Scenario of inflationary cosmology from the phenomenological $\Lambda$ models

TL;DR

This paper compares three phenomenological models of a dynamical cosmological term in flat and curved universes, demonstrating their equivalence in flat space and supporting the inflationary expansion of the universe through numerical and qualitative analysis.

Contribution

It introduces a comparative numerical analysis of three phenomenological $\Lambda$ models and shows their equivalence in flat universe, supporting inflationary cosmology.

Findings

Models are equivalent for flat universe $k=0$

Numerical evolution plots support inflationary expansion

Qualitative analysis aligns with expanding universe hypothesis

Abstract

Choosing the three phenomenological models of the dynamical cosmological term $\Lambda$, viz., $\Lambda \sim (\dot a/a)^2$, $\Lambda \sim {\ddot a/a}$ and $\Lambda \sim \rho$ where $a$ is the cosmic scale factor, it has been shown by the method of numerical analysis that the three models are equivalent for the flat Universe $k=0$. The evolution plots for dynamical cosmological term $\Lambda$ vs. time $t$ and also the cosmic scale factor $a$ vs. $t$ are drawn here for $k=0, +1$. A qualitative analysis has been made from the plots which supports the idea of inflation and hence expanding Universe.