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Heavy fields coupled to the inflaton reduce the speed of sound in the effective theory of the adiabatic mode each time the background inflationary trajectory deviates from a geodesic. This can result in features in the primordial spectra. We compute the corresponding bispectrum and show that if a varying speed of sound induces features in the power spectrum, the change in the bispectrum is given by a simple formula involving the change in the power spectrum and its derivatives. In this manner, we provide a uniquely discriminable signature of a varying sound speed for the adiabatic mode during inflation that indicates the influence of heavy fields. We find that features in the bispectrum peak in the equilateral limit and, in particular, in the squeezed limit we find considerable enhancement entirely consistent with the single field consistency relation. From the perspective of the underlying effective theory, our results generalize to a wide variety of inflationary models where features are sourced by the time variation of background quantities. A positive detection of such correlated features would be unambiguous proof of the inflaton's nature as a single light scalar degree of freedom embedded in a theory that is UV completable., Comment: 5 pages, 1 figure; matches published version

The application of Effective Field Theory (EFT) methods to inflation has taken a central role in our current understanding of the very early universe. The EFT perspective has been particularly useful in analyzing the self-interactions determining the evolution of co-moving curvature perturbations (Goldstone boson modes) and their influence on low-energy observables. However, the standard EFT formalism, to lowest order in spacetime differential operators, does not provide the most general parametrization of a theory that remains weakly coupled throughout the entire low-energy regime. Here we study the EFT formulation by including spacetime differential operators implying a scale dependence of the Goldstone boson self-interactions and its dispersion relation. These operators are shown to arise naturally from the low-energy interaction of the Goldstone boson with heavy fields that have been integrated out. We find that the EFT then stays weakly coupled all the way up to the cutoff scale at which ultraviolet degrees of freedom become operative. This opens up a regime of new physics where the dispersion relation is dominated by a quadratic dependence on the momentum \omega ~ p^2. In addition, provided that modes crossed the horizon within this energy range, the prediction of inflationary observables - including non-Gaussian signatures - are significantly affected by the new scales characterizing it., Comment: 36 pages, v2: references added, minor changes to match published version

We discuss and clarify the validity of effective single field theories of inflation obtained by integrating out heavy degrees of freedom in the regime where adiabatic perturbations propagate with a suppressed speed of sound. We show by construction that it is indeed possible to have inflationary backgrounds where the speed of sound remains suppressed and slow-roll persists for long enough. In this class of models, heavy fields influence the evolution of adiabatic modes in a manner that is consistent with decoupling of physical low and high energy degrees of freedom. We emphasize the distinction between the effective masses of the isocurvature modes and the eigenfrequencies of the propagating high energy modes. Crucially, we find that the mass gap that defines the high frequency modes increases with the strength of the turn, even as the naive heavy (isocurvature) and light (curvature) modes become more strongly coupled. Adiabaticity is preserved throughout, and the derived effective field theory remains in the weakly coupled regime, satisfying all current observational constraints on the resulting primordial power spectrum. In addition, these models allow for an observably large equilateral non-Gaussianity., Comment: 8 pages, v2: minor changes, typos corrected

We compute the low energy effective field theory (EFT) expansion for single-field inflationary models that descend from a parent theory containing multiple other scalar fields. By assuming that all other degrees of freedom in the parent theory are sufficiently massive relative to the inflaton, it is possible to derive an EFT valid to arbitrary order in perturbations, provided certain generalized adiabaticity conditions are respected. These conditions permit a consistent low energy EFT description even when the inflaton deviates off its adiabatic minimum along its slowly rolling trajectory. By generalizing the formalism that identifies the adiabatic mode with the Goldstone boson of this spontaneously broken time translational symmetry prior to the integration of the heavy fields, we show that this invariance of the parent theory dictates the entire non-perturbative structure of the descendent EFT. The couplings of this theory can be written entirely in terms of the reduced speed of sound of adiabatic perturbations. The resulting operator expansion is distinguishable from that of other scenarios, such as standard single inflation or DBI inflation. In particular, we re-derive how certain operators can become transiently strongly coupled along the inflaton trajectory, consistent with slow-roll and the validity of the EFT expansion, imprinting features in the primordial power spectrum, and we deduce the relevant cubic operators that imply distinct signatures in the primordial bispectrum which may soon be constrained by observations., Comment: (v1) 25 pages, 1 figure; (v2) references added and typos corrected, to appear in Journal of High Energy Physics

