Cardone, Vincenzo F., Camera, Stefano and Diaferio, Antonaldo (2012), "An updated analysis of two classes of f (R) theories of gravity", JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS, 2.
Abstract: The observed accelerated cosmic expansion can be a signature of
fourth-order gravity theories, where the acceleration of the Universe is
a consequence!) of departures from Einstein General Relativity, rather
than the sign of the existence of a fluid with negative pressure. In the
fourth-order gravity theories, the gravity Lagrangian is described by an
analytic function f(R) of the scalar curvature R subject to the
demanding conditions that no detectable deviations from standard GR is
observed on the Solar System scale. Here we consider two classes of f
(R) theories able to pass Solar System tests and investigate their
viability on cosmological scales. To this end, we fit the theories to a
large dataset including the combined Hubble diagram of Type Ia
Supernovae and Gamma Ray Bursts, the Hubble parameter H(z) data from
passively evolving red galaxies, Baryon Acoustic Oscillations extracted
from the seventh data release of the Sloan lAgital Sky Survey (SDSS) and
the distance priors from the Wilkinson Microwave Anisotropy Probe seven
years (WMAP7) data. We find that both classes of f(B) fit very well this
large dataset with the present-day values of the matter density. Hubble
constant and deceleration parameter in agreement with previous
estimates; however, the strong degeneracy among the f(R) parameters
prevents us from strongly constraining their values. We also derive the
growth factor g = d In delta/d In a, with delta = delta pm/pm the matter
density perturbation, and show that it can still be well approximated by
g(z) alpha Omega(M)(z)(gamma). We finally constrain gamma (on some
representative scales) and investigate its redshift dependence to see
whether future data can discriminate between these classes of f (R)
theories and standard dark energy models.
Keywords: modified gravity; dark energy theory; supernova type Ia - standard
candles; baryon acoustic oscillations