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We discuss the most general field equations for cosmological spacetimes for theories of gravity based on non-linear extensions of the non-metricity scalar and the torsion scalar. Our approach is based on a systematic symmetry-reduction of the metric-affine geometry which underlies these theories. While for the simplest conceivable case the connection disappears from the field equations and one obtains the Friedmann equations of General Relativity, we show that in $f(mathbb{Q})$ cosmology the connection generically modifies the metric field equations and that some of the connection components become dynamical. We show that $f(mathbb{Q})$ cosmology contains the exact General Relativity solutions and also exact solutions which go beyond. In $f(mathbb{T})$~cosmology, however, the connection is completely fixed and not dynamical.
We investigate the qualitative evolution of (D+1)-dimensional cosmological models in f(R) gravity for the general case of the function f(R). The analysis is specified for various examples, including the (D+1)-dimensional generalization of the Starobi
The simplest possible classical model leading to a cosmological bounce is examined in the light of the non-Gaussianities it can generate. Concentrating solely on the transition between contraction and expansion, and assuming initially purely Gaussian
We consider gravity theory with varying speed of light and varying gravitational constant. Both constants are represented by non-minimally coupled scalar fields. We examine the cosmological evolution in the near curvature singularity regime. We find
In this paper the dynamics of free gauge fields in Bianchi type I-VII$_{h}$ space-times is investigated. The general equations for a matter sector consisting of a $p$-form field strength ($p,in,{1,3}$), a cosmological constant ($4$-form) and perfect
We study general dynamical equations describing homogeneous isotropic cosmologies coupled to a scalaron $psi$. For flat cosmologies ($k=0$), we analyze in detail the gauge-independent equation describing the differential, $chi(alpha)equivpsi^prime(al