A cosmological model in Weyl$ndash$Cartan spacetime: I. Field equations and solutions

Abstract

Abstract. In this first article of a series on alternative cosmological models we present an extended version of a cosmological model in Weyl-Cartan spacetime. The new model can be viewed as a generalization of a model developed earlier jointly with Tresguerres. Within this model the non-Riemannian quantities, i.e. torsion T α and nonmetricity Q αβ , are proportional to the Weyl 1-form. The hypermomentum ∆ αβ depends on our ansatz for the nonmetricity and vice versa. We derive the explicit form of the field equations for different cases and provide solutions for a broad class of parameters. We demonstrate that it is possible to construct models in which the non-Riemannian quantities die out with time. We show how our model fits into the more general framework of metric-affine gravity (MAG).

Rotating Black Holes in Metric-Affine Gravity

“…Alternatively, instead of torsion and nonmetricity, we could display the connection of our solution. It can be read off from (48). Since Q = 0, we have…”

“…21 . The group of Dereli, Tucker, and Wang 17,58,59 applied such theories to the dark matter problem, inter alia, Minkevich et al 33,37,34,35,36 , Puetzfeld et al 48,49,50,51 , and Babourova & Frolov 3,2,4 mainly to cosmological solutions. New exact solutions were found, amongst others, by Vassiliev & King 31,60,61,43 .…”

A cosmological model in Weyl$ndash$Cartan spacetime: II. Magnitude-redshift relation

“…We will not discuss the details of this model at this point, therefore the reader should consult sections 2-4 of [8] in order to get an idea which assumptions were made during the derivation of the field equations of this model.…”

“…This function stems from an ansatz for the Weyl 1-form Q which governs the non-Riemannian features of the model, cf. section 4 of [8]. Here k denotes the usual parameter within the Robertson-Walker metric, χ, a 4 , a 6 , c, and κ are coupling constants, and Λ is the so-called induced cosmological constant.…”

“…Subsequently, we have to choose an equation of state and an appropriate ansatz for ζ. We choose the eos to be of the form p = wµ with w = const, and make use of the solution for µ obtained in [8] equation (65) …”