parameters, determined by the UV physics described by the Boltzmann equation, are measured from N-body simulations. We find that the speed of sound of the effective fluid is c_s^2 10^(-6) and that the viscosity contributions are of the same order. The fluid describes all the relevant physics at long scales k and permits a manifestly convergent perturbative expansion in the size of the matter perturbations δ(k) for all the observables. As an example, we calculate the correction to the power spectrum at order δ(k)^4. The predictions of the effective field theory are found to be in much better agreement with observation than standard cosmological perturbation theory, already reaching percent precision at this order up to a relatively short scale k \sim 0.24 h/Mpc.

astro-ph.CO↗

arXiv2012

The Effective Field Theory of Multifield Inflation

We generalize the Effective Field Theory of Inflation to include additional light scalar degrees of freedom that are in their vacuum at the time the modes of interest are crossing the horizon. In order to make the scalars light in a natural way we consider the case where they are the Goldstone bosons of a global symmetry group or are partially protected by an approximate supersymmetry. We write the most general Lagrangian that couples the scalar mode associated to the breaking of time translation during inflation to the additional light scalar fields. This Lagrangian is constrained by diffeomorphism invariance and the additional symmetries that keep the new scalars light. This Lagrangian describes the fluctuations around the time of horizon crossing and it is supplemented with a general parameterization describing how the additional fluctuating fields can affect cosmological perturbations. We find that multifield inflation can reproduce the non-Gaussianities that can be generated in single field inflation but can also give rise to new kinds of non-Gaussianities. We find several new three-point function shapes. We show that in multifield inflation it is possible to naturally suppress the three-point function making the four-point function the leading source of detectable non-Gaussianities. We find that under certain circumstances, i.e. if specific shapes of non-Gaussianities are detected in the data, one could distinguish between single and multifield inflation and sometimes even among the various mechanisms that kept the additional fields light.

hep-th↗

arXiv2012

On Loops in Inflation III: Time Independence of zeta in Single Clock Inflation

Studying loop corrections to inflationary perturbations, with particular emphasis on infrared factors, is important to understand the consistency of the inflationary theory, its predictivity and to establish the existence of the slow-roll eternal inflation phenomena and its recently found volume bound. In this paper we prove that the zeta correlation function is time-independent at one-loop level in single clock inflation. While many of the one-loop diagrams lead to a time-dependence when considered individually, the time-dependence beautifully cancels out in the overall sum. We identify two subsets of diagrams that cancel separately due to different physical reasons. The first cancellation is related to the change of the background cosmology due to the renormalization of the stress tensor. It results in a cancellation between the non-1PI diagrams and some of the diagrams made with quartic vertices. The second subset of diagrams that cancel is made up of cubic operators, plus the remaining quartic ones. We are able to write the sum of these diagrams as the integral over a specific three-point function between two very short wavelengths and one very long one. We then apply the consistency condition for this three-point function in the squeezed limit to show that the sum of these diagrams cannot give rise to a time dependence. This second cancellation is thus a consequence of the fact that in single clock inflation the attractor nature of the solution implies that a long wavelength zeta perturbation is indistinguishable from a trivial rescaling of the background, and so results in no physical effect on short wavelength modes.

hep-th↗

arXiv2012

A Note on the Consistency Condition of Primordial Fluctuations

We show that the squeezed limit of (N+1)-point functions of primordial correlation functions in which one of the modes has a very small wavenumber can be inferred from the spatial variation of locally measured N-point function. We then show how in single clock inflation a long wavelength perturbation can be re-absorbed in the background cosmology and how in computing correlation functions the integrals of the interaction Hamiltonian are dominated by conformal times of order of the short wavelength modes, when the long mode is already outside of the horizon. This allows us to generalize the consistency condition for N-point functions to the case in which the short wavelength fluctuations are inside the horizon and derivatives acts on them. We further discuss the consistency condition in the soft internal squeezed limit in which in an (N+M)-point function with (N+M) short modes the sum of the first N modes is a very soft momentum. These results are very useful to study infrared effects in Inflation.

