Power-law solutions and accelerated expansion in scalar-tensor theories

Abstract

We find exact power-law solutions for scalar-tensor theories and clarify the conditions under which they can account for an accelerated expansion of the Universe. These solutions have the property that the signs of both the Hubble rate and the deceleration parameter in the Jordan frame may be different from the signs of their Einstein-frame counterparts. For special parameter combinations we identify these solutions with asymptotic attractors that have been obtained in the literature through dynamical-system analysis. We establish an effective general-relativistic description for which the geometrical equivalent of dark energy is associated with a time dependent equation of state. The present value of the latter is consistent with the observed cosmological ``constant". We demonstrate that this type of power-law solutions for accelerated expansion cannot be realized in f(R) theories.Comment: 22 pages, 1 figure, substantially rewritten, presentation improved. Accepted for publication in Phys.Rev.

Matter growth in extended ΛCDM cosmology

“…The constant parameter m describes deviations from the standard ΛCDM model which corresponds to the limit m = 0 ⇒ A = Φ = 1. With (13) we found an explicit expression for the scalar-field variable without having solved the basic scalar-field equation. We have solved the system of energy-balance equations for a simple case [1].…”

“…The point here is that the dynamics on the level of the fluid energy densities does not require the exact solution of the scalar-field equation (3). On the other hand, the specific features of our fluid dynamics imply the existence of the effective scalar field Φ of the form of (13). Strictly speaking, we are no longer in the framework of JBD theory, which, however, provided the motivation for our model.…”

“…Theories of this type represent generalizations of Einstein's General Relativity (GR). Studies of different aspects of scalar-tensor theories have been performed, e.g., in [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Scalar-tensor extension of the ΛCDM model

“…This may be seen as a geometrization of DE. Different aspects of scalar-tensor theories in general or subclasses of them have been investigated in [8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Visser’s massive graviton bimetric theory revisited

“…In a first class of models, the usual thermodynamic properties of the constituents of the universe are modified and the acceleration of the expansion is driven by a negative pressure term associated either to particle production (see, for instance, [5] and references therein) or to a bulk viscosity term ( [6] and references therein). In other class of models, the existence of new fields in nature responsible for the acceleration are postulated (scalar fields in GR) as well as modifications in the Einstein-Hilbert action (f (R) theories) [7][8][9] or scalar-tensor theories [9][10][11][12][13][14][15][16][17].…”