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Future Cosmic Microwave Background (CMB) experiments will deliver extremely accurate measurements of the E-modes pattern of the CMB polarization field. Given the sharpness of the E-modes transfer functions, such surveys make for a powerful detector of high-frequency signals from primordial features that may be lurking in current data sets. With a handful of toy models that increase the fit to the latest Planck data, but are of marginal statistical significance, we use a state-of-the-art forecast pipeline to illustrate the promising prospects to test primordial features in the next decade. Not only will future experiments allow us to detect such features in data, but they will also be able to discriminate between models and narrow down the physical mechanism originating them with high statistical significance. On the other hand, if the anomalies in the currently measured CMB spectra are just statistical fluctuations, all the current feature best fit candidates will be ruled out. Either way, our results show that primordial features are a clear target of forthcoming CMB surveys beyond the detection of tensor modes., Comment: 36 pages, 15 figures; v2 matches version published in JCAP

Primordial non-Gaussianities of the scalar(tensor)-tensor-tensor type supporting a non-trivial squeezed component are known to induce anisotropies in the stochastic gravitational wave background. We derive the explicit form of such anisotropies by making use, for the first time in this context, of the in-in formalism for cosmological correlation functions. After illustrating the general method and using it for the minimal single-field slow-roll case, we apply it to multi-field models, providing both a tree-level and a one-loop example. First, we make contact with previous results on anisotropies due to the presence of an extra spin-2 field during inflation. Secondly, we calculate the 1-loop scalar-tensor-tensor three-point function in the context of so-called supersolid inflation. The corresponding gravitational wave anisotropy is induced atop a gravitational signal that may be sufficiently large for detection., v2: 35 pages, 5 figures, minor modifications, version published in JCAP

In this article, we study in detail the linear dynamics and cubic interactions for any number $N_\mathrm{field}$ of scalar fields during inflation, directly in terms of the observable curvature perturbation $\zeta$ and $N_\mathrm{field}-1$ entropic fluctuations, a choice that is more suitable for analytical works. In the linear equations of motion for the perturbations, we uncover rich geometrical effects beyond terms involving just the scalar curvature of the field space, and that come from the non-canonical kinetic structure of the scalar fields when the dimension of the field space is larger than two. Moreover, we show that a fast rotation of the local entropic basis can result in negative eigenvalues for the entropic mass matrix, potentially destabilising the background dynamics when $N_\mathrm{field} \geqslant 3$. We also explain how to render manifest the sizes of cubic interactions between the adiabatic and the entropic fluctuations, extending a previous work of ours to any number of interacting fields. As a first analytical application of our generic formalism, we derive the effective single-field theory for perturbations up to cubic order when all entropic fluctuations are heavy enough to be integrated out. In a slow-varying limit, we recover the cubic action expected from the effective field theory of inflation, but with a prediction for the usual Wilson coefficients in terms of the multifield parameters, thus proposing a new interpretation of the bispectrum in this generic $N_\mathrm{field}$ context., Comment: 30 pages, 1 figure

The robustness of multi-field inflation to the physics of reheating is investigated. In order to carry out this study, reheating is described in detail by means of a formalism which tracks the evolution of scalar fields and perfect fluids in interaction (the inflatons and their decay products). This framework is then used to establish the general equations of motion of the background and perturbative quantities controlling the evolution of the system during reheating. Next, these equations are solved exactly by means of a new numerical code. Moreover, new analytical techniques, allowing us to interpret and approximate these solutions, are developed. As an illustration of a physical prediction that could be affected by the micro-physics of reheating, the amplitude of non-adiabatic perturbations in double inflation is considered. It is found that ignoring the fine-structure of reheating, as usually done in the standard approach, can lead to differences as big as $\sim 50\%$, while our semi-analytic estimates can reduce this error to $\sim 10\%$. We conclude that, in multi-field inflation, tracking the perturbations through the details of the reheating process is important and, to achieve good precision, requires the use of numerical calculations., 80 pages + appendices