astro-ph.CO↗

arXiv2012

Dissipative effects in the Effective Field Theory of Inflation

We generalize the effective field theory of single clock inflation to include dissipative effects. Working in unitary gauge we couple a set of composite operators in the effective action which is constrained solely by invariance under time-dependent spatial diffeomorphisms. We restrict ourselves to situations where the degrees of freedom responsible for dissipation do no contribute to the density perturbations at late time. The dynamics of the perturbations is then modified by the appearance of `friction' and noise terms, and assuming certain locality properties for the Green's functions of these composite operators, we show that there is a regime characterized by a large friction term γ>> H in which the ζ-correlators are dominated by the noise and the power spectrum can be significantly enhanced. We also compute the three point function <ζζζ> for a wide class of models and discuss under which circumstances large friction leads to an increased level of non-Gaussianities. In particular, under our assumptions, we show that strong dissipation together with the required non-linear realization of the symmetries implies |f_NL| ~ γ/(c_s^2H) >> 1. As a paradigmatic example we work out a variation of the `trapped inflation' scenario with local response functions and perform the matching with our effective theory. A detection of the generic type of signatures that result from incorporating dissipative effects during inflation, as we describe here, would teach us about the dynamics of the early universe and also extend the parameter space of inflationary models.

hep-th↗

arXiv2011

Universality of the Volume Bound in Slow-Roll Eternal Inflation

It has recently been shown that in single field slow-roll inflation the total volume cannot grow by a factor larger than e^(S_dS/2) without becoming infinite. The bound is saturated exactly at the phase transition to eternal inflation where the probability to produce infinite volume becomes non zero. We show that the bound holds sharply also in any space-time dimensions, when arbitrary higher-dimensional operators are included and in the multi-field inflationary case. The relation with the entropy of de Sitter and the universality of the bound strengthen the case for a deeper holographic interpretation. As a spin-off we provide the formalism to compute the probability distribution of the volume after inflation for generic multi-field models, which might help to address questions about the population of vacua of the landscape during slow-roll inflation.

hep-th↗

arXiv2011

Galaxy Bias and non-Linear Structure Formation in General Relativity

Length scales probed by large scale structure surveys are becoming closer to the horizon scale. Further, it has been recently understood that non-Gaussianity in the initial conditions could show up in a scale dependence of the bias of galaxies at the largest distances. It is therefore important to include General Relativistic effects. Here we provide a General Relativistic generalization of the bias, valid both for Gaussian and non-Gaussian initial conditions. The collapse of objects happens on very small scales, while long-wavelength modes are always in the quasi linear regime. Around every collapsing region, it is therefore possible to find a reference frame that is valid for all times and where the space time is almost flat: the Fermi frame. Here the Newtonian approximation is applicable and the equations of motion are the ones of the N-body codes. The effects of long-wavelength modes are encoded in the mapping from the cosmological frame to the local frame. For the linear bias, the effect of the long-wavelength modes on the dynamics is encoded in the local curvature of the Universe, which allows us to define a General Relativistic generalization of the bias in the standard Newtonian setting. We show that the bias due to this effect goes to zero as the squared ratio of the physical wavenumber with the Hubble scale for modes longer than the horizon, as modes longer than the horizon have no dynamical effects. However, the bias due to non-Gaussianities does not need to vanish for modes longer than the Hubble scale, and for non-Gaussianities of the local kind it goes to a constant. As a further application, we show that it is not necessary to perform large N-body simulations to extract information on long-wavelength modes: N-body simulations can be done on small scales and long-wavelength modes are encoded simply by adding curvature to the simulation and rescaling the coordinates.

