Non-linear terms in 2D cosmology

– 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 energymomentum 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. Introduction. – The study of theories of gravity in lower dimensions has received extensive consideration in the literature [1]. Taking the particular case of two-dimensional (2D) theories, the gravity formulation proposed by Teitelboim and Jackiw [2] (JT model) provided consistent results at the classical and quantum levels [1]. This model is the most imediate substitute of general relativity in 2D field formulations, since the Einstein theory furnish no dynamics in 2D [1]. The JT model was under investigation also in a cosmological context [3, 6]. The results obtained include the description of a Universe filled with ordinary matter or/and electromagnetic radiation, an inflationary 2D universe and a three-eras universe where a cosmological constant was responsible for a final accelerated period, that could de associated to the effects of dark energy [3]. In fact, the dark energy problem, as a fundamental discussion in cosmology, has been analised using different approaches. Recently, it was proposed a geometrical formulation for the dark energy behavior in a 4D universe [5]. This idea comes in substitution of the standard formulations that takes the dark energy as an usual source [5]. This geometrical formulation has as central point a modification in the Einstein action that includes a non-linear term in the scalar curvature R, that would be key ingredient behind the present accelerated expansion in the universe [5]. () [email protected]