Coupling parameters and the form of the potential via Noether symmetry

We explore the conditions for the existence of Noether symmetries in the dynamics of FRW metric, non minimally coupled with a scalar field, in the most general situation, and with nonzero spatial curvature. When such symmetries are present we find general exact solution for the Einstein equations. We also show that non Noether symmetries can be found. Finally,we present an extension of the procedure to the Kantowski- Sachs metric which is particularly interesting in the case of degenerate Lagrangian.Comment: 13 pages, no figure

Cosmological models in scalar tensor theories of gravity and observations: a class of general solutions

We consider cosmological models in scalar tensor theories of gravity that describe an accelerating universe, and we study a family of inverse power law potentials, for which exact solutions of the Einstein equations are known. We also compare theoretical predictions of our models with observations. For this we use the following data: the publicly available catalogs of type Ia supernovae and high redshift Gamma Ray Bursts, the parameters of large scale structure determined by the 2-degree Field Galaxy Redshift Survey (2dFGRS), and measurements of cosmological distances based on the Sunyaev-Zel'dovich effect, among others.Comment: 26 pages,23 figures, accepted for publication in A&

Dynamics of tachyon field in spatially curved FRW universe

The dynamics of a tachyon field plus a barotropic fluid is investigated in spatially curved FRW universe. We perform a phase-plane analysis and obtain scaling solutions accompanying with a discussion on their stability. Furthermore, we construct the form of scalar potential which may give rise to stable solutions for spatially open and closed universe separately.Comment: 16 pages, 2 figures, version to be published in PL

A unified approach to scaling solutions in a general cosmological background

Our ignorance about the source of cosmic acceleration has stimulated study of a wide range of models and modifications to gravity. Cosmological scaling solutions in any of these theories are privileged because they represent natural backgrounds relevant to dark energy. We study scaling solutions in a generalized background $H^2 \propto \rho_T^n$ in the presence of a scalar field \vp and a barotropic perfect fluid, where $H$ is a Hubble rate and $\rho_T$ is a total energy density. The condition for the existence of scaling solutions restricts the form of Lagrangian to be p=X^{1/n}g(Xe^{n\lambda \vp}), where X=-g^{\mu\nu} \partial_\mu \vp \partial_\nu \vp /2 and $g$ is an arbitrary function. This is very useful to find out scaling solutions and corresponding scalar-field potentials in a broad class of dark energy models including (coupled)-quintessence, ghost-type scalar field, tachyon and k-essence. We analytically derive the scalar-field equation of state w_\vp and the fractional density \Omega_\vp and apply it to a number of dark energy models.Comment: 7 pages, no figures, references updated; final version to appear in PL

WMAP constraints on low redshift evolution of dark energy

The conceptual difficulties associated with a cosmological constant have led to the investigation of alternative models in which the equation of state parameter, $w=p/\rho$, of the dark energy evolves with time. We show that combining the supernova type Ia observations {\it with the constraints from WMAP observations} restricts large variation of $\rho(z)$ at low redshifts. The combination of these two observational constraints is stronger than either one. The results are completely consistent with the cosmological constant as the source of dark energy.Comment: Final version to appear in MNRAS (Letters); discussion enlarged and clarifications and references added; 6 pages; 3 figure

Understanding the origin of CMB constraints on Dark Energy

We study the observational constraints of CMB temperature and polarization anisotropies on models of dark energy, with special focus on models with variation in properties of dark energy with time. We demonstrate that the key constraint from CMB observations arises from the location of acoustic peaks. An additional constraint arises from the limits on Omega_nr from the relative amplitudes of acoustic peaks. Further, we show that the distance to the last scattering surface is not how the CMB observations constrain the combination of parameters for models of dark energy. We also use constraints from Supernova observations and show that unlike the Gold and Silver samples, the SNLS sample prefers a region of parameter space that has a significant overlap with the region preferred by the CMB observations. This is a verification of a conjecture made by us in an earlier work. We discuss combined constraints from WMAP5 and SNLS observations. We find that models with w ~ -1 are preferred for models with a constant equation of state parameters. In case of models with a time varying dark energy, we show that constraints on evolution of dark energy density are almost independent of the type of variation assumed for the equation of state parameter. This makes it easy to get approximate constraints from CMB observations on arbitrary models of dark energy. Constraints on models with a time varying dark energy are predominantly due to CMB observations, with Supernova constraints playing only a marginal role.Comment: 12 pages, 10 figures, accepted for publication in MNRA

Extended Theories of Gravity and their Cosmological and Astrophysical Applications

We review Extended Theories of Gravity in metric and Palatini formalism pointing out their cosmological and astrophysical application. The aim is to propose an alternative approach to solve the puzzles connected to dark components.Comment: 44 pages, 11 figure

Extended Theories of Gravity

Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is aimed to address conceptual and experimental problems recently emerged in Astrophysics, Cosmology and High Energy Physics. In particular, the goal is to encompass, in a self-consistent scheme, problems like Inflation, Dark Energy, Dark Matter, Large Scale Structure and, first of all, to give at least an effective description of Quantum Gravity. We review the basic principles that any gravitational theory has to follow. The geometrical interpretation is discussed in a broad perspective in order to highlight the basic assumptions of General Relativity and its possible extensions in the general framework of gauge theories. Principles of such modifications are presented, focusing on specific classes of theories like f (R)-gravity and scalar-tensor gravity in the metric and Palatini approaches. The special role of torsion is also discussed. The conceptual features of these theories are fully explored and attention is payed to the issues of dynamical and conformal equivalence between them considering also the initial value problem. A number of viability criteria are presented considering the post-Newtonian and the post-Minkowskian limits. In particular, we discuss the problems of neutrino oscillations and gravitational waves in Extended Gravity. Finally, future perspectives of Extended Gravity are considered with possibility to go beyond a trial and error approach.Comment: 184 pages, 3 figures, survey to appear in Physics Report