Non-linear terms in 2D cosmology

Departamento de Física, Universidade Federal do Paraná Caixa Postal 19044, 81531-990, Curitiba, Brazil

Corresponding author: devecchi@fisica.ufpr.br

Received: 21 February 2005
Accepted: 11 May 2005

Abstract

In this work we investigate the behavior of two-dimensional (2D) cosmological models, starting with the Jackiw-Teitelboim (JT) theory of gravitation. A geometrical term, non-linear in the scalar curvature R, is added to the JT dynamics to test if it could play the role of dark energy in a 2D expanding universe. This formulation makes possible, first, the description of an early (inflationary) 2D universe, when the van der Waals (vdW) equation of state is used to construct the energy-momentum tensor of the gravitational sources. Second, it is found that for later times the non-linear term in R can generate an old 2D universe in accelerated expansion, where an ordinary matter-dominated era evolves into a decelerated/accelerated transition, giving to the dark energy effects a geometrical origin. The results emerge through numerical analysis, following the evolution in time of the scale factor, its acceleration, and the energy densities of constituents.