Cosmology of Quadratic Metric-Affine Gravity

Abstract

We investigate the cosmological aspects of the most general parity preserving Metric-Affine Gravity theory quadratic in torsion and non-metricity in the presence of a cosmological hyperfluid. The equations of motion are obtained by varying the action with respect to the metric and the independent affine connection. Subsequently, considering a Friedmann-Lemaître-Robertson-Walker background, we derive the most general form of the modified Friedmann equations for the full quadratic theory. We then focus on a characteristic sub-case involving only two quadratic contributions given in terms of torsion and non-metricity vectors. In this setup, studying the modified Friedmann equations along with the conservation laws of the perfect cosmological hyperfluid, we provide exact solutions both for purely dilation and for purely spin hypermomentum sources. We then discuss the physical consequences of our model and the prominent role of torsion and non-metricity in this cosmological setup.

Three-dimensional non-relativistic supergravity and torsion

“…See, e.g.,[90,91] for a recent review on non-Riemannian structures and applications in (super)gravity. Besides, we refer the reader to, e.g.,[92][93][94][95][96] for further implications of a non-vanishing torsion and non-Riemannian structures in gravity and supergravity theories.…”

Quadratic Metric-Affine Gravity: Solving for the Affine-Connection

“…Some recent developments in MAG and applications include[8,[10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] 2 For an interesting possible relation among the shear current and the hadronic properties of matter see[26] 3. The Cosmology of the full 11 parameter quadratic Theory in the presence of a Cosmological hyperfluid has been recently studied in[24].…”

Metric-Affine Vector-Tensor Correspondence and Implications in $F(R,T,Q,\mathcal{T},\mathcal{D})$ gravity

“…With this in mind, in the present work we extend some results of antecedent literature [41][42][43][44][45][46][47][48][49][50] by studying a general quadratic MAG action in vacuum (namely in the absence of matter) in n spacetime dimensions. More precisely, in [45,46] the authors examined a quadratic theory involving also a piece quadratic in the so-called homothetic curvature tensor, while in [47] only contributions quadratic in the torsion tensor were considered.…”

“…The theory we consider here involves, besides the usual (non-Riemannian) Einstein-Hilbert contribution, all the parity even quadratic terms in torsion and non-metricity plus a Lagrangian quadratic in the field-strengths of the torsion and nonmetricity vectors. The gravitational action represents a generalization of the one studied in [45,46] and an extension of the quadratic model analyzed in [50] by including quadratic contributions in all the aforementioned field-strengths. The paper is organized as follows: In Section 2 we review the geometric framework, adopting the same notation and conventions of [31].…”