A quantum mechanical derivation of Gamow's relation for the time and temperature of the expanding Universe

TL;DR

This paper uses a quantum mechanical approach to derive a relation between the universe's age and temperature, matching Gamow's classical result and aligning with recent measurements of cosmic background radiation.

Contribution

It presents a novel quantum mechanical derivation of the universe's temperature-age relation, providing results consistent with established observations and calculations.

Findings

Derived a temperature of approximately 2.91 K for the cosmic background radiation.

Calculated photon density and entropy consistent with known values.

Estimated the photon-to-nucleon ratio aligning with previous results.

Abstract

The quantum mechanical approach developed by us recently for the evolution of the universe is used to derive an alternative derivation connecting the temperature of the cosmic background radiation and the age of the universe which is found to be similar to the one obtained by Gamow long back. By assuming the age of the universe to be $\approx$ 20 billion years, we reproduce a value of $\approx$ 2.91 K for the cosmic back-ground radiation, agreeing well with the recently measured experimental value of 2.728 K. Besides, this theory enables us to calculate the photon density and entropy associated with the background radiation and the ratio of the number of photons to the number of nucleons, which quantitatively agree with the results obtained by others.