Bounce Cosmology in Generalized Modified Gravities

Abstract

We investigate the bounce realization in the framework of generalized modified gravities arising from Finsler and Finsler-like geometries. In particular, the richer intrinsic geometrical structure is reflected in the appearance of extra degrees of freedom in the Friedmann equations that can drive the bounce. We examine various Finsler and Finsler-like constructions. In the cases of general very special relativity as well as of Finsler-like gravity on the tangent bundle we show that a bounce cannot be easily obtained. However, in the Finsler-Randers space the induced scalar anisotropy can fulfill the bounce conditions and bouncing solutions are easily obtained. Finally, for the general class of theories that include a nonlinear connection a new scalar field is induced, leading to a scalar-tensor structure that can easily drive a bounce. These features reveal the capabilities of Finsler and Finsler-like geometries. 95.36.+x, 04.50.Kd

Cosmology of Lorentz fiber-bundle induced scalar-tensor theories

“…Moreover, the space is equipped with a nonlinear connection with local components N (α) µ (x ν , φ (β) ). The nonlinear connection plays a fundamental role in the theory of Lorentz tangent bundle and vector bundles [20][21][22]. It is a geometrical structure that connects the externalx (horizontal) spacetime with the internal-y (vertical) space.…”

“…where dx (N ) = d 4 x ∧ dφ (1) ∧ dφ (2) . Following [21] we will consider two cases of Lagrangian densities:…”

“…Going into a more realistic inflationary realization, with a successful exit after a desired e-folding, and the desired scalar spectral index and tensor-to-scalar ratio, we can follow the method applied in [21] and reconstruct the potential V (φ) that produces any given form of H(t).…”

“…One interesting class of modified gravity theories may arise through the more radical modification of the underlying geometry itself, namely considering Finsler and Finsler-like geometries [15][16][17][18][19][20][21]. These geometries extend in a natural way the Riemannian one, by allowing the physical quantities to have a dependence on the observer 4-velocity, which in turn reflects the Lorentz-violating character of the kinematics [22][23][24][25][26][27][28][29][30][31][32][33].…”

“…If one applies the above into a cosmological framework he obtains Finsler and Finsler-like cosmologies. The basic feature of these is the appearance of extra terms in the Friedmann equations due to the intrinsic geometrical spacetime anisotropy of Finsler and Finsler-like geometries [19][20][21][22][36][37][38] (note that the term "spacetime anisotropy" in this framework is related to the Lorentz violation features of the geometry and should not be con-fused with the spatial anisotropy that can exist in Riemannian geometry too, e.g. in Bianchi cases).…”