Cosmic Acceleration With A Positive Cosmological Constant

TL;DR

This paper explores a cosmological model with a phenomenological cosmological constant proportional to the acceleration of the universe, showing it leads to an accelerating universe with specific decay laws for b3, and discusses implications for the universe's age and gravitational constant.

Contribution

It introduces a new phenomenological model for b3 involving the acceleration of the universe and analyzes its implications for cosmic acceleration and the evolution of fundamental constants.

Findings

Universe must be accelerating with positive b3

b3 decreases as t^{-2} over time

Model yields de-Sitter type inflationary solution

Abstract

We have considered a cosmological model with a phenomenological model for the cosmological constant of the form $\Lambda=\bt\fr{\ddot R}{R}$, $ \bt$ is a constant. For age parameter consistent with observational data the Universe must be accelerating in the presence of a positive cosmological constant. The minimum age of the Universe is $H_0^{-1}$, where $H_0$ is the present Hubble constant. The cosmological constant is found to decrease as $t^{-2}$. Allowing the gravitational constant to change with time leads to an ever increasing gravitational constant at the present epoch. In the presence of a viscous fluid this decay law for $\Lambda$ is equivalent to the one with $\Lambda=3\alpha H^2$ ($\alpha=\rm const.$) provided $\alpha=\fr{\bt}{3(\bt-2)}$. The inflationary solution obtained from this model is that of the de-Sitter type.