Matter power spectrum in $f(R)$ gravity

Modified gravity can be considered as an alternative to dark energy. In a generalized theory of gravity, the Universe may accelerate while containing only baryonic and dark matter. We study, in particular, the evolution of matter fluctuations in $f(R)$ models within the Palatini approach, and find that the resulting matter power spectrum is sensitive to a nonlinear dependence on the curvature scalar in the gravitational action. The constraints that arise from comparison to the form of the observed matter power spectrum tighten the previous constraints derived from background expansion by several orders of magnitude. Models in the allowed parameter space are practically indistinguishable from general relativity with a cosmological constant when the background expansion is considered.

Figure 1

The 68%, 90%, and 99% confidence contours arising from fitting the CMB shift parameter.

Figure 2

The matter power spectra for $\beta =-0.00001$ (solid line), $\beta =-0.00005$ (dash-dotted line), $\beta =0.00001$ (dotted line), and $\beta =0.00005$ (dashed line). In all the cases ${\Omega }_m=0.3$ and $n_S=1$. (We do not use the data points at the three smallest scales, and instead of the error bars plotted here we use the exact window functions.)

Figure 3

The 68%, 90%, and 99% confidence contours arising from fitting to the SDSS data. The left panel is for $n_S=1\pm 0.2$ and the right panel corresponds to scale-invariant spectrum of primordial fluctuations.