Testing Dark Energy and Cardassian Expansion for Causality

TL;DR

This paper examines the transition from decelerated to accelerated cosmic expansion in dark energy and Cardassian models, revealing potential causality violations based on observational data.

Contribution

It demonstrates that current dark energy and Cardassian models conflict with causality constraints given observational parameters.

Findings

Dark energy and Cardassian models violate causality with current data

Transition to acceleration occurs before matter domination ends

Observational data favors models incompatible with causality constraints

Abstract

Causality principle is a powerful criterion that allows us to discriminate between what is possible or not. In this paper we study the transition from decelerated to accelerated expansion in the context of Cardassian and dark energy models. We distinguish two important events during the transition. The first one is the end of the matter-dominated phase, which occurs at some time $t_{eq}$. The second one is the actual crossover from deceleration to acceleration, which occurs at some $t_{T}$. Causality requires $t_{T} \geq t_{eq}$. We demonstrate that dark energy models, with constant $w$, and Cardassian expansion, are compatible with causality only if $(\Omega_{M} - \bar{q}) \leq 1/2$. However, observational data indicate that the most probable option is $(\Omega_{M} - \bar{q}) > 1/2$. Consequently, the transition from deceleration to acceleration in dark energy and Cardassian models occurs before the matter-dominated epoch comes to an end, i.e., $t_{eq} > t_{T}$. Which contradicts causality principle.