Anisotropic Conformal Dark Gravity on the Lorentz Tangent Bundle Spacetime

TL;DR

This paper explores an anisotropic conformal framework for dark gravity within a generalized Lagrange geometric setting on the Lorentz tangent bundle, applying it to Minkowski and FLRW cosmologies to derive extended gravitational models.

Contribution

It introduces a novel anisotropic conformal structure incorporating dark gravity on the Lorentz tangent bundle, extending traditional models with new geometric and cosmological insights.

Findings

Derived anisotropic conformal de-Sitter-like space with extra curvature.

Formulated generalized Friedmann-like equations on the Lorentz tangent bundle.

Connected the new models to classical general relativity under specific conditions.

Abstract

In this work we investigate the anisotropic conformal structure of the gravitational field incorporating dark gravity in a generalized Lagrange geometric framework on the Lorentz tangent bundle and we present two applications; the anisotropic conformal Minkowski spacetime and the anisotropic conformal FLRW cosmology. In the first application, the conformal factor induces an anisotropic conformal de-Sitter-like space with extra curvature which causes extra gravity and allows for Sasaki-type Finsler-like structures which could potentially describe certain gravitational phenomena in a more extended form. The cosmological properties of the model are also studied using a FLRW metric structure for the underlying base manifold in the second application, where we derive generalized Friedmann-like equations for the horizontal subspace of the Lorentz tangent bundle spacetime that reduce under certain conditions to those given by A. Triantafyllopoulos and P. C. Stavrinos (2018) [Class. Quantum Grav. 35 085011] as well as those of general relativity.