On A Cosmological Invariant as an Observational Probe in the Early Universe

TL;DR

This paper explores a cosmological invariant derived from k-essence scalar field models that could serve as an observational tool to probe the early universe and potentially confirm dark energy indirectly.

Contribution

It introduces a new invariant quadratic form involving the Hubble parameter and scale factor logarithm, linking scalar field dynamics to observable cosmological parameters.

Findings

Derivation of a cosmological invariant from k-essence models

Potential for this invariant to serve as an observational probe

Implication for confirming dark energy presence

Abstract

k-essence scalar field models are usually taken to have lagrangians of the form ${\mathcal L}=-V(\phi)F(X)$ with $F$ some general function of $X=\nabla_{\mu}\phi\nabla^{\mu}\phi$. Under certain conditions this lagrangian in the context of the early universe can take the form of that of an oscillator with time dependent frequency. The Ermakov invariant for a time dependent oscillator in a cosmological scenario then leads to an invariant quadratic form involving the Hubble parameter and the logarithm of the scale factor. In principle, this invariant can lead to further observational probes for the early universe. Moreover, if such an invariant can be observationally verified then the presence of dark energy will also be indirectly confirmed.