Energy conditions and current acceleration of the universe

TL;DR

This paper examines the use of energy conditions to study the universe's acceleration, highlighting the importance of direct analysis over integrated observational variables to avoid misinterpretation, and confirms that current data support past acceleration.

Contribution

It emphasizes the need for careful interpretation of integrated observational variables when applying energy conditions to cosmology, providing a more accurate analysis of the universe's acceleration history.

Findings

Energy conditions support a past acceleration phase of the universe.

Integrated variables like $E(z)$ can mislead about the transition point.

Current data strongly indicate a past acceleration epoch.

Abstract

The energy conditions provide a very promising model-independent study of the current acceleration of the universe. However, in order to connect these conditions with observations, one often needs first to integrate them, and then find the corresponding constraints on some observational variables, such as the distance modulus. Those integral forms can be misleading, and great caution is needed when one interprets them physically. A typical example is that the transition point of the deceleration parameter $q(z)$ is at about $z \simeq 0.76$ in the $\Lambda$CDM model. However, with the same model when we consider the dimensionless Hubble parameter $E(z)$, which involves the integration of $q(z)$, we find that $E(z)$ does not cross the line of $q(z) = 0$ before $z = 2$. Therefore, to get the correct result, we cannot use the latter to determine the transition point. With these in mind, we carefully study the constraints from the energy conditions, and find that, among other things, the current observational data indeed strongly indicate that our universe has ocne experienced an accelerating expansion phase between the epoch of galaxy formation and the present.