Two viable quintessence models of the Universe: Confrontation of theoretical predictions with observational data

¹ Institute for Theoretical Physics, University of Warsaw, Hoza 69, 00-681 Warsaw, Poland
² Theoretical Astrophysics Center, Juliane Maries Vej 30, 2100 Copenhagen, Denmark
³ Department of Astronomy, Williams College, Williamstown, Ma 01267, USA
⁴ Dipartimento di Scienze Fisiche, Università di Napoli Federico II, Compl. Univ. Monte S. Angelo, 80126 Naples, Italy e-mail: ester@na.infn.it
⁵ Istituto Nazionale di Fisica Nucleare, Sez. Napoli, Via Cinthia, Compl. Univ. Monte S. Angelo, 80126 Naples, Italy

Received: 22 June 2004
Accepted: 30 September 2004

Abstract

We use some of the recently released observational data to test the viability of two classes of minimally coupled scalar field models of quintessence with exponential potentials for which exact solutions of the Einstein equations are known. These models are very sturdy, depending on only one parameter – the Hubble constant. To compare predictions of our models with observations we concentrate on the following data: the power spectrum of the CMBR anisotropy as measured by WMAP, the publicly available data on type Ia supernovae, and the parameters of large scale structure determined by the 2-degree Field Galaxy Redshift Survey (2dFGRS). We use the WMAP data on the age of the universe and the Hubble constant to fix the free parameters in our models. We then show that the predictions of our models are consistent with the observed positions and relative heights of the first 3 peaks in the CMB power spectrum, with the energy density of dark energy as deduced from observations of distant type Ia supernovae, and with parameters of the large scale structure as determined by 2dFGRS, in particular with the average density of dark matter. Our models are also consistent with the results of the Sloan Digital Sky Survey (SDSS). Moreover, we investigate the evolution of matter density perturbations in our quintessential models, solve exactly the evolution equation for the density perturbations, and obtain an analytical expression for the growth index f. We verify that the approximate relation also holds in our models.