At the end of inflation, the inflaton oscillates at the bottom of its potential and these oscillations trigger a parametric instability for scalar fluctuations with wavelength $\lambda$ comprised in the instability band $(3H m)^{-1/2}, Comment: 27 pages, 7 figures, matches published version

Stochastic inflation is an effective theory describing the super-Hubble, coarse-grained, scalar fields driving inflation, by a set of Langevin equations. We previously highlighted the difficulty of deriving a theory of stochastic inflation that is invariant under field redefinitions, and the link with the ambiguity of discretisation schemes defining stochastic differential equations. In this paper, we solve the issue of these "inflationary stochastic anomalies" by using the Stratonovich discretisation satisfying general covariance, and identifying that the quantum nature of the fluctuating fields entails the existence of a preferred frame defining independent stochastic noises. Moreover, we derive physically equivalent It\^o-Langevin equations that are manifestly covariant and well suited for numerical computations. These equations are formulated in the general context of multifield inflation with curved field space, taking into account the coupling to gravity as well as the full phase space in the Hamiltonian language, but this resolution is also relevant in simpler single-field setups. We also develop a path-integral derivation of these equations, which solves conceptual issues of the heuristic approach made at the level of the classical equations of motion, and allows in principle to compute corrections to the stochastic formalism. Using the Schwinger-Keldysh formalism, we integrate out small-scale fluctuations, derive the influence action that describes their effects on the coarse-grained fields, and show how the resulting coarse-grained effective Hamiltonian action can be interpreted to derive Langevin equations with manifestly real noises. Although the corresponding dynamics is not rigorously Markovian, we show the covariant, phase-space Fokker-Planck equation for the Probability Density Function of fields and momenta when the Markovian approximation is relevant [...], Comment: 55 pages + appendices, 3 figures. Except updated title, same as v2: version published in JCAP with minor modifications compared to v1

The stochastic approach aims at describing the long-wavelength part of quantum fields during inflation by a classical stochastic theory. It is usually formulated in terms of Langevin equations, giving rise to a Fokker-Planck equation for the probability distribution function of the fields, and possibly their momenta. The link between these two descriptions is ambiguous in general, as it depends on an implicit discretisation procedure, the two prominent ones being the It\^o and Stratonovich prescriptions. Here we show that the requirement of general covariance under field redefinitions is verified only in the latter case, however at the expense of introducing spurious `frame' dependences. This stochastic anomaly disappears when there is only one source of stochasticity, like in slow-roll single-field inflation, but manifests itself when taking into account the full phase space, or in the presence of multiple fields. Despite these difficulties, we use physical arguments to write down a covariant Fokker-Planck equation that describes the diffusion of light scalar fields in non-linear sigma models in the overdamped limit. We apply it to test scalar fields in de Sitter space and show that some statistical properties of a class of two-field models with derivative interactions can be reproduced by using a correspondence with a single-field model endowed with an effective potential. We also present explicit results in a simple extension of the single-field $\lambda \phi^4$ theory to a hyperbolic field space geometry. The difficulties we describe seem to be the stochastic counterparts of the notoriously difficult problem of maintaining general covariance in quantum theories, and the related choices of operator ordering and path-integral constructions. Our work thus opens new avenues of research at the crossroad between cosmology, statistical physics, and quantum field theory., Comment: 9 pages, 2 figures, additional numerical results, version published as a Letter in Classical and Quantum Gravity

