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

On exact solutions for quintessential (inflationary) cosmological models with exponential potentials

We first study dark energy models with a minimally-coupled scalar field and exponential potentials, admitting exact solutions for the cosmological equations: actually, it turns out that for this class of potentials the Einstein field equations exhibit alternative Lagrangians, and are completely integrable and separable (i.e. it is possible to integrate the system analytically, at least by quadratures). We analyze such solutions, especially discussing when they are compatible with a late time quintessential expansion of the universe. As a further issue, we discuss how such quintessential scalar fields can be connected to the inflationary phase, building up, for this class of potentials, a quintessential inflationary scenario: actually, it turns out that the transition from inflation toward late-time exponential quintessential tail admits a kination period, which is an indispensable ingredient of this kind of theoretical models. All such considerations have also been done by including radiation into the model.Comment: Revtex4, 10 figure

Exact Hypersurface-Homogeneous Solutions in Cosmology and Astrophysics

A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian formulation. This class includes the spatially homogeneous cosmological models and the astrophysically interesting static spherically symmetric models as well as the stationary cylindrically symmetric models. The framework involves methods for finding and exploiting hidden symmetries and invariant submanifolds of the Hamiltonian formulation of the field equations. It unifies, simplifies and extends most known work on hypersurface-homogeneous exact solutions. It is shown that the same framework is also relevant to gravitational theories with a similar structure, like Brans-Dicke or higher-dimensional theories.Comment: 41 pages, REVTEX/LaTeX 2.09 file (don't use LaTeX2e !!!) Accepted for publication in Phys. Rev.

Viability of Noether symmetry of F(R) theory of gravity

Canonization of F(R) theory of gravity to explore Noether symmetry is performed treating R - 6(\frac{\ddot a}{a} + \frac{\dot a^2}{a^2} + \frac{k}{a^2}) = 0 as a constraint of the theory in Robertson-Walker space-time, which implies that R is taken as an auxiliary variable. Although it yields correct field equations, Noether symmetry does not allow linear term in the action, and as such does not produce a viable cosmological model. Here, we show that this technique of exploring Noether symmetry does not allow even a non-linear form of F(R), if the configuration space is enlarged by including a scalar field in addition, or taking anisotropic models into account. Surprisingly enough, it does not reproduce the symmetry that already exists in the literature (A. K. Sanyal, B. Modak, C. Rubano and E. Piedipalumbo, Gen.Relativ.Grav.37, 407 (2005), arXiv:astro-ph/0310610) for scalar tensor theory of gravity in the presence of R^2 term. Thus, R can not be treated as an auxiliary variable and hence Noether symmetry of arbitrary form of F(R) theory of gravity remains obscure. However, there exists in general, a conserved current for F(R) theory of gravity in the presence of a non-minimally coupled scalar-tensor theory (A. K. Sanyal, Phys.Lett.B624, 81 (2005), arXiv:hep-th/0504021 and Mod.Phys.Lett.A25, 2667 (2010), arXiv:0910.2385 [astro-ph.CO]). Here, we briefly expatiate the non-Noether conserved current and cite an example to reveal its importance in finding cosmological solution for such an action, taking F(R) \propto R^{3/2}.Comment: 16 pages, 1 figure. appears in Int J Theoretical Phys (2012

Cosmology with exponential potentials

We examine in the context of general relativity the dynamics of a spatially flat Robertson-Walker universe filled with a classical minimally coupled scalar field \phi of exponential potential ~ e^{-\mu\phi} plus pressureless baryonic matter. This system is reduced to a first-order ordinary differential equation, providing direct evidence on the acceleration/deceleration properties of the system. As a consequence, for positive potentials, passage into acceleration not at late times is generically a feature of the system, even when the late-times attractors are decelerating. Furthermore, the structure formation bound, together with the constraints on the present values of \Omega_{m}, w_{\phi} provide, independently of initial conditions and other parameters, necessary conditions on \mu. Special solutions are found to possess intervals of acceleration. For the almost cosmological constant case w_{\phi} ~ -1, as well as, for the generic late-times evolution, the general relation \Omega_{\phi}(w_{\phi}) is obtained.Comment: RevTex4, 9 pages, 2 figures, References adde

Cosmology With Non-Minimally Coupled K-Field

We consider non-minimally coupled (with gravity) scalar field with non-canonical kinetic energy. The form of the kinetic term is of Dirac-Born-Infeld (DBI) form.We study the early evolution of the universe when it is sourced only by the k-field, as well as late time evolution when both the matter and k-field are present. For the k-field, we have considered constant potential as well as potential inspired from Boundary String Field Theory (B-SFT). We show that it is possible to have inflationary solution in early time as well as late time accelerating phase. The solutions also exhibit attractor property in a sense that it does not depend on the initial conditions for a certain values of the parameters.Comment: 10 pages, Revtex style, 14 eps figures, to appear in General Relativity and Gravitatio

Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology

We discuss the Hamiltonian dynamics for cosmologies coming from Extended Theories of Gravity. In particular, minisuperspace models are taken into account searching for Noether symmetries. The existence of conserved quantities gives selection rule to recover classical behaviors in cosmic evolution according to the so called Hartle criterion, that allows to select correlated regions in the configuration space of dynamical variables. We show that such a statement works for general classes of Extended Theories of Gravity and is conformally preserved. Furthermore, the presence of Noether symmetries allows a straightforward classification of singularities that represent the points where the symmetry is broken. Examples of nonminimally coupled and higher-order models are discussed.Comment: 20 pages, Review paper to appear in EPJ

Recovering the effective cosmological constant in extended gravity theories

In the framework of extended gravity theories, we discuss the meaning of a time dependent "cosmological constant" and give a set of conditions to recover asymptotic de Sitter behaviour for a class of cosmological models independently of initial data. To this purpose we introduce a time-dependent (effective) quantity which asymptotically becomes the true cosmological constant. We will deal with scalar-tensor, fourth and higher than fourth-order theories.Comment: 24 pages, Latex, submitted to Gen.Rel.and Gra

Dark energy and dark matter from an inhomogeneous dilaton

A cosmological scenario is proposed where the dark matter (DM) and dark energy (DE) of the universe are two simultaneous manifestations of an inhomogenous dilaton. The equation of state of the field is scale-dependent and pressureless at galactic and larger scales and it has negative pressure as a DE at very large scales. The dilaton drives an inflationary phase followed by a kinetic energy-dominated one, as in the "quintessential inflation" model introduced by Peebles & Vilenkin, and soon after the end of inflation particle production seeds the first inhomogeneities that lead to galaxy formation. The dilaton is trapped near the minimum of the potential where it oscillates like a massive field, and the excess of kinetic energy is dissipated via the mechanism of "gravitational cooling" first introduced by Seidel & Suen. The inhomogeneities therefore behave like solitonic oscillations around the minimum of the potential, known as "oscillatons", that we propose account for most DM in galaxies. Those regions where the dilaton does not transform enough kinetic energy into reheating or carry an excess of it from regions that have cooled, evolve to the tail of the potential as DE, driving the acceleration of the universe.Comment: 9 pages, 8 figures, uses revtex, submitted PR