Homogeneous cosmologies in scalar tensor theory

TL;DR

This paper investigates homogeneous cosmologies within scalar-tensor theory based on Lyra geometry, deriving exact solutions for various matter contents and challenging the traditional equivalence between Lyra-based scalar theories and Einstein's gravity.

Contribution

It provides new exact models of FRW cosmologies in Lyra geometry and clarifies the relationship between Lyra scalar theory and Einstein's gravity, especially regarding the role of displacement vectors.

Findings

Exact exponential expansion solutions for different matter groups.

Displacement vector components are not equivalent to a cosmological constant.

Scalar theory solutions are more general than Einstein's theory.

Abstract

In this study, FRW-cosmologies with some matter groups such as monopole-domain wall, monopole-Chaplygin gas and monopole-strange quark matter in the scalar theory of gravitation based on Lyra geometry are investigated. We expand two exact models as static case and time-depended case for each matter groups in order to solve field equations in the scalar theory. For each matter groups, the solutions are introduced as the models of expanding universe, exponentially. Hubble parameters in the case of k=0,-1,1 are obtained for these models. Furthermore, we realize interesting result which the well-known relation between scalar theory based on Lyra geometry and Einstein's theory is an incomplete idea. In opposition to the well accepted idea in the literature, we suggest that Einstein's theory with no cosmological constant is equivalent of scalar theory based on Lyra geometry with zero displacement vector, completely. If the components of displacement vector in the scalar theory are any constant functions, the scalar theory couldn't correspond to Einstein's theory, identically. Even if the components of displacement vector in the scalar theory are the constant, the field equations and their solutions contain the Einstein's field equations and their solutions, but they are variously more general than Einstein's theory of gravitation. So, coefficients of constant displacement vector don't play the role of cosmological constant in keeping with the Einstein's theory. Finally, the results have been discussed.