Friedmann-like universes with non-metricity

TL;DR

This paper explores how spacetime non-metricity, modeled via hyperfluids with hypermomentum, can influence cosmological evolution, potentially mimicking matter effects and affecting early universe dynamics.

Contribution

It introduces a framework for incorporating non-metricity into cosmology using hyperfluid models, generalizing Friedmann equations and revealing new effects on universe evolution.

Findings

Non-metricity can mimic unconventional matter equations of state.

Certain hypermomentum types act as effective stiff fluids.

Non-metricity influences late-time cosmic dynamics.

Abstract

We study the potential effects of spacetime non-metricity in cosmology. In the spirit of Einstein-Cartan gravity, but with non-metricity replacing torsion, we consider the Einstein-Hilbert action and assume zero torsion. Adopting certain hyperfluid models, with non-vanishing hypermomentum that can source spacetime non-metricity, we add a matter component into the action and derive the field equations, along with the conservation laws. Applying our formulae to cosmology, we generalize the Friedmann and the Raychaudhuri equations in the presence of non-metricity. Our results show that, in a number of cases, non-metricity can mimic the effects of matter with unconventional equation of state. For instance, specific types of hypermomentum are found to act as an effective stiff fluid, thus opening the possibility that non-metricity could have played a significant role in the early stages of the universe's evolution. Alternative forms of hypermomentum can dominate the universal dynamics at late times. In either case, the equilibrium moment depends on the initial conditions and it is determined by a simple relation between the matter component and the hyperfluid.