Cosmological solutions and finite time singularities in Finslerian geometry

Abstract

We consider a very general scenario of our universe where its geometry is characterized by the Finslerian structure on the underlying spacetime manifold, a generalization of the Riemannian geometry. Now considering a general energy-momentum tensor for matter sector, we derive the gravitational field equations in such spacetime. Further, to depict the cosmological dynamics in such spacetime proposing an interesting equation of state identified by a sole parameter γ which for isotropic limit is simply the barotropic equation of state p = (γ − 1)ρ (γ ∈ R being the barotropic index), we solve the background dynamics. The dynamics offers several possibilities depending on this sole parameter as follows − (i) only an exponential expansion, or (ii) a finite time past singularity (big bang) with late accelerating phase, or (iii) a nonsingular universe exhibiting an accelerating scenario at late time which finally predicts a big rip type singularity. We also discuss several energy conditions and the possibility of cosmic bounce. Finally, we establish the first law of thermodynamics in such spacetime. PACS numbers: 98.80.+k; 95.36.+x

Geometrical Origin of Growth of Matter Perturbations

“…We have considered density perturbation of a Finslerian cosmological model in which the background spacetime is FLRW spacetime with Finslerian perturbation. This background spacetime of the universe has been shown [5] to be a (α, β) -Finsler space. By using the barotropic equation of state for the anisotropic fluid , we have derived the equation for scale factor a(t) from the modified gravitational field equations of the Finsler space, which is, in fact, a natural generalisation of Riemann space .…”

“…For the background spacetime of the universe we have introduced the following Finslerian Structure [5,6]:…”

“…It is to be noted that the background Finslerian spacetime of the universe, that we are considering here is, in fact, a spatially flat FLRW spacetime of scale factor a(t) with Finslerian perturbation as shown in [5,6].…”

“…So far, in these approaches of the linear growth of perturbation, the processes involving cold dark matter, collision matter and scalar field have to be introduced. Recently , we have introduced a Finslerian cosmology [5,6] and here we shall show how this consideration can account for the density perturba-tion without any additional input into the system, thus, making it possible to ascertain the geometrical origin of inhomogeneity and anisotropy. The paper is organized as follows.…”