Cosmological hyperfluids, torsion and non-metricity
- PDF / 467,019 Bytes
- 20 Pages / 595.276 x 790.866 pts Page_size
- 88 Downloads / 214 Views
Regular Article - Theoretical Physics
Cosmological hyperfluids, torsion and non-metricity Damianos Iosifidisa Department of Physics, Institute of Theoretical Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Received: 6 July 2020 / Accepted: 31 October 2020 © The Author(s) 2020
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.
Contents 1 2 3 4 5 6 7
8
Introduction . . . . . . . . . . . . . . . . . . . . . Non-Riemannian geometry . . . . . . . . . . . . . Hypermomentum, canonical and metrical energy momentum tensors . . . . . . . . . . . . . . . . . Unconstrained hyperfluid . . . . . . . . . . . . . . Cosmology with torsion and non-metricity . . . . . Application of the unconstrained hyperfluid model to cosmology . . . . . . . . . . . . . . . . . . . . Novel model for cosmological perfect hyperfluid . 7.1 Conservation laws . . . . . . . . . . . . . . . 7.2 Conservation laws in FLRW Universes . . . . 7.3 Fluid motion . . . . . . . . . . . . . . . . . . Friedmann equations with torsion and non-metricity 8.1 The case of pure torsion . . . . . . . . . . . .
a e-mail:
[email protected] (corresponding author)
0123456789().: V,-vol
. . . . . . . . . . . .
8.2 The case of pure non-metricity . . . . . . . . . 8.2.1 Weyl non-metricity . . . . . . . . . . . 8.2.2 General non-metricity . . . . . . . . . . 9 Friedmann equations with both torsion and non-metricity 10 Hypermomentum matter types . . . . . . . . . . . . 11 Conclusions . . . . . . . . . . . . . . . . . . . . . . Appendix A: Diffeomorphisms . . . . . . . . . . . . . . Appendix B: Divergence of palatini tensor . . . . . . . . Appendix C: Scalar field coupled to the connection . . . References . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction General relativity is undoubtedly one of the most well established, mathematically beautiful and properly formulated Theories of Physics. Its nice geometrical interpretation along with its solid predictions give enough reasons to call the latter a successful Theory. However, despite its great success general relativity falls sho
Data Loading...
