Constraints on f(R) cosmology in the Palatini formalism

In this work we derive the covariant and gauge invariant perturbation equations in general theories of f(R) gravity in the Palatini formalism to linear order and calculate the cosmic microwave background (CMB) and matter power spectra for an extensively discussed model, f(R)=R+alpha(-R)(beta), which is a possible candidate for the late-time cosmic accelerating expansion found recently. These spectra are discussed and found to be sensitively dependent on the value of beta. We are thus able to make stringent constraints on beta from cosmological data on CMB and matter power spectra: The three-year Wilkinson Microwave Anisotropy Probe (WMAP) data alone give a constraint |beta|less than or similar to O(10(-3)) while the joint WMAP, Supernova Lagacy Survey (SNLS), and Sloan Digital Sky Survey (SDSS) data sets tighten this to beta similar to O(10(-6)), about an order of magnitude more stringent than the constraint from SDSS data alone, which makes this model practically indistinguishable from the standard Lambda CDM paradigm.