In this methodological note we discuss several topics related to interpretation of some basic cosmological principles. We demonstrate that one of the key points is the usage of synchronous reference frames. The Friedmann-Robertson-Walker one is the m
ost known example of them. We describe how different quantities behave in this frame. Special attention is paid to potentially observable parameters. We discuss different variants for choosing measures of velocity and acceleration representing the Hubble flow, and present illustrative calculations of apparent acceleration in flat $Lambda CDM$ model for various epochs. We generalize description of the tethered galaxies problem for different velocity measures and equations of state, and illustrate time behavior of velocities and redshifts in the $Lambda CDM$ model.
In this paper we propose a scheme which allows one to find all possible exponential solutions of special class -- non-constant volume solutions -- in Lovelock gravity in arbitrary number of dimensions and with arbitrate combinations of Lovelock terms
. We apply this scheme to (6+1)- and (7+1)-dimensional flat anisotropic cosmologies in Einstein-Gauss-Bonnet and third-order Lovelock gravity to demonstrate how our scheme does work. In course of this demonstration we derive all possible solutions in (6+1) and (7+1) dimensions and compare solutions and their abundance between cases with different Lovelock terms present. As a special but more physical case we consider spaces which allow three-dimensional isotropic subspace for they could be viewed as examples of compactification schemes. Our results suggest that the same solution with three-dimensional isotropic subspace is more probable to occur in the model with most possible Lovelock terms taken into account, which could be used as kind of anthropic argument for consideration of Lovelock and other higher-order gravity models in multidimensional cosmologies.
We investigate the cosmological dynamics in teleparallel gravity with nonminimal coupling. We analytically extract several asymptotic solutions and we numerically study the exact phase-space behavior. Comparing the obtained results with the correspon
ding behavior of nonminimal scalar-curvature theory, we find significant differences, such is the rare stability and the frequent presence of oscillatory behavior.
