Non-linear terms in 2D cosmologyF. P. Devecchi and M. L. Froehlich
Departamento de Física, Universidade Federal do Paraná Caixa Postal 19044, 81531-990, Curitiba, Brazil
received 21 February 2005; accepted in final form 11 May 2005
published online 10 June 2005
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.
04.50.+h - Gravity in more than four dimensions, Kaluza-Klein theory, unified field theories; alternative theories of gravity.
98.80.-k - Cosmology.
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