Several recent proposals to embed inflation into high-energy physics rely on inflationary dynamics characterized by a strongly non-geodesic motion in negatively curved field space. This naturally leads to a transient instability of perturbations on sub-Hubble scales, and to their exponential amplification. Supported by first-principle numerical computations, and by the analytical insight provided by the effective field theory of inflation, we show that the bispectrum is enhanced in flattened configurations, and we argue that an analogous result holds for all higher-order correlation functions. These ``hyper non-Gaussianities'' thus provide powerful model-independent constraints on non-standard inflationary attractors motivated by the search for ultraviolet completions of inflation., Comment: 5 pages + appendices, 5 figures. Claim regarding the loss of perturbative control removed. New result of the enhancement of higher-order correlation functions in flattened configurations

The Dark Energy Spectroscopic Instrument (DESI), a multiplexed fiber-fed spectrograph, is a Stage-IV ground-based dark energy experiment aiming to measure redshifts for 29 million Emission-Line Galaxies (ELG), 4 million Luminous Red Galaxies (LRG), and 2 million Quasi-Stellar Objects (QSO). The survey design includes a pattern of tiling on the sky and the locations of the fiber positioners in the focal plane of the telescope, with the observation strategy determined by a fiber assignment algorithm that optimizes the allocation of fibers to targets. This strategy allows a given region to be covered on average five times for a five-year survey, but with coverage varying between zero and twelve, which imprints a spatially-dependent pattern on the galaxy clustering. We investigate the systematic effects of the fiber assignment coverage on the anisotropic galaxy clustering of ELGs and show that, in the absence of any corrections, it leads to discrepancies of order ten percent on large scales for the power spectrum multipoles. We introduce a method where objects in a random catalog are assigned a coverage, and the mean density is separately computed for each coverage factor. We show that this method reduces, but does not eliminate the effect. We next investigate the angular dependence of the contaminated signal, arguing that it is mostly localized to purely transverse modes. We demonstrate that the cleanest way to remove the contaminating signal is to perform an analysis of the anisotropic power spectrum $P(k,\mu)$ and remove the lowest $\mu$ bin, leaving $\mu>0$ modes accurate at the few-percent level. Here, $\mu$ is the cosine of the angle between the line-of-sight and the direction of $\vec{k}$. We also investigate two alternative definitions of the random catalog and show they are comparable but less effective than the coverage randoms method., Comment: Submitted to JCAP

Inflationary scenarios motivated by high-energy physics generically contain a plethora of degrees of freedom beyond the primordial curvature perturbation. The latter interacts in a simple way with what we name "inflationary flavor eigenstates", which differ, in general, from freely propagating "mass eigenstates". We show that the mixing between these misaligned states results in new striking behaviors in the squeezed limit of the curvature perturbation three-point function, depending not only on the mass spectrum but also on the "mixing angles" of the theory. These results bring about a new perspective on the cosmological collider program: contrary to a widespread belief, the primordial signal needs not be dominated by the lightest extra degree of freedom. Instead, we show that it may display either modulated oscillations, a broken power law, or a transition from oscillations to a power law, thus offering a detailed cosmic spectroscopy of the particle content of inflation., Comment: v2: 7 pages, 4 figures, minor modifications, version published as a Letter in PRD

Recent studies of inflation with multiple scalar fields have highlighted the importance of non-canonical kinetic terms in novel types of inflationary solutions. This motivates a thorough analysis of non-Gaussianities in this context, which we revisit here by studying the primordial bispectrum in a general two-field model. Our main result is the complete cubic action for inflationary fluctuations written in comoving gauge, i.e. in terms of the curvature perturbation and the entropic mode. Although full expressions for the cubic action have already been derived in terms of fields fluctuations in the flat gauge, their applicability is mostly restricted to numerical evaluations. Our form of the action is instead amenable to several analytical approximations, as our calculation in terms of the directly observable quantity makes manifest the scaling of every operator in terms of the slow-roll parameters, what is essentially a generalization of Maldacena's single-field result to non-canonical two-field models. As an important application we derive the single-field effective field theory that is valid when the entropic mode is heavy and may be integrated out, underlining the observable effects that derive from a curved field space., Comment: 23 pages + appendices. Minor modifications. Matches version published in JHEP