Abstract
We develop a novel model for cosmological hyperfluids, that is fluids with intrinsic hypermomentum that induce spacetime torsion and non-metricity. Imposing the cosmological principle to metric-affine spaces, we present the most general covariant form of the hypermomentum tensor in an FLRW Universe along with its conservation laws and therefore construct a novel hyperfluid model for cosmological purposes. Extending the previous model of the unconstrained hyperfluid in a cosmological setting we establish the conservation laws for energy–momentum and hypermomentum and therefore provide the complete cosmological setup to study non-Riemannian effects in Cosmology. With the help of this we find the forms of torsion and non-metricity that were earlier reported in the literature and also obtain the most general form of the Friedmann equations with torsion and non-metricity. We also discuss some applications of our model, make contact with the known results in the literature and point to future directions.
Highlights
Having obtained the complete cosmological setup for the perfect cosmological hyperfluid, we consider a Metric-affine gravity (MAG) model consisting of the usual Einstein–Hilbert action and consider the matter sector to be that of the perfect cosmological hyperfluid
We have developed a novel model for a Cosmological hyperfluid, namely a fluid that carries hypermomentum and subsequently induces torsional and non-metric degrees of freedom
In constructing the model we essentially imposed the same conservation laws with the unconstrained hyperfluid [13] but we have considered a different ansatz for the covariant form of the hypermomentum that is compatible with the Cosmological principle
Summary
Riemmannian geometry and set up the definitions for the various geometrical objects we are going to be using throughout. Given a torsion tensor contracting it in its last two indices we may define the torsion vector. Without the use of any metric, we can construct the two independent contractions for the Riemann tensor. In a generic non-Riemannian space the metric need not be covariantly conserved, and we say that the connection is not metric-compatible This deviation from compatibility, defines the non-metricity tensor. Given a matter action, we define as usual the metrical (symmetric) energy–momentum tensor(MEMT) by. It is worth mentioning that the conservation law for angular momentum receives, in general, contributions from nonmetricity as is obvious from the above exposure It is evident from (23) that for matter with no microstructure ( αμν ≡ 0) the canonical and the metrical energy– momentum tensors coincide. Corresponding to the cases of a conformally invariant, a frame rescaling invariant and special projective transformation invariant Theories respectively (see [23])
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