astro-ph.CO↗

arXiv2011

Primordial non-Gaussianity in the Bispectrum of the Halo Density Field

The bispectrum vanishes for linear Gaussian fields and is thus a sensitive probe of non-linearities and non-Gaussianities in the cosmic density field. Hence, a detection of the bispectrum in the halo density field would enable tight constraints on non-Gaussian processes in the early Universe and allow inference of the dynamics driving inflation. We present a tree level derivation of the halo bispectrum arising from non-linear clustering, non-linear biasing and primordial non-Gaussianity. A diagrammatic description is developed to provide an intuitive understanding of the contributing terms and their dependence on scale, shape and the non-Gaussianity parameter fNL. We compute the terms based on a multivariate bias expansion and the peak-background split method and show that non-Gaussian modifications to the bias parameters lead to amplifications of the tree level bispectrum that were ignored in previous studies. Our results are in a good agreement with published simulation measurements of the halo bispectrum. Finally, we estimate the expected signal to noise on fNL and show that the constraint obtainable from the bispectrum analysis significantly exceeds the one obtainable from the power spectrum analysis.

astro-ph.CO↗

arXiv2011

Scale-Invariance and the Strong Coupling Problem

The effective theory of adiabatic fluctuations around arbitrary Friedmann-Robertson-Walker backgrounds - both expanding and contracting - allows for more than one way to obtain scale-invariant two-point correlations. However, as we show in this paper, it is challenging to produce scale-invariant fluctuations that are weakly coupled over the range of wavelengths accessible to cosmological observations. In particular, requiring the background to be a dynamical attractor, the curvature fluctuations are scale-invariant and weakly coupled for at least 10 e-folds only if the background is close to de Sitter space. In this case, the time-translation invariance of the background guarantees time-independent n-point functions. For non-attractor solutions, any predictions depend on assumptions about the evolution of the background even when the perturbations are outside of the horizon. For the simplest such scenario we identify the regions of the parameter space that avoid both classical and quantum mechanical strong coupling problems. Finally, we present extensions of our results to backgrounds in which higher-derivative terms play a significant role.

hep-th↗

arXiv2011

Non-Gaussianities in Single Field Inflation and their Optimal Limits from the WMAP 5-year Data

Using the recently developed effective field theory of inflation, we argue that the size and the shape of the non-Gaussianities generated by single-field inflation are generically well described by two parameters: f_NL^equil, which characterizes the size of the signal that is peaked on equilateral configurations, and f_NL^orthog, which instead characterizes the size of the signal which is peaked both on equilateral configurations and flat-triangle configurations (with opposite signs). The shape of non-Gaussianities associated with f_NL^orthog is orthogonal to the one associated to f_NL^equil, and former analysis have been mostly blind to it. We perform the optimal analysis of the WMAP 5-year data for both of these parameters. We find no evidence of non-Gaussianity, and we have the following constraints: -125 < f_NL^equil < 435, -369 < f_NL^orthog < 71 at 95% CL. We show that both of these constraints can be translated into limits on parameters of the Lagrangian of single-field inflation. For one of them, the speed of sound of the inflaton fluctuations, we find that it is either bounded to be c_s > 0.011 at 95% CL. or alternatively to be so small that the higher-derivative kinetic term dominate at horizon crossing. We are able to put similar constraints on the other operators of the inflaton Lagrangian.

astro-ph.CO↗

arXiv2010

Cosmological Non-Linearities as an Effective Fluid

The universe is smooth on large scales but very inhomogeneous on small scales. Why is the spacetime on large scales modeled to a good approximation by the Friedmann equations? Are we sure that small-scale non-linearities do not induce a large backreaction? Related to this, what is the effective theory that describes the universe on large scales? In this paper we make progress in addressing these questions. We show that the effective theory for the long-wavelength universe behaves as a viscous fluid coupled to gravity: integrating out short-wavelength perturbations renormalizes the homogeneous background and introduces dissipative dynamics into the evolution of long-wavelength perturbations. The effective fluid has small perturbations and is characterized by a few parameters like an equation of state, a sound speed and a viscosity parameter. These parameters can be matched to numerical simulations or fitted from observations. We find that the backreaction of small-scale non-linearities is very small, being suppressed by the large hierarchy between the scale of non-linearities and the horizon scale. The effective pressure of the fluid is always positive and much too small to significantly affect the background evolution. Moreover, we prove that virialized scales decouple completely from the large-scale dynamics, at all orders in the post-Newtonian expansion. We propose that our effective theory be used to formulate a well-defined and controlled alternative to conventional perturbation theory, and we discuss possible observational applications. Finally, our way of reformulating results in second-order perturbation theory in terms of a long-wavelength effective fluid provides the opportunity to understand non-linear effects in a simple and physically intuitive way.

