# A Study of the Time Evolution of Brans-Dicke Parameter and its Role in Cosmic Expansion

## TL;DR

This paper investigates how the Brans-Dicke parameter varies over time across different cosmological eras and its influence on cosmic expansion, linking theoretical models with observational data on gravitational constant variation.

## Contribution

It provides explicit expressions for the time dependence of the Brans-Dicke parameter and explores its impact on key cosmological parameters during universe expansion.

## Key findings

- Derived the explicit time dependence of the Brans-Dicke parameter.
- Connected the variation of the BD parameter with observational data on gravitational constant.
- Demonstrated the role of the BD parameter in cosmic acceleration and matter-energy dynamics.

## Abstract

The dependence of Brans-Dicke (BD) parameter upon the scalar field, for different cosmological era of the expanding universe, has been explored. The time dependence of the scalar field has been determined and thereby the explicit time dependence of the BD parameter has been obtained. Experimental observations regarding the time dependence of the gravitational constant has been considered for this study. The scale factor, Hubble parameter, deceleration parameter, matter density, gravitational constant and the density parameters for matter and dark energy have been expressed in terms of the BD parameter and its time derivatives, showing its role in cosmic expansion.