We study the realization of cosmic inflation in bigravity theories. By analyzing the evolution of scalar, vector, and tensor perturbations in de Sitter-like spacetimes, we find strong stability constraints on the class of viable vacua offered by these theories. More specifically, the only stable de Sitter vacua contain two nondecoupled gravitons (one of which is massive) with different maximal propagation speeds. We derive an effective theory for the massless graviton, which is found to propagate at an intermediate speed, limited by the two maximal values. For inflation, while the spectrum of density perturbations remains nearly scale invariant, the power spectrum of tensor modes is found to depart from the usual prediction found in standard slow-roll inflation. In particular, both the tensor to scalar ratio $r$ and the spectral index of tensor modes $n_T$ receive sizable contributions from the couplings of the theory, leading to specific signals that may be tested in future cosmological probes of CMB polarization., Comment: 5 pages, v2: discussion changed, published version

We argue that the eta-problem in supergravity inflation cannot be solved without knowledge of the ground state of hidden sectors that are gravitationally coupled to the inflaton. If the hidden sector breaks supersymmetry independently, its fields cannot be stabilized during cosmological evolution of the inflaton. We show that both the subsequent dynamical mixing between sectors as well as the lightest mass of the hidden sector are set by the scale of supersymmetry breaking in the hidden sector. The true cosmological eta-parameter arises from a linear combination of the lightest mode of the hidden sector with the inflaton. Generically, either the true eta deviates considerably from the na\"ive eta implied by the inflaton sector alone, or one has to consider a multifield model. Only if the lightest mass in the hidden sector is much larger than the inflaton mass and if the inflaton mass is much larger than the scale of hidden sector supersymmetry breaking, is the effect of the hidden sector on the slow-roll dynamics of the inflaton negligible., Comment: 27 pages, 6 figures; v2, published version, minor adjustments to the introduction, minor corrections to section 2.2 for improved clarity, references added

In this work we study the effects of field space curvature on scalar field perturbations around an arbitrary background field trajectory evolving in time. Non-trivial imprints of the 'heavy' directions on the low energy dynamics arise when the vacuum manifold of the potential does not coincide with the span of geodesics defined by the sigma model metric of the full theory. When the kinetic energy is small compared to the potential energy, the field traverses a curve close to the vacuum manifold of the potential. The curvature of the path followed by the fields can still have a profound influence on the perturbations as modes parallel to the trajectory mix with those normal to it if the trajectory turns sharply enough. We analyze the dynamical mixing between these non-decoupled degrees of freedom and deduce its non-trivial contribution to the low energy effective theory for the light modes. We also discuss the consequences of this mixing for various scenarios where multiple scalar fields play a vital role, such as inflation and low-energy compactifications of string theory., Comment: 16 pages, 2 figures, typeset in PRD style. v2: Minor changes throughout to emphasize that the analysis also applies to sharp and/or prolonged turns. References added

It is well understood that spatial non-commutativity, if indeed realized in nature, is a phenomenon whose effects are not just felt at energy scales comparable to the non-commutativity scale. Loop effects can transmit signatures of any underlying non-commutativity to macroscopic scales (a manifestation of a phenomenon that has come to be known as UV/IR mode mixing) and offer a potential lever to constrain the amount of non-commutativity present in nature, if present at all. Field theories defined on non-commutative spaces (realized in string theory when D-branes are coupled to backgrounds of non-trivial RR background flux), can exhibit strong UV/IR mode mixing, manifesting in a non-local one loop effective action. In the context of inflation in the presence of any background non-commutativity, we demonstrate how this UV/IR mixing at the loop level can allow us to place severe constraints on the scale of non-commutativity if we presume inflation is responsible for large scale structure. We demonstrate that any amount of non-commutativity greatly suppresses the CMB power at all observable scales, {\it independent} of the scale of inflation, and independent of whether or not the non-commutativity tensor redshifts during inflation, therefore nullifying a very salient and successful prediction of inflation., Comment: Version to appear in Phys. Rev. D; references added, 11 pages, 2 figures, RevTeX4