A theory of evolving natural constants embracing Einstein's theory of general relativity and Dirac's large number hypothesis

TL;DR

This paper proposes a generalized theory of gravity with a variable gravitational constant G, integrating Dirac's large number hypothesis, and develops a framework for evolving natural constants that remain constant over cosmological timescales.

Contribution

It introduces a systematic theory of evolving natural constants based on a variable G, extending Einstein's general relativity to accommodate cosmologically long-term variations.

Findings

A modified gravity theory with variable G replaces the cosmological constant.

Development of cosmic combined constants for fundamental natural constants.

Natural constants are effectively constant over recent centuries due to minimal variation in G.

Abstract

Taking a hint from Dirac's large number hypothesis, we note the existence of cosmic combined conservation laws that work to cosmologically long time. We thus modify or generalize Einstein's theory of general relativity with fixed gravitation constant $G$ to a theory for varying $G$, which can be applied to cosmology without inconsistency, where a tensor arising from the variation of G takes the place of the cosmological constant term. We then develop on this basis a systematic theory of evolving natural constants $m_{e},m_{p},e,\hslash ,k_{B}$ by finding out their cosmic combined counterparts involving factors of appropriate powers of $G$ that remain truly constant to cosmologically long time. As $G$ varies so little in recent centuries, so we take these natural constants to be constant.