Alessandro Tronconi

Integrable cosmological models with non-minimally coupled scalar fields

We obtain general solutions for some flat Friedmann universes filled with a scalar field in induced gravity models and models including the Hilbert-Einstein curvature term plus a scalar field conformally coupled to gravity. As is well known, these models are connected to minimally coupled models through the combination of a conformal transformation and a transformation of the scalar field. The explicit forms of the self-interaction potentials for six exactly solvable models are presented here. We obtain the general solution for one of the integrable models, namely, the induced gravity model with a power-law potential for the self-interaction of the scalar field. We argue that although being mathematically in a one-to-one correspondence with the solutions in the minimally coupled models, the solutions in the corresponding non-minimally coupled models are physically different. This is because the cosmological evolutions seen by an internal observer connected with the cosmic time can be quite different. The study of a few induced gravity models with particular potentials gives us an explicit example of such a difference.

Reconstruction of Scalar Potentials in Modified Gravity Models

We employ the superpotential technique for the reconstruction of cosmological models with a non-minimally coupled scalar field evolving on a spatially flat Friedmann-Robertson-Walker background. The key point in this method is that the Hubble parameter is considered as a function of the scalar field and this allows one to reconstruct the scalar field potential and determine the dynamics of the field itself, without a priori fixing the Hubble parameter as a function of time or of the scale factor. The scalar field potentials that lead to de Sitter or asymptotic de Sitter solutions, and those that reproduce the cosmological evolution given by Einstein-Hilbert action plus a barotropic perfect fluid, have been obtained.

Inflation and reheating in induced gravity

Abstract Inflation is studied in the context of induced gravity (IG) γ σ 2 R , where R is the Ricci scalar, σ a scalar field and γ a dimensionless constant. We study in detail cosmological perturbations in IG and examine both a Landau–Ginzburg (LG) and a Coleman–Weinberg (CW) potential toy models for small field and large field (chaotic) inflation and find that small field inflationary models in IG are constrained to γ ≲ 3 × 10 − 3 by WMAP 5-yrs data. Finally we describe the regime of coherent oscillations in induced gravity by an analytic approximation, showing how the homogeneous inflaton can decay in its short-scale fluctuations when it oscillates around a non-zero value σ 0 .

Reconstruction of Scalar Potentials in Induced Gravity and Cosmology

We develop a technique for the reconstruction of the potential for a scalar field in cosmological models based on induced gravity. The potentials reproducing cosmological evolutions driven by barotropic perfect fluids, a cosmological constant, a Chaplygin gas and a modified Chaplygin gas are constructed explicitly.

Inflation and reheating in spontaneously generated gravity

Inflation is studied in the context of induced gravity (IG) {gamma}{sigma}{sup 2}R, where R is the Ricci scalar, {sigma} a scalar field and {gamma} a dimensionless constant, and diverse symmetry-breaking potentials V({sigma}) are considered. In particular we compared the predictions for Landau-Ginzburg and Coleman-Weinberg type potentials and their possible generalizations with the most recent data. We find that large field inflation generally leads to fewer constraints on the parameters and the shape of the potential whereas small field inflation is more problematic and, if viable, implies more constraints, in particular, on the parameter {gamma}. We also examined the reheating phase and obtained an accurate analytical solution for the dynamics of the inflaton and the Hubble parameter by using a multiple scale analysis. The solutions were then used to study the average expansion of the Universe, the average equation of state for the scalar field and both the perturbative and resonant decays of the inflaton field.

Interdependence between integrable cosmological models with minimal and non-minimal coupling

We consider the relation between exact solutions of cosmological models having minimally and non-minimally coupled scalar fields. This is done for a particular class of solvable models which, in the Einstein frame, have potentials depending on hyperbolic functions and in the Jordan frame, where the non- minimal coupling is conformal, possess a relatively simple dynamics. We show that a particular model in this class can be generalized to the cases of closed and open Friedmann universes and still exhibits a simple dynamics. Further we illustrate the conditions for the existences of bounces in some sub-classes of the set of integrable models we have considered.

Dynamical Dark Energy and Spontaneously Generated Gravity

Abstract We study the cosmological evolution of an induced gravity model with a scale symmetry breaking potential for the scalar field and the presence of barotropic fluids. The radiation to matter transition, following inflation and reheating, influences the dynamics of such a field through its non-minimal coupling. Indeed one finds, as a consequence of such a transition, that the scalar field is shifted from the potential minimum (which is associated with a zero cosmological constant). We illustrate how, under certain conditions on the potential, such a dynamics can lead to a suitable amount of dark energy explaining the present accelerated expansion. In such an approach, however, for long enough times, the dark energy will disappear.

Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities

We study the relation between the Jordan-Einstein frame transition and the possible description of the crossing of singularities in flat Friedmann universes, using the fact that the regular evolution in one frame can correspond to crossing singularities in the other frame. We show that some interesting effects arise in simple models such as one with a massless scalar field or another wherein the potential is constant in the Einstein frame. The dynamics in these models and in their conformally coupled counterparts are described in detail, and a method for the continuation of such cosmological evolutions beyond the singularity is developed. We compare our approach with some other, recently developed, approaches to the problem of the crossing of singularities.

Inflation and quantum gravity in a Born–Oppenheimer context

A general equation, describing the lowest order corrections coming from quantum gravitational effects to the spectrum of cosmological scalar fluctuations is obtained. These corrections are explicitly estimated for the case of a de Sitter evolution.

Signatures of quantum gravity in a Born–Oppenheimer context

We solve a general equation describing the lowest order corrections arising from quantum gravitational effects to the spectrum of cosmological fluctuations. The spectra of scalar and tensor perturbations are calculated to first order in the slow roll approximation and the results are compared with the most recent observations. The slow roll approximation gives qualitatively new quantum gravitational effects with respect to the pure de Sitter case.