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

¹ Institute for Theoretical Physics, University of Warsaw, Hoza 69, 00-681 Warsaw, Poland
² Department of Astronomy, Williams College, Williamstown, MA 01267, USA
³ Dipartimento di Scienze Fisiche, Università di Napoli Federico II, Compl. Univ. Monte S. Angelo, 80126 Naples, Italy e-mail: ester@na.infn.it
⁴ Istituto Nazionale di Fisica Nucleare, Sez. Napoli, Via Cinthia, Compl. Univ. Monte S. Angelo, 80126 Naples, Italy

Received: 29 December 2006
Accepted: 6 November 2007

Abstract

Aims. We study cosmological models in scalar tensor theories of gravity with power-law potentials as models of an accelerating universe.

Methods. We consider cosmological models in scalar tensor theories of gravity that describe an accelerating universe and 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.

Results. We present a class of cosmological models that describe the evolution of a homogeneous and isotropic universe filled with dust-like matter and a scalar field that is non minimally-coupled to gravity. We show that this class of models depends on three parameters: V₀ – the amplitude of the scalar field potential, – the present value of the Hubble constant, and a real parameter s that determines the overall evolution of the universe. It turns out that these models have a very interesting feature naturally producing an epoch of accelerated expansion. We fix the values of these parameters by comparing predictions of our model with observational data. It turns out that our model is compatible with the presently available observational data.