Form invariant transformations between n-- and m-- dimensional flat Friedmann--Robertson--Walker cosmologies

TL;DR

This paper explores symmetry transformations in flat Friedmann-Robertson-Walker cosmologies across different dimensions, revealing how these transformations relate cosmic fluid properties and enable phenomena like assisted inflation and phantom cosmologies.

Contribution

It characterizes the symmetry group acting on n- and m-dimensional flat FRW cosmologies, uncovering new duality transformations and their implications for cosmic evolution.

Findings

Identifies symmetry transformations preserving Einstein equations in any dimension.

Shows how these transformations relate energy density and pressure to expansion.

Demonstrates the role of dimensional freedom in enabling assisted inflation and phantom cosmologies.

Abstract

We illustrate how the group of symmetry transformations, which preserve the form of the n--dimensional flat Friedmann--Robertson--Walker cosmologies satisfying Einstein equations, acts in any dimension. This group relates the energy density and the isotropic pressure of the cosmic fluid to the expansion rate. The freedom associated with the dimension of the space time yields assisted inflation even when the energy density of the fluid is a dimensional invariant and enriches the set of duality transformations leading to phantom cosmologies.