Models which accelerate the expansion of the universe through the addition of a function of the Ricci scalar $f(R)$ leave a characteristic signature in the large-scale structure of the universe at the Compton wavelength scale of the extra scalar degree of freedom. We search for such a signature in current cosmological data sets: the WMAP cosmic microwave background (CMB) power spectrum, Supernovae Legacy Survey supernovae distance measures, the Sloan Digital Sky Survey luminous red galaxy power spectrum, and galaxy-CMB angular correlations. Because of theoretical uncertainties in the nonlinear evolution of $f(R)$ models, the galaxy power spectrum conservatively yields only weak constraints on the models despite the strong predicted signature in the linear matter power spectrum. Currently the tightest constraints involve the modification to the integrated Sachs-Wolfe effect from growth of gravitational potentials during the acceleration epoch. This effect is manifest for large Compton wavelengths in enhanced low multipole power in the CMB and anticorrelation between the CMB and tracers of the potential. They place a bound on the Compton wavelength of the field to be less than of order the Hubble scale.

• Received 19 June 2007

DOI:https://doi.org/10.1103/PhysRevD.76.063517