Abstract: Supersymmetric versions of induced-gravity inflation are formulated within Supergravity (SUGRA) employing two gauge singlet chiral super fields. The proposed super-potential is uniquely determined by applying a continuous R and a discrete Z(n) symmetry. We select two types of logarithmic Kahler potentials, one associated with a no-scale-type SU(2, 1)/SU(2) x U(1)(R) x Z(n) Kahler manifold and one more generic. In both cases, imposing a lower bound on the parameter c R involved in the coupling between the inflaton and the Ricci scalar curvature – e.g. c(R) greater than or similar to 76, 105, 310 for n – 2, 3 and 6 respectively -, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity. In the case of no-scale SUGRA we show that, for every n, the inflationary observables remain unchanged and in agreement with the current data while the inflaton mass is predicted to be 3 . 10(13) GeV. Beyond no-scale SUGRA the inflationary observables depend mildly on n and crucially on the coefficient involved in the fourth order term of the Kahler potential which mixes the inflaton with the accompanying non-inflaton field.

Abstract: We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous and isotropic cosmological scenario where we explicitly establish the relation between the auxiliary metric and the spacetime metric tensor perturbations. As a general result, we show that both tensor perturbations coincide in the absence of anisotropic stresses.

Abstract: We consider eternal inflation in hilltop-type inflation models, favored by current data, in which the scalar field in inflation rolls off of a local maximum of the potential. Unlike chaotic or plateau-type inflation models, in hilltop inflation the region of field space which supports eternal inflation is finite, and the expansion rate H-EI during eternal inflation is almost exactly the same as the expansion rate H-* during slow roll inflation. Therefore, in any given Hubble volume, there is a finite and calculable expectation value for the lifetime of the “eternal” inflation phase, during which quantum flucutations dominate over classical field evolution. We show that despite this, inflation in hilltop models is nonetheless eternal in the sense that the volume of the spacetime at any finite time is exponentially dominated by regions which continue to inflate. This is true regardless of the energy scale of inflation, and eternal inflation is supported for inflation at arbitrarily low energy scale.

Abstract: A novel realization of the Starobinsky inflationary model within a moderate extension of the Minimal Supersymmetric Standard Model (MSSM) is presented. The proposed superpotential is uniquely determined by applying a continuous R and a Z2 discrete symmetry, whereas the Kahler potential is associated with a no-scale-type SU(54, 1)/ SU(54) x U(1) R X Z2 Kahler manifold. The inflaton is identified with a Higgs-like modulus whose the vacuum expectation value controls the gravitational strength. Thanks to a strong enough coupling (with a parameter CT involved) between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton with CT >= 76 and the corresponding effective theory being valid up to the Planck scale. The inflationary observables turn out to be in agreement with the current data and the inflaton mass is predicted to be 3 10(3) GeV. At the cost of a relatively small superpotential coupling constant, the model offers also a resolution of the f,t problem of MSSM for CT <= 4500 and gravitino heavier than about 10(4) GeV. Supplementing MSSM by three right-handed neutrinos we show that spontaneously arising couplings between the inflaton and the particle content of MSSM not only ensure a sufficiently low reheating temperature but also support a scenario of non-thermal leptogenesis consistently with the neutrino oscillation parameters.

Abstract: We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and FLRW backgrounds, we introduce the basic tools for the discretization of field theories, including lattice gauge invariant techniques. Following, we discuss and classify numerical algorithms, ranging from methods of O(delta t(2)) accuracy like staggered leapfrog and Verlet integration, to Runge-Kutta methods up to O(delta t(4)) accuracy, and the Yoshida and Gauss-Legendre higher-order integrators, accurate up to O(delta t(10)) We adapt these methods for their use in classical lattice simulations of the non-linear dynamics of scalar and gauge fields in an expanding grid in 3+1 dimensions, including the case of 'self-consistent' expansion sourced by the volume average of the fields' energy and pressure densities. We present lattice formulations of canonical cases of: i) Interacting scalar fields, ii) Abelian U(1) gauge theories, and iii) Non-Abelian SU(2) gauge theories. In all three cases we provide symplectic integrators, with accuracy ranging from O(delta t(2)) up to O(delta t(10)) For each algorithm we provide the form of relevant observables, such as energy density components, field spectra and the Hubble constraint. We note that all our algorithms for gauge theories always respect the Gauss constraint to machine precision, including when 'self-consistent' expansion is considered. As a numerical example we analyze the post-inflationary dynamics of an oscillating inflaton charged under SU(2) x U(1). We note that the present manuscript is meant to be part of the theoretical basis for the code CosmoLattice, a multi-purpose MPI-based package for simulating the non-linear evolution of field theories in an expanding universe, publicly available at http://www.cosrnolattice.net.