Perturbative and Numerical Analysis of Tilted Cosmological Models of Bianchi type V

TL;DR

This paper analyzes tilted Bianchi type V and I cosmological models with a perfect fluid and cosmological constant, using perturbative and numerical methods to explore their dynamics and solutions.

Contribution

It introduces a tetrad-based approach to reduce Einstein's equations for these models to a manageable system of five coupled ODEs, including perturbative and numerical analyses.

Findings

Perturbative solutions align well with numerical results in relevant domains.

The full line element for Bianchi V and I models is explicitly derived.

Numerical solutions are provided for non-perturbative regimes.

Abstract

Cosmological models of Bianchi type V and I containing a perfect fluid with a linear equation of state plus cosmological constant are investigated using a tetrad approach where our variables are the Riemann tensor, the Ricci rotation coefficients and a subset of the tetrad vector components. This set, in the following called S, describes a spacetime when its elements are constrained by certain integrability conditions and due to a theorem by Cartan this set gives a complete local description of the spacetime. The system obtained by imposing the integrability conditions and Einstein's equations can be reduced to an integrable system of five coupled first order ordinary differential equations. The general solution is tilted and describes a fluid with expansion, shear and vorticity. With the help of standard bases for Bianchi V and I the full line element is found in terms of the elements in S. We then construct the solutions to the linearized equations around the open Friedmann model. The full system is also studied numerically and the perturbative solutions agree well with the numerical ones in the appropriate domains. We also give some examples of numerical solutions in the non-perturbative regime.