Fluid observers and tilting cosmology

TL;DR

This paper investigates tilted perfect fluid cosmological models with constant equation of state, analyzing their future evolution, extreme tilt behavior, and connections to phantom and quintessence cosmologies.

Contribution

It introduces boost formulae relating physical variables in different frames and explores the late-time behavior of tilted models with various equations of state.

Findings

Ultra-radiative equations lead to finite-time singularities with infinite expansion.

Sub-radiative equations can produce effective quintessence-like behavior.

Tilt becomes extreme at late times, affecting the universe's asymptotic evolution.

Abstract

We study perfect fluid cosmological models with a constant equation of state parameter $\gamma$ in which there are two naturally defined time-like congruences, a geometrically defined geodesic congruence and a non-geodesic fluid congruence. We establish an appropriate set of boost formulae relating the physical variables, and consequently the observed quantities, in the two frames. We study expanding spatially homogeneous tilted perfect fluid models, with an emphasis on future evolution with extreme tilt. We show that for ultra-radiative equations of state (i.e., $\gamma>4/3$), generically the tilt becomes extreme at late times and the fluid observers will reach infinite expansion within a finite proper time and experience a singularity similar to that of the big rip. In addition, we show that for sub-radiative equations of state (i.e., $\gamma < 4/3$), the tilt can become extreme at late times and give rise to an effective quintessential equation of state. To establish the connection with phantom cosmology and quintessence, we calculate the effective equation of state in the models under consideration and we determine the future asymptotic behaviour of the tilting models in the fluid frame variables using the boost formulae. We also discuss spatially inhomogeneous models and tilting spatially homogeneous models with a cosmological constant.