Galilean symmetry in the effective theory of inflation: new shapes of non-Gaussianity

We study the consequences of imposing an approximate Galilean symmetry on the Effective Theory of Inflation, the theory of small perturbations around the inflationary background. This approach allows us to study the effect of operators with two derivatives on each field, which can be the leading interactions due to non-renormalization properties of the Galilean Lagrangian. In this case cubic non-Gaussianities are given by three independent operators, containing up to six derivatives, two with a shape close to equilateral and one peaking on flattened isosceles triangles. The four-point function is larger than in models with small speed of sound and potentially observable with the Planck satellite.Comment: 23 pages, 6 figures. v2: minor changes to match JCAP published versio

The consistency condition for the three-point function in dissipative single-clock inflation

We generalize the consistency condition for the three-point function in single field inflation to the case of dissipative, multi-field, single-clock models. We use the recently introduced extension of the effective field theory of inflation that accounts for dissipative effects, to provide an explicit proof to leading (non-trivial) order in the generalized slow roll parameters and mixing with gravity scales. Our results illustrate the conditions necessary for the validity of the consistency relation in situations with many degrees of freedom relevant during inflation, namely that there is a preferred clock. Departures from this condition in forthcoming experiments would rule out not only single field but also a large class of multi-field models.Comment: 26+11 page

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.Comment: [v1] 21 pages, 7 figures. [v2] minor changes matching published versio

Consistency relation for single scalar inflation

Single scalar field inflation with a generic, non-quadratic in derivatives, field Lagrangian is considered. It is shown that non-Gaussianity of curvature perturbations is characterized by two dimensionless amplitudes. One of these amplitudes can be expressed in terms of the usual inflationary observables -- the scalar power, the tensor power, and the tensor index. This consistency relation provides an observational test for the single scalar inflation.Comment: 6 page

Conformal consistency relations for single-field inflation

We generalize the single-field consistency relations to capture not only the leading term in the squeezed limit---going as 1/q^3, where q is the small wavevector---but also the subleading one, going as 1/q^2. This term, for an (n+1)-point function, is fixed in terms of the variation of the n-point function under a special conformal transformation; this parallels the fact that the 1/q^3 term is related with the scale dependence of the n-point function. For the squeezed limit of the 3-point function, this conformal consistency relation implies that there are no terms going as 1/q^2. We verify that the squeezed limit of the 4-point function is related to the conformal variation of the 3-point function both in the case of canonical slow-roll inflation and in models with reduced speed of sound. In the second case the conformal consistency conditions capture, at the level of observables, the relation among operators induced by the non-linear realization of Lorentz invariance in the Lagrangian. These results mean that, in any single-field model, primordial correlation functions of \zeta are endowed with an SO(4,1) symmetry, with dilations and special conformal transformations non-linearly realized by \zeta. We also verify the conformal consistency relations for any n-point function in models with a modulation of the inflaton potential, where the scale dependence is not negligible. Finally, we generalize (some of) the consistency relations involving tensors and soft internal momenta.Comment: 26 pages, 1 figure. v2. Corrected typos, notably a sign error in eq. (54). Matches JCAP published versio

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 $\omega\sim c_s k$, 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 $\omega\sim k^2/M$ a similar construction can be carried out and additional shapes are possible.Comment: 13 pages, 1 figure. v2: extended discussion on near-de-Sitter model

Khronon inflation

We study the possibility that the approximate time shift symmetry during inflation is promoted to the full invariance under time reparametrization t \to \tilde t(t), or equivalently under field redefinition of the inflaton \phi \to \tilde\phi(\phi). The symmetry allows only two operators at leading order in derivatives, so that all n-point functions of scalar perturbations are fixed in terms of the power spectrum normalization and the speed of sound. During inflation the decaying mode only decays as 1/a and this opens up the possibility to violate some of the consistency relations in the squeezed limit, although this violation is suppressed by the (small) breaking of the field reparametrization symmetry. In particular one can get terms in the 3-point function that are only suppressed by 1/k_L in the squeezed limit k_L \to 0 compared to the local shape.Comment: 15 pages, 1 figure, v2. changes regarding the violation of the consistency relation. JCAP published versio

Quantum Contributions to Cosmological Correlations II: Can These Corrections Become Large?

This is a sequel to a previous detailed study of quantum corrections to cosmological correlations. It was found there that except in special cases these corrections depend on the whole history of inflation, not just on the behavior of fields at horizon exit. It is shown here that at least in perturbation theory these corrections can nevertheless not be proportional to positive powers of the Robertson--Walker scale factor, but only at most to powers of its logarithm, and are therefore never large.Comment: 10 pages. Some explanations and references added. Paper now accepted for publication in Physical Revie

Conformal Symmetries of Adiabatic Modes in Cosmology

We remark on the existence of non-linearly realized conformal symmetries for scalar adiabatic perturbations in cosmology. These conformal symmetries are present for any cosmological background, beyond any slow-roll or quasi-de Sitter approximation. The dilatation transformation shifts the curvature perturbation by a constant, and corresponds to the well-known symmetry under spatial rescaling. We argue that the scalar sector is also invariant under special conformal transformations, which shift the curvature perturbation by a term linear in the spatial coordinates. We discuss whether these conformal symmetries can be extended to include tensor perturbations. Tensor modes introduce their own set of non-linearly realized symmetries. We identify an infinite set of large gauge transformations which maintain the transverse, traceless gauge condition, while shifting the tensor mode non-trivially.Comment: 16 page

A smooth bouncing cosmology with scale invariant spectrum

We present a bouncing cosmology which evolves from the contracting to the expanding phase in a smooth way, without developing instabilities or pathologies and remaining in the regime of validity of 4d effective field theory. A nearly scale invariant spectrum of perturbations is generated during the contracting phase by an isocurvature scalar with a negative exponential potential and then converted to adiabatic. The model predicts a slightly blue spectrum, n_S >~ 1, no observable gravitational waves and a high (but model dependent) level of non-Gaussianities with local shape. The model represents an explicit and predictive alternative to inflation, although, at present, it is clearly less compelling.Comment: 20 pages, 1 fig. v2: references added, JCAP published versio