C. Rubano

Nöther symmetries in cosmology

ConclusionsFrom the above discussions, it is clear that the cosmological problem can be approached in several ways. The issue is essentially connected with the fact that no «ultimate» theory still exists. However, some definitive results seem to have been acquired in the past decades both from the theoretical and the observational point of view. First of all, the standard cosmological model, which describes the observed Universe sufficiently well, fails in the very early stages of evolution since it cannot coherently solve some shortcomings. They essentially are the flatness, the horizon, the isotropy problems and, mainly, the singularity problem, that is the failure of GR at primordial eras. Furthermore, in that framework, it is not possible to explain the large-scale structure starting from some theory of primordial perturbations.

Physical non-equivalence of the Jordan and Einstein frames

PMM gratefully acknowledges the financial support provided by the I3P framework of CSIC and the European Social Fund.

NOETHER SYMMETRY APPROACH IN PHANTOM QUINTESSENCE COSMOLOGY

In the framework of phantom quintessence cosmology, we use the Noether Symmetry Approach to obtain general exact solutions for the cosmological equations. This result is achieved by the quintessential (phantom) potential determined by the existence of the symmetry itself. A comparison between the theoretical model and observations is worked out. In particular, we use type Ia supernovae and large-scale structure parameters determined from the 2-degree Field Galaxy Redshift Survey and from the Wide part of the VIMOS-VLT Deep Survey ). It turns out that the model is compatible with the presently available observational data. Moreover we extend the approach to include radiation. We show that it is compatible with data derived from recombination and it seems that quintessence do not affect nucleosynthesis results.

Exponential potentials for tracker fields

We show that a general, exact cosmological solution, where dynamics of scalar field is assigned by an exponential potential, fulfils all the issues of dark energy approach, both from a theoretical point of view and in comparison with available observational data. Moreover, tracking conditions are discussed, with a new treatment of the well known condition

Tracker fields from nonminimally coupled theory

\Gamma>1

Dark energy and dust matter phases from an exact f(R)-cosmology model

. We prove that the currently used expression for

Nöther Symmetries in Bianchi Universes

\Gamma

On Some Exponential Potentials for a Cosmological Scalar Field as Quintessence

is wrong.

Noether symmetry in the higher order gravity 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.

Scaling Solutions and Reconstruction of Scalar Field Potentials

Abstract We show that dust matter–dark energy combined phases can be achieved by the exact solution derived from a power law f ( R ) cosmological model. This example answers the query by which a dust-dominated decelerated phase, before dark-energy accelerated phase, is needed in order to form large scale structures.