# Brans-Dicke Scalar Field Cosmological Model in Lyra's Geometry

## TL;DR

This paper develops a new anisotropic cosmological model combining Lyra's geometry and Brans-Dicke theory, explaining the universe's acceleration and aligning with supernova observations.

## Contribution

It introduces a novel cosmological model using Lyra's geometry and Brans-Dicke modifications, exploring dark energy candidates and universe acceleration.

## Key findings

- Model exhibits current acceleration and past deceleration.
- Model aligns with supernovae observations.
- Dark energy candidate explains acceleration.

## Abstract

In this paper, we have developed a new cosmological model in Einstein's modified gravity theory using two types of modification.(i) Geometrical modification, in which we have used Lyra's geometry in the left hand side of the Einstein field equations (EFE) and (ii) Modification in gravity (energy momentum tensor) on right hand side of EFE, as per Brans-Dicke (BD) model. With these two modifications, we have investigated a spatially homogeneous and anisotropic Bianchi type-I cosmological models of Einstein's Brans-Dicke theory of gravitation in Lyra geometry. The model represents accelerating universe at present and decelerating in past and is considered to be dominated by dark energy. Gauge function $\beta$ and BD-scalar field $\phi$ are considered as a candidate for the dark energy and is responsible for the present acceleration. The derived model agrees at par with the recent supernovae (SN Ia) observations. We have set BD-coupling constant $\omega$ to be greater than 40000, seeing the solar system tests and evidences. We have discussed the various physical and geometrical properties of the models and have compared them with the corresponding relativistic models.