Gravity at cosmological distances: Explaining the accelerating expansion without dark energy

TL;DR

This paper proposes a new gravitational theory that explains the universe's accelerating expansion without dark energy by deriving a modified field equation and solution that naturally produce acceleration at large distances.

Contribution

A novel gravitational field equation satisfying specific criteria is introduced, leading to a solution that explains cosmic acceleration without dark energy.

Findings

Derived a generalized Schwarzschild solution with a new $r^4$ term

Provided a cosmological model showing transition from deceleration to acceleration

Achieved acceleration explanation without negative pressure or cosmological constant

Abstract

Three theoretical criteria for gravitational theories beyond general relativity are considered: obtaining the cosmological constant as an integration constant, deriving the energy conservation law as a consequence of the field equations, rather than assuming it, and not necessarily considering conformally flat metrics as vacuum solutions. Existing theories, including general relativity, do not simultaneously fulfill all three criteria. To address this, a new gravitational field equation is proposed that satisfies these criteria. From this equation, a spherically symmetric exact solution is derived, which is a generalization of the Schwarzschild solution. It incorporates three terms: the Schwarzschild term, the de Sitter term, and a newly discovered term, which is proportional to $r^4$ in a radial coordinate, that becomes significant only at large distances. The equation is further applied to cosmology, deriving an equation for the scale factor. It then presents a solution that describes the transition from decelerating to accelerating expansion in a matter-dominated universe. This is achieved without the need for negative pressure as dark energy or the positive cosmological constant. This provides a novel explanation for the current accelerating expansion of the universe.