Ruggiero de Ritis

Nöther's symmetries and exact solutions in flat non-minimally coupled cosmological models

Adopting the method described in previous papers, we search for Nothers symmetries in point-like Friedman--Robertson--Walker (FRW) Lagrangians derived for general non-minimally coupled gravitational theories. We obtain exact solutions for flat models capable of producing inflation and recovering the Einstein regime at the present time (i.e. the scalar field and the coupling become constants directly related to the Newton constant ).

Relation between the potential and nonminimal coupling in inflationary cosmology

Abstract In the context of nonminimally coupled theories of gravity, the existence of Noether symmetries in pointlike Friedman- Robertson-Walker (FRW) Lagrangians allows one to exactly integrate the dynamics. These solutions have cosmological interest because they exhibit inflationary behavior and some of them imply Einstein gravity in the present epoch.

Tracker fields from nonminimally coupled theory

We extend the concept of quintessence to a flat nonminimally coupled scalar - tensor theories of gravity. By means of Noethers symmetries for the cosmological pointlike Lagrangian L, it is possible to exhibit exact solutions for a class of models depending on a free parameter s. This parameter comes out in the relationship existing between the coupling F(\phi) and the potential V(\phi) because of such a symmetry for L. When inverse power law potentials are taken in account, a whole family of exact solutions parametrized by such an s is proposed as a class of tracker fields, and some considerations are made about them.

NÖTHER’S SYMMETRIES IN (n+1)-DIMENSIONAL NONMINIMALLY COUPLED COSMOLOGIES

We perform a systematic analysis of nonminimally coupled cosmologies in (n+1)-dimensional homogeneous and isotropic spacetimes, searching for Nother’s symmetries and generalizing the results of our previous works. We obtain (i) the absence of symmetries when the spatial curvature constant k is nonzero and n=2, 3, but their existence for all the other n; (ii) the existence of such symmetries for every number of spatial dimensions (except n=1) when k=0. In this latter case, we are able to find a general transformation through which we recover the string-dilaton effective action in (n+1) dimensions and the major peculiarity of string cosmology: the scale factor duality. Furthermore, the symmetry fixes a relation among the coupling F(ϕ), the potential V(ϕ) of the scalar field ϕ, the number of spatial dimensions and the spatial curvature constant. When this is the case, it is possible to find a constant of motion and then get the general solution of the dynamics. Finally, in the framework of the so-called Induced Gravity Theories, we are able to obtain the Newton constant at the present time (t→∞) depending on the number of spatial dimensions and directly related to the constant of motion existing in such a model.

Nonminimal coupling and cosmic no-hair theorem

Abstract We give (sufficient) conditions for the extension of the cosmic no-hair conjecture to nonminimally coupled scalar-tensor theories in which the coupling is not given a priori. Furthermore, in a Friedman-Robertson-Walker spacetime, we get exact solutions for such theories using the so-called Noether symmetry approach. The results are interesting because we obtain behaviours able to avoid the initial singularity.

Noether’s Symmetries in Quantum Cosmology

We construct minisuperspace models for a class of theories of gravity nonminimally coupled with a scalar field. We show that when a Nother symmetry exists, it is always possible to integrate the Wheeler-DeWitt equation and recover the semiclassical regime for the wave function of the universe. In this sense, we can interpret the Nother symmetries as a selection rule in the philosophy of the so called Hartle criterion: when they exist, it is possible to select classical universes.

String dilaton cosmology with exponential potential

Abstract The effective action of a stringlike theory is considered in the cosmological context. We discuss a nonminimally coupled cosmological model and we find the existence of a Noether symmetry in the pointlike Friedman-Robertson-Walker (FRW) Lagrangian describing the model: this allows one to get interesting cosmological solutions.

Cosmological solutions of a quadratic theory of gravity with torsion

Abstract Following the general approach of Hehl, and Hayashi and Shirafuji, we give the gravity equations for the lagrangian L =( e /2L 2 )(F+ 1 2 ×F 2 ) + L M . We have found the explicit Einstein-de Sitter solutions for a spinless dust. We have discussed in this case the singularity problem for the metric and for the torsion.

SCALE FACTOR DUALITY AND GENERAL TRANSFORMATIONS FOR STRING COSMOLOGY

We adopt a general point of view to obtain the scale factor duality for a class of nonminimally coupled gravitational Lagrangians which comprises the tree-level effective Lagrangian of string-dilaton cosmology. We show that in a new system of coordinates the duality is a reflection and the Lagrangians become cyclic with respect to a coordinate. When this is the situation, the dynamics is simplified and it is easier to obtain exact solutions.

Nonminimal coupling and matter cosmologies

Abstract We discuss nonminimally coupled cosmologies including matter searching for exact solutions. As main result, we get that the quadratic coupling and the quartic potential for the scalar field φ, plus a dust-like matter imply a model starting with inflation, recovering Einstein gravity and ending up with a de Sitter stage, as requested by cosmic no-hair theorem. Furthermore, the today observed Newton constant can be interpreted as a remnant of SSB at GUT scales.