astro-ph.CO↗

arXiv2010

A Naturally Large Four-Point Function in Single Field Inflation

Non-Gaussianities of the primordial density perturbations have emerged as a very powerful possible signal to test the dynamics that drove the period of inflation. While in general the most sensitive observable is the three-point function in this paper we show that there are technically natural inflationary models where the leading source of non-Gaussianity is the four-point function. Using the recently developed Effective Field Theory of Inflation, we are able to show that it is possible to impose an approximate parity symmetry and an approximate continuos shift symmetry on the inflaton fluctuations that allow, when the dispersion relation is of the form $ω\sim c_s k$, for a unique quartic operator, while approximately forbidding all the cubic ones. The resulting shape for the four-point function is unique. In the models where the dispersion relation is of the form $ω\sim k^2/M$ a similar construction can be carried out and additional shapes are possible.

hep-th↗

arXiv2010

Spherical collapse in quintessence models with zero speed of sound

We study the spherical collapse model in the presence of quintessence with negligible speed of sound. This case is particularly motivated for w<-1 as it is required by stability. As pressure gradients are negligible, quintessence follows dark matter during the collapse. The spherical overdensity behaves as a separate closed FLRW universe, so that its evolution can be studied exactly. We derive the critical overdensity for collapse and we use the extended Press-Schechter theory to study how the clustering of quintessence affects the dark matter mass function. The effect is dominated by the modification of the linear dark matter growth function. A larger effect occurs on the total mass function, which includes the quintessence overdensities. Indeed, here quintessence constitutes a third component of virialized objects, together with baryons and dark matter, and contributes to the total halo mass by a fraction ~ (1+w) Omega_Q / Omega_m. This gives a distinctive modification of the total mass function at low redshift.

astro-ph.CO↗

arXiv2009

On Loops in Inflation

We study loop corrections to correlation functions of inflationary perturbations. Previous calculations have found that the two-point function can have a logarithmic running of the form log(k/mu), where k is the wavenumber of the perturbation, and mu is the renormalization scale. We highlight that this result would have profound consequences for both eternal inflation and the predictivity of standard inflation. We find a different result. We consider two sets of theories: one where the inflaton has a large cubic self-interaction and one where the inflaton interacts gravitationally with N massless spectator scalar fields. We find that there is a logarithmic running but of the form log(H/mu), where H is the Hubble constant during inflation. We find this result in three independent ways: by performing the calculation with a sharp cutoff in frequency-momentum space, in dimensional regularization and by the simple procedure of making the loop integral dimensionless. For the simplest of our theories we explicitly renormalize the correlation function proving that the divergencies can be reabsorbed and that the correlation function for super-horizon modes does not depend on time (once the tadpole terms have been properly taken into account). We prove the time-independence of the super-horizon correlation function in several additional ways: by doing the calculation of the correlation function at finite time using both the regularizations and by developing a formalism which expresses loop corrections directly in terms of renormalized quantities at each time. We find this last formalism particularly helpful to develop intuition which we then use to generalize our results to higher loops and different interactions.

hep-th↗

arXiv2009

Optimal limits on f_{NL}^{local} from WMAP 5-year data

We have applied the optimal estimator for f_{NL}^{local} to the 5 year WMAP data. Marginalizing over the amplitude of foreground templates we get -4 < f_{NL}^{local} < 80 at 95% CL. Error bars of previous (sub-optimal) analyses are roughly 40% larger than these. The probability that a Gaussian simulation, analyzed using our estimator, gives a result larger in magnitude than the one we find is 7%. Our pipeline gives consistent results when applied to the three and five year WMAP data releases and agrees well with the results from our own sub-optimal pipeline. We find no evidence of any residual foreground contamination.

astro-ph.CO↗