Non-linear terms in 2D cosmology

Abstract

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 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].

3d Gravity and Nonlinear Cosmology

“…This is also the case to describe the transition to a final period (leaving the matter dominated era) when the non-linear term in R starts to show its effects and promotes the desired accelerated regime, that would correspond to the dark energy dominated era. The results have also shown that the role of the non-linear term is similar to the one found in 2D (when it is used the JT model [7]); although this parallel can be done only qualitatively: different forms in the explicit expressions for the dynamics are found and also different values of parameters are necessary to select the more interesting scenarios. In both cases the analysis and results remain as theoretical explorations of hypothetical universes in lower dimensions.…”

“…These ideas come in substitution to the standard formulations that take the dark energy as a "usual" source [6]. This approach was tested in a 2D context recently by these authors [7], working with the Jackiw-Teitelboim (JT) model [1,9].…”

“…The results include (using the 3D Robertson-Walker metric) the description of periods dominated by matter and/or radiation [4], inflationary young 3D universes and finally old universes dominated by dark energy in transition from a matter dominated period [8]; where the dark energy constituent is modeled using different equations of state [4,5,8]. As we mentioned before the central idea of this work is to include in the field equations a new term, non-linear in the curvature scalar R. This discussion was done in [6] for 4D models and in [7] for 2D models. We start with the new field equations…”

“…The normalized boundary conditions are in this case : a(0) = 1, ȧ(0) = 1 e ρ(0) = 1. These conditions simulate a young 3D universe, in the beginning of an inflationary period [5,7,8].…”