Dominance of gauge artifact in the consistency relation for the primordial bispectrum

The conventional cosmological perturbation theory has been performed under the assumption that we know the whole spatial region of the universe with infinite volume. This is, however, not the case in the actual observations because observable portion of the universe is limited. To give a theoretical prediction to the observable fluctuations, gauge-invariant observables should be composed of the information in our local observable universe with finite volume. From this point of view, we reexamine the primordial non-Gaussianity in single field models, focusing on the bispectrum in the squeezed limit. A conventional prediction states that the bispectrum in this limit is related to the power spectrum through the so-called consistency relation. However, it turns out that, if we adopt a genuine gauge invariant variable which is naturally composed purely of the information in our local universe, the leading term for the bispectrum in the squeezed limit predicted by the consistency relation vanishes.Comment: 12 pages; v2: accepted version in JCA

The Kramers-Moyal Equation of the Cosmological Comoving Curvature Perturbation

Fluctuations of the comoving curvature perturbation with wavelengths larger than the horizon length are governed by a Langevin equation whose stochastic noise arise from the quantum fluctuations that are assumed to become classical at horizon crossing. The infrared part of the curvature perturbation performs a random walk under the action of the stochastic noise and, at the same time, it suffers a classical force caused by its self-interaction. By a path-interal approach and, alternatively, by the standard procedure in random walk analysis of adiabatic elimination of fast variables, we derive the corresponding Kramers-Moyal equation which describes how the probability distribution of the comoving curvature perturbation at a given spatial point evolves in time and is a generalization of the Fokker-Planck equation. This approach offers an alternative way to study the late time behaviour of the correlators of the curvature perturbation from infrared effects.Comment: 27 page

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.Comment: 13 pages, 1 figure; v2: JHEP published version, added minor comments and reference

A non-Gaussian landscape

Primordial perturbations with wavelengths greater than the observable universe shift the effective background fields in our observable patch from their global averages over the inflating space. This leads to a landscape picture where the properties of our observable patch depend on its location and may significantly differ from the expectation values predicted by the underlying fundamental inflationary model. We show that if multiple fields are present during inflation, this may happen even if our horizon exit would be preceded by only a few e-foldings of inflation. Non-Gaussian statistics are especially affected: for example models of local non-Gaussianity predicting |f_NL|>> 10 over the entire inflating volume can have a probability up to a few tens of percent to generate a non-detectable bispectrum in our observable patch |fNL^{obs.}|<10. In this work we establish systematic connections between the observable local properties of primordial perturbations and the global properties of the inflating space which reflect the underlying high energy physics. We study in detail the implications of both a detection and non-detection of primordial non-Gaussianity by Planck, and discover novel ways of characterising the naturalness of different observational configurations

Inhomogeneous non-Gaussianity

We propose a method to probe higher-order correlators of the primordial density field through the inhomogeneity of local non-Gaussian parameters, such as f_NL, measured within smaller patches of the sky. Correlators between n-point functions measured in one patch of the sky and k-point functions measured in another patch depend upon the (n+k)-point functions over the entire sky. The inhomogeneity of non-Gaussian parameters may be a feasible way to detect or constrain higher-order correlators in local models of non-Gaussianity, as well as to distinguish between single and multiple-source scenarios for generating the primordial density perturbation, and more generally to probe the details of inflationary physics.Comment: 16 pages, 2 figures; v2: Minor changes and references added. Matches the published versio

Scale-dependent non-Gaussianity probes inflationary physics

We calculate the scale dependence of the bispectrum and trispectrum in (quasi) local models of non-Gaussian primordial density perturbations, and characterize this scale dependence in terms of new observable parameters. They can help to discriminate between models of inflation, since they are sensitive to properties of the inflationary physics that are not probed by the standard observables. We find consistency relations between these parameters in certain classes of models. We apply our results to a scenario of modulated reheating, showing that the scale dependence of non-Gaussianity can be significant. We also discuss the scale dependence of the bispectrum and trispectrum, in cases where one varies the shape as well as the overall scale of the figure under consideration. We conclude providing a formulation of the curvature perturbation in real space, which generalises the standard local form by dropping the assumption that f_NL and g_NL are constants.Comment: 27 pages, 2 figures. v2: Minor changes to match the published versio

Issues Concerning Loop Corrections to the Primordial Power Spectra

We expound ten principles in an attempt to clarify the debate over infrared loop corrections to the primordial scalar and tensor power spectra from inflation. Among other things we note that existing proposals for nonlinear extensions of the scalar fluctuation field $\zeta$ introduce new ultraviolet divergences which no one understands how to renormalize. Loop corrections and higher correlators of these putative observables would also be enhanced by inverse powers of the slow roll parameter $\epsilon$. We propose an extension which should be better behaved.Comment: 36 pages, uses LaTeX2e, version 3 revised for publication with a much expanded section 4, proving that our proposed extension of the zeta-zeta correlator absorbs the one loop infrared divergences from graviton

de Sitter invariance of the dS graviton vacuum

The two-point function of linearized gravitons on de Sitter space is infrared divergent in the standard transverse traceless synchronous gauge defined by $k=0$ cosmological coordinates (also called conformal or Poincare coordinates). We show that this divergence can be removed by adding a linearized diffeomorphism to each mode function; i.e., by an explicit change of gauge. It follows that the graviton vacuum state is well-defined and de Sitter invariant in agreement with various earlier arguments.Comment: 14 pages, 1 figur

IR Divergences in Inflation and Entropy Perturbations

We study leading order perturbative corrections to the two point correlation function of the scalar field describing the curvature perturbation in a slow-roll inflationary background, paying particular attention to the contribution of entropy mode loops. We find that the infrared divergences are worse than in pure de Sitter space: they are power law rather than logarithmic. The validity of perturbation theory and thus of the effective field theory of cosmological perturbations leads to stringent constraints on the coupling constants describing the interactions, in our model the quartic self-interaction coupling constant of the entropy field. If the self coupling constant is larger than some critical value which depends in particular on the duration of the inflationary phase, then perturbation theory breaks down. Our analysis may have implications for the stability of de Sitter space: the quantum effects which lead to an instability of de Sitter space will be larger in magnitude in the presence of entropy fluctuations.Comment: 28 pages, minor changes in Sec 3.3, reference adde

Squeezed tensor non-Gaussianity in non-attractor inflation

We investigate primordial tensor non-Gaussianity in single field inflation, during a phase of non-attractor evolution when the spectrum of primordial tensor modes can be enhanced to a level detectable at interferometer scales. Making use of a tensor duality we introduced in arXiv:1808.10475, we analytically compute the full bispectrum of primordial tensor fluctuations during the non-attractor era. During this epoch the shape of the tensor bispectrum is enhanced in the squeezed limit, its amplitude can be amplified with respect to slow-roll models, and tensor non-Gaussianity can exhibit a scale dependence distinctive of our set-up. We prove that our results do not depend on the frame used for the calculations. Squeezed tensor non-Gaussianity induces a characteristic quadrupolar anisotropy on the power spectrum of the stochastic background of primordial tensor perturbations. As a step to make contact with gravitational wave experiments, we discuss the response function of a ground based Michelson interferometer to a gravitational wave background with such a feature.Comment: 34 pages, 4 figure