Non-linear terms in 2D cosmology

TL;DR

This paper explores how adding a non-linear scalar curvature term to 2D cosmological models can produce early inflation and late-time accelerated expansion, suggesting a geometric origin for dark energy.

Contribution

It introduces a non-linear curvature term into 2D gravity models, demonstrating its role in simulating inflation and dark energy effects in a simplified universe.

Findings

Non-linear curvature term induces early inflation in 2D models.

The model exhibits a transition from matter-dominated to accelerated expansion.

Numerical results show geometrical origin of dark energy effects.

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.