Generalizing the Cosmic Energy Equation

TL;DR

This paper extends the cosmic energy equation to include modified gravitational potentials that depend on time and space, deriving a generalized Friedmann equation and applying it to dark matter interactions.

Contribution

It introduces a generalized cosmic energy equation accommodating time-dependent gravitational potentials, providing a new tool to study dark matter and dark energy.

Findings

Derived a generalized Friedmann equation with a renormalized gravitational constant.

Applied the generalized energy equation to modified dark matter interactions.

Highlighted the potential of the energy equation to probe universe expansion history.

Abstract

We generalize the cosmic energy equation to the case when massive particles interact via a modified gravitational potential of the form phi(a, r), which is allowed to explicitly depend upon the cosmological time through the expansion factor a(t). Using the nonrelativistic approximation for particle dynamics, we derive the equation for the cosmological expansion which has the form of the Friedmann equation with a renormalized gravitational constant. The generalized Layzer-Irvine cosmic energy equation and the associated cosmic virial theorem are applied to some recently proposed modifications of the Newtonian gravitational interaction between dark-matter particles. We also draw attention to the possibility that the cosmic energy equation may be used to probe the expansion history of the universe thereby throwing light on the nature of dark matter and dark energy.