On higher dimensional gravity: the Lagrangian, its dimensional reduction and a cosmological model

TL;DR

This paper explores higher-dimensional gravity by reducing Lovelock Lagrangian to four dimensions, deriving effective field equations, and discussing a cosmological model with an n-torus internal space.

Contribution

It introduces a method for dimensional reduction of Lovelock gravity and analyzes a specific cosmological model with an n-torus internal space.

Findings

Derived effective four-dimensional field equations from Lovelock Lagrangian.

Obtained expressions for cosmological and gravitational constants.

Discussed a cosmological model with n-torus internal space.

Abstract

By dimensional reduction of the Lovelock Lagrangian, effective four-dimensional field equations and expressions for the cosmological and gravitational constants are obtained. A cosmological model is discussed with the n-torus as internal space.