An analytical description for the cosmological constant

TL;DR

This paper derives analytical solutions for the scale factor in quantum cosmology, supporting an inverse-square law for the cosmological constant and exploring its implications for matter creation and universe age.

Contribution

It introduces new analytical solutions for the scale factor in quantum cosmology, extending existing models and examining the time variation of the cosmological constant.

Findings

Supports inverse-square law for $\

a0Provides analytical solutions for scale factor evolution

Abstract

From the principles of quantum cosmologies we can justify the reason for an inverse-square law for the cosmological constant with no conflict with observations. Although this general expression for $\Lambda$ is well known in the literature, in this work we introduce some analytical solutions for the scale factor different from the literature. The underlying motivation to carry out these solutions is the fact that the time variation of $\Lambda$ can lead to a creation of matter and/or radiation such as to help in the investigation of the age of the Universe. The knowledge of the scale factor behavior might shed some light on these questions since the entire evolution of a homogeneous isotropic Universe is contained in the scale factor.