FRW-Type Universe With Vacuum Energy Density

TL;DR

This paper proposes a cosmological model with a dynamic vacuum energy density that decreases over time, explores its implications for universe evolution, and finds solutions consistent with inflation and observational constraints.

Contribution

It introduces a new form of the cosmological constant dependent on the scale factor's derivatives and analyzes its effects on universe dynamics and vacuum energy evolution.

Findings

Vacuum energy density decreases as t^{-2} over time.

Solutions align with standard FRW models under specific parameter conditions.

The model can explain inflation and is consistent with observational vacuum energy estimates.

Abstract

We have considered a cosmological model with a cosmological constant of the form $\Lambda=3\alpha\frac{\dot R^2}{R^2}+\bt\frac{\ddot R}{R} \alpha, \bt=\rm const.$ The cosmological constant is found to decrease as $t^{-2}$ and the rate of particle creation is smaller than the Steady State value. We have found that this behavior gives $\frac{\Lambda_{Pl}}{\Lambda_p}=10^{120}$ where $\Lambda_{Pl}$ is the value of $\Lambda$ at Planck time. Solutions with $\bt=3\alpha$ in the radiation dominated era and $\bt=6\alpha$ in the matter dominated era are equivalent to the FRW results. We have found an inflationary solution of the de-Sitter type with $\bt=3-3\alpha$. Some problems of the Standard Model may be resolved with the presence of the above cosmological constant in the Einstein's equation. Since observations suggest a contribution of the vacuum energy density in the range $0.40<\Omega^\Lambda<0.76$, one gets $4<\beta<12$. If $\alpha=0$ the minimum age of the universe is found to be $H_p^{-1}$ ($H_p$ is the present Hubble constant) with $\beta=\infty$.