Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We calculate quasilinear effects in the growth of structure in $f(R)$ models of gravity using perturbation theory. We find significant deviations in the bispectrum that depend on cosmic time, length scale and triangle shape. However the deviations in the reduced bispectrum $Q$ for $f(R)$ models are at the percent level, much smaller than the deviations in the bispectrum itself. This implies that three-point correlations can be predicted to a good approximation simply by using the modified linear growth factor in the standard gravity formalism. Our results suggest that gravitational clustering in the weakly nonlinear regime is not fundamentally altered, at least for a class of gravity theories that are well described in the Newtonian regime by the parameters $G_{\mathrm{eff}}$ and $\Phi /\Psi$. This approximate universality was also seen in the N-body simulation measurements of the power spectrum by Stabenau & Jain (2006), and in other recent studies based on simulations. Thus predictions for such modified gravity models in the regime relevant to large-scale structure observations may be less daunting than expected on first principles. We discuss the many caveats that apply to such predictions.

• Received 2 December 2008

DOI:https://doi.org/10.1103/PhysRevD.79.103506