An unification of general theory of relativity with Dirac's large number hypothesis

TL;DR

This paper proposes a modified theory of general relativity with a variable gravitational constant G, inspired by Dirac's large number hypothesis, which aligns with cosmological observations and retains Einstein's theory at smaller scales.

Contribution

It introduces a new cosmological theory unifying general relativity with Dirac's hypothesis by allowing G to vary, naturally replacing the cosmological constant.

Findings

The theory is consistent with Dirac's large number hypothesis.

It provides a theoretical Hubble's relation compatible with observations.

It reduces to Einstein's theory for short-duration phenomena.

Abstract

Taking a hint from Dirac's large number hypothesis, we note the existence of cosmologically combined conservation laws that work to cosmologically long time. We thus modify Einstein's theory of general relativity with fixed gravitation constant $G$ to a theory for varying $G$, with a tensor term arising naturally from the derivatives of $G$ in place of the cosmological constant term usually introduced \textit{ad hoc}. The modified theory, when applied to cosmology, is consistent with Dirac's large number hypothesis, and gives a theoretical Hubble's relation not contradicting the observational data. For phenomena of duration and distance short compared with that of the universe, our theory reduces to Einstein's theory with $G$ being constant outside the gravitating matter, and thus also passes the crucial tests of Einstein's theory.