f(R) Gravity and its Cosmological Implications

Abstract: We have investigated the evolution of a homogeneous isotropic background of the Universe and inhomogeneous subhorizon matter density perturbations in viable $f(R)$ models of present dark energy and cosmic acceleration analytically and numerically. It is found that viable $f(R)$ models generically exhibit recent crossing of the phantom boundary $w_{\rm DE}=-1$. Furthermore, it is shown that the growth index of perturbations depends both on time and wavenumber. This anomalous growth may explain properties of the observational matter power spectrum from the SDSS data and can also partially counteract the spectrum suppression by massive neutrinos making larger values of the total sum of neutrino rest masses possible.