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.Introduction.-Negatively curved field space plays a crucial role in modern embeddings of inflation in highenergy physics. Non-linear sigma models with a hyperbolic target space arise naturally in top-down realizations of inflation, particularly within supergravity, giving rise to the α-attractor class of models (see e.g. [1][2][3]). Independently of the question of their ultraviolet completions, non-minimal kinetic terms of the hyperbolic type lead to interesting dynamics, allowing for non-trivial inflationary trajectories characterized by a strongly non-geodesic motion [4][5][6][7]. This in turn relaxes the conditions of slow-roll to allow for potentials that are steep in Planck units [8,9], a welcome feature in view of the eta problem and the recently much discussed swampland conjectures [10,11]. Lastly, internal field spaces with negative curvature are at the origin of the phenomenon of geometrical destabilization [12][13][14][15][16], in which non-inflationary degrees of freedom, even heavy ones, can dramatically affect the fate of inflation.A concrete scenario in which the consequences of a hyperbolic field space have been studied is the proposal of "hyperinflation" [17], that has recently been under scrutiny [18,19]. The intuitive picture of this set-up is that of an inflationary trajectory corresponding to a circular motion around the minimum of a (circularly symmetric) scalar potential. The hyperbolic geometry is crucial to compensate for the loss of angular velocity to the Hubble friction, allowing inflation to last long enough, even if the potential is too steep to inflate along a radial trajectory. Within this circumstance, hyperinflation proceeds along a strongly non-geodesic trajectory, and a striking outcome is an exponential growth of the curvature power spectrum around the time of Hubble crossing, and the corresponding suppression of the tensor-toscalar ratio. With such an amplification, assessing the size of nonlinear effects in this setup appears to be crucial, while previous studies have restricted their attention to the analysis of linear fluctuations.In this context, this Letter presents a general framework to study non-Gaussianities in the presence of strongly non-geodesic motion typical of hyperbolic-type geometry, ...

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.

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 λ comprised in the instability band (3H m)−1/2 <λ < H−1, where H is the Hubble parameter and m the curvature of the potential at its minimum. This “metric preheating” instability, which proceeds in the narrow resonance regime, leads to various interesting phenomena such as early structure formation, production of gravitational waves and formation of primordial black holes. In this work we study its fate in the presence of interactions with additional degrees of freedom, in the form of perturbative decay of the inflaton into a perfect fluid. Indeed, in order to ensure a complete transition from inflation to the radiation-dominated era, metric preheating must be considered together with perturbative reheating. We find that the decay of the inflaton does not alter the instability structure until the fluid dominates the universe content. As an application, we discuss the impact of the inflaton decay on the production of primordial black holes from the instability. We stress the difference between scalar field and perfect fluid fluctuations and explain why usual results concerning the formation of primordial black holes from perfect fluid inhomogeneities cannot be used, clarifying some recent statements made in the literature.

1 We concentrate on these two well known discretisations, but one can easily consider more general α-discretisatons [27], where 0 ≤ α ≤ 1, recovering Itô calculus for α = 0 and the Stratonovich

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 Itô-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, and we give analytical approximations for the noises' amplitudes in multifield scenarios.

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, µ) and remove the lowest µ bin, leaving µ > 0 modes accurate at the few-percent level. Here, µ is the cosine of the angle between the line-of-sight and the direction of k. We also investigate two alternative definitions of the random catalog and show they are comparable but less effective than the coverage randoms method.

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational-wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational-wave observations by LISA to probe the universe.

In this article, we study in detail the linear dynamics and cubic interactions for any number Nfield of scalar fields during inflation, directly in terms of the observable curvature perturbation ζ and Nfield-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 Nfield⩾ 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 Nfield context.