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.

This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective transformation of the connection, a rescaling of the orthonormal frame, and a combination of the two. The most general second order quadratic metric-affine action, including the parity-violating terms, is constructed in each of the three cases. The results can be straightforwardly generalised by including higher derivatives, and implemented in the general metric-affine, teleparallel, and symmetric teleparallel geometries.

This article presents a systematic way to solve for the affine connection in metric-affine geometry. We start by adding to the Einstein–Hilbert action, a general action that is linear in the connection and its partial derivatives and respects projective invariance. We then generalize the result for metric-affine theories. Finally, we generalize even further and add an action (to the Einstein–Hilbert) that has an arbitrary dependence on the connection and its partial derivatives. We wrap up our results as three consecutive theorems. We then apply our theorems to some simple examples in order to illustrate how the procedure works and also discuss the cases of dynamical/non-dynamical connections.

We study a metric-affine gravitational theory given by the Einstein–Hilbert (EH) action plus a parity violating contribution (which we will refer to as the Hojman term, also known as Holst term) in vacuum. We find out that for a certain value of the Barbero–Immirzi (BI) parameter the total action possesses a remarkable invariance under particular transformations of the affine connection. We prove that in all cases, with appropriate gauge choices, the connection reduces to the Levi-Civita one and that the theory turns out to be equivalent to general relativity (GR) in vacuum. Subsequently, we generalize our discussion and analyze the case of metric-affine f ( R ) gravity plus the Hojman term. In particular, we show that for f ′( R ) ≠ constant the theory results to be on-shell equivalent to a metric-compatible torsionless scalar–tensor model with a propagating pseudo-scalar. Matter coupling of the aforementioned models is also discussed, together with explicit examples and applications.

We consider the most general quadratic metric-affine gravity setup in the presence of generic matter sources with non-vanishing hypermomentum. The gravitational action consists of all 17 quadratic invariants (both parity even and odd) in torsion and non-metricity as well as their mixings, along with the terms that are linear in the curvature namely the Ricci scalar and the totally antisymmetric Riemann piece. Adding also a matter sector to the latter we first obtain the field equations for the generalized quadratic theory. Then, using a recent theorem, we successfully find the exact form of the affine connection under some quite general non-degeneracy conditions. Having obtained the exact and unique solution of the affine connection we subsequently derive the closed forms of spacetime torsion and non-metricity and also recast the metric field equations into a GR form with modified source terms that are quadratic in the hypermomentum and linear in its derivatives. We also study the vacuum quadratic theory and prove that in this instance, or more generally for vanishing hypermomentum, the connection becomes the Levi-Civita one. Therefore, we also find exactly to what does the quadratic vacuum theory correspond to. Finally, we generalize our result even further and also discuss the physical consequences and applications of our study.

We set the foundation and formulate the Perfect (Ideal) Hyperfluid. The latter represents the natural generalization of the usual perfect fluid structure where now the microscopic characteristics of matter (spin, shear, dilation) are also taken into account, sourcing a non-Riemannian arena (i.e spacetime torsion and non-metricity) for Metric-Affine Gravity. We derive the energy tensors of this Hyperfluid structure and subsequently present the conservation laws obeyed by them. Finally, we consider a Cosmological application of this Perfect Hyperfluid and classify some possible forms of this fluid structure.