A Scaling Relation in Inhomogeneous Cosmology with k-essence scalar fields

TL;DR

This paper derives a scaling relation for inhomogeneous cosmologies with k-essence scalar fields, linking inhomogeneous models to homogeneous ones and exploring cosmic acceleration.

Contribution

It introduces a new scaling relation for inhomogeneous k-essence cosmologies and connects inhomogeneous solutions to homogeneous limits.

Findings

Scaling relation reduces to known homogeneous case.

LTB universe exhibits late-time accelerated expansion.

Solutions relate metric functions to scalar fields.

Abstract

We obtain a scaling relation for spherically symmetric k-essence scalar fields $\phi(r,t)$ for an inhomogeneous cosmology with the Lemaitre-Tolman- Bondi (LTB) metric. We show that this scaling relation reduces to the known relation for a homogeneous cosmology when the LTB metric reduces to the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric under certain identifications of the metric functions. A k-essence lagrangian is set up and the Euler-Lagrangian equations solved assuming $\phi(r,t)=\phi_{1}(r) + \phi_{2}(t)$. The solutions enable the LBT metric functions to be related to the fields. The LTB inhomogeneous universe exhibits late time accelerated expansion i.e.cosmic acceleration driven by negative pressure.