Friedmann-like universes with non-metricity

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.

FLRW solutions in $f(Q)$ theory: the effect of using different connections

“…1 For the convenience of the reader, and to avoid possible confusion, we just mention that there is a minor typo in the expression of the connection (19) as is given in [38]. The authors there use χ = √ 1 − kr 2 inside the connection, when actually, as we see from (19), it should be χ 2 = 1 − kr 2 .…”

“…The f (Q)-theory as a dark energy model is investigated in [16][17][18]. A recent work on the properties of the effective fluid, owed to the non-metricity, can be found in [19]. Some anisotropic spacetimes were studied in [20][21][22][23][24][25].…”