Variation of the fundamental constants over the cosmological time: veracity of Dirac's intriguing hypothesis

TL;DR

This paper examines how fundamental constants like the speed of light, Planck constant, and electron charge varied over cosmological time, finding the fine structure constant invariant, and supports Dirac's hypothesis of varying gravitational constant at early universe times.

Contribution

It provides a detailed analysis of the variation of fundamental constants over cosmic history, confirming the invariance of the fine structure constant and supporting Dirac's hypothesis of a time-varying gravitational constant.

Findings

Speed of light was higher near the Planck scale.

Fine structure constant remained invariant over time.

Gravitational constant diverges at the Planck scale.

Abstract

We investigate how the universal constants, including the fine structure constant, have varied since the early universe close to the Planck energy scale ($E_P\sim 10^{19}$GeV) and, thus, how they have evoluted over the cosmological time related to the temperature of the expanding universe. We have already shown that the speed of light was much higher close to the Planck scale. In the present work, we will go further, first by showing that both the Planck constant and the electron charge were also too large in the early universe. However, we conclude that the fine structure constant ($\alpha\cong 1/137$) has remained invariant with the age and temperature of the universe, which is in agreement with laboratory tests and some observational data. Furthermore, we will obtain the divergence of the electron (or proton) mass and also the gravitational constant ($G$) at the Planck scale. Thus, we will be able to verify the veracity of Dirac's belief about the existence of "coincidences" between dimensionless ratios of sub-atomic and cosmological quantities, leading to a variation of $G$ with time, i.e., the ratio of the electrostatic to gravitational force between an electron and a proton ($\sim 10^{41}$) is roughly equal to the age of the universe divided by an elementary time constant, so that the strength of gravity, as determined by $G$, must vary inversely with time just in the approximation of lower temperature or for times very far from the early period, in order to compensate for the time-variation of the Hubble parameter ($H\sim t^{-1}$). In short, we will show the validity of Dirac's hypothesis only for times very far from the early period or $T\sim T_P\sim 10^{32}$K.