Abstract: We compute the primordial trispectrum for curvature perturbations produced during cosmic inflation in models with standard kinetic terms, when the initial quantum state is not necessarily the vacuum state. The presence of initial perturbations enhances the trispectrum amplitude for configuration in which one of the momenta, say k(3), is much smaller than the others, k(3) << k(1,2,4). For those squeezed con figurations the trispectrum acquires the so-called local form, with a scale dependent amplitude that can get values of order epsilon(k(1)/k(3))(2). This amplitude could be larger than the prediction of the so-called Maldacena consistency relation by a factor as large as 10(6), and could reach the sensitivity of forthcoming observations, even for single-field inflationary models.

Abstract: We present a discussion on lattice techniques for the simulation of non-canonical field theory circumstances, complementing our previous monograph [1] on canonical cases. We begin by reviewing basic aspects of lattice field theory, including symplectic and nonsymplectic evolution algorithms. We then introduce lattice implementations of non-canonical interactions, considering scalars with a non-minimal coupling to gravity, phi 2R, non-minimal scalar kinetic theories, Gab({phi c})partial derivative & micro;phi a partial derivative & micro;phi b, and axion-like particle (ALP) interactions with Abelian gauge fields, phi F & micro;nu F & micro;nu. Next, we discuss methods to set up special field configurations, including the creation of cosmic defect networks towards scaling (e.g. cosmic strings and domain walls), field configurations based on arbitrary power spectra or spatial profiles, and probabilistic methods as required e.g. for thermal configurations. We further extend the notion of non-canonical theories, discussing the discretization of scalar field dynamics in d + 1 dimensions, with d =/ 3. Unrelated to non-canonical aspects, we also discuss implementation(s) of gravitational wave (GW) dynamics on the lattice. This document represents the theoretical basis for the non-canonical field theory aspects (interactions, initial conditions, dimensionality) and GW dynamics implemented in CosmoLattice v2.0 to be released in 2026.

Abstract: We show that “spiralized” models of new-inflation can be experimentally identified mostly by their positive spectral running in direct contrast with most chaotic-inflation models which have negative runnings typically in the range of O(10(-4)-10(-3)).

Abstract: We generalize the ultraviolet sector of gravitation via a Born-Infeld action using lessons from massive gravity. The theory contains all of the elementary symmetric polynomials and is treated in the Palatini formalism. We show how the connection can be solved algebraically to be the Levi-Civita connection of an effective metric. The non-linearity of the algebraic equations yields several branches, one of which always reduces to General Relativity at low curvatures. We explore in detail a minimal version of the theory, for which we study solutions in the presence of a perfect fluid with special attention to the cosmological evolution. In vacuum we recover Ricci-flat solutions, but also an additional physical solution corresponding to an Einstein space. The existence of two physical branches remains for non-vacuum solutions and, in addition, the branch that connects to the Einstein space in vacuum is not very sensitive to the specific value of the energy density. For the branch that connects to the General Relativity limit we generically find three behaviours for the Hubble function depending on the equation of state of the fluid, namely: either there is a maximum value for the energy density that connects continuously with vacuum, or the energy density can be arbitrarily large but the Hubble function saturates and remains constant at high energy densities, or the energy density is unbounded and the Hubble function grows faster than in General Relativity. The second case is particularly interesting because it could offer an interesting inflationary epoch even in the presence of a dust component. Finally, we discuss the possibility of avoiding certain types of singularities within the minimal model.

Abstract: In the framework of Born-Infeld inspired gravity theories, which deviates from General Relativity (GR) in the high curvature regime, we discuss the viability of Cosmic Inflation without scalar fields. For energy densities higher than the new mass scale of the theory, a gravitating (lust component is shown to generically induce an accelerated expansion of the Universe. Within such a simple scenario, inflation gracefiffly exits when the CR regime is recovered, but the Universe would remain matter dominated. In order to implement a reheating era after inflation, we then consider inflation to be driven by a mixture of unstable dust species decaying into radiation. Because the speed of sound gravitates within the BornInfeld model under consideration, our scenario ends up being predictive on various open questions of the inflationary paradigm. The total number of e-folds of acceleration is given by the lifetime of the unstable dust components and is related to the duration of reheating. As a result, inflation does not last much longer than the number of e-folds of deceleration allowing a small spatial curvature and large scale deviations to isotropy to be observable today. Energy densities are self-regulated as inflation can only start for a total energy density less than a threshold value, again related to the species' lifetime. Above this threshold, the Universe may bc nee thereby avoiding a singularity. Another distinctive feature is that the accelerated expansion is of the superinflationary ldnd, namely the first Hubble flow function is negative. We show however that the tensor modes are never excited and the tensor-to-scalar ratio is always vanishing, independently of the energy scale of inflation.