f(R) gravity, torsion and non-metricity

For both f(R) theories of gravity with an independent symmetric connection (no torsion), usually referred to as Palatini f(R) gravity theories, and for f(R) theories of gravity with torsion but no non-metricity, called U4 theories, it has been shown that the independent connection can actually be eliminated algebraically, as long as this connection does not couple to matter. Remarkably, the outcome in both case is the same theory, which is dynamically equivalent with an \omega_0=-3/2 Brans--Dicke theory. It is shown here that even for the most general case of an independent connection with both non-metricity and torsion one arrives at exactly the same theory as in the more restricted cases. This generalizes the previous results and explains why assuming that either the torsion or the the non-metricity vanishes ultimately leads to the same theory. It also demonstrates that f(R) actions cannot support an independent connection which carries dynamical degrees of freedom, irrespectively of how general this connection is, at least as long as there is no connection-matter coupling.Comment: v2: slightly shortened version published in CQG as a Fast Track Communicatio

Bounding the Hubble flow in terms of the w parameter

The last decade has seen increasing efforts to circumscribe and bound the cosmological Hubble flow in terms of model-independent constraints on the cosmological fluid - such as, for instance, the classical energy conditions of general relativity. Quite a bit can certainly be said in this regard, but much more refined bounds can be obtained by placing more precise constraints (either theoretical or observational) on the cosmological fluid. In particular, the use of the w-parameter (w=p/rho) has become increasingly common as a surrogate for trying to say something about the cosmological equation of state. Herein we explore the extent to which a constraint on the w-parameter leads to useful and nontrivial constraints on the Hubble flow, in terms of constraints on density rho(z), Hubble parameter H(z), density parameter Omega(z), cosmological distances d(z), and lookback time T(z). In contrast to other partial results in the literature, we carry out the computations for arbitrary values of the space curvature k in [-1,0,+1], equivalently for arbitrary Omega_0 <= 1.Comment: 15 page