Unscreening Modified Gravity in the Matter Power Spectrum

Viable modifications of gravity that may produce cosmic acceleration need to be screened in high-density regions such as the Solar System, where general relativity is well tested. Screening mechanisms also prevent strong anomalies in the large-scale structure and limit the constraints that can be inferred on these gravity models from cosmology. We find that by suppressing the contribution of the screened high-density regions in the matter power spectrum, allowing a greater contribution of unscreened low densities, modified gravity models can be more readily discriminated from the concordance cosmology. Moreover, by variation of density thresholds, degeneracies with other effects may be dealt with more adequately. Specializing to chameleon gravity as a worked example for screening in modified gravity, employing $N$-body simulations of $f(R)$ models and the halo model of chameleon theories, we demonstrate the effectiveness of this method. We find that a percent-level measurement of the clipped power at $k<0.3h/\mathrm{Mpc}$ can yield constraints on chameleon models that are more stringent than what is inferred from Solar System tests or distance indicators in unscreened dwarf galaxies. Finally, we verify that our method is also applicable to the Vainshtein mechanism.

Figure 1

Left: fractional difference between simulated matter power spectra of $f(R)$ gravity $(|f_{R0}|={10}^{-6})$ and $\mathrm{\Lambda }\mathrm{CDM}$ at two different $k$ bins. By clipping high densities, contributions from self-screened regions are downweighted and unscreened features enhanced (dashed curves). In the reverse case of applying a minimum threshold to the density field, contributions from unscreened low densities are downweighted, enhancing screened regions, and the power spectra converge (dotted lines). Middle: fractional departure from the $\mathrm{\Lambda }\mathrm{CDM}$ power spectrum in three different $f(R)$ models for unclipped fields (solid lines), linear perturbation theory (dashed lines), clipped fields with power at the largest scales reduced by 50% (dot-dashed curves), and logarithmic density transformation with matching to the $\mathrm{\Lambda }\mathrm{CDM}$ power at the lowest $k$ bin (dotted curves). Right: clipped $f(R)$ power spectra from simulations (circles) compared to weighting linear and one-loop contributions (dashed curves). Increased clipping strength enhances the weight of the unscreened linear (dotted curves) relative to the one-loop power.

Figure 2

Forecast of upper bounds on the chameleon field amplitude $1-{\overline{\phi }}_0$ from the clipped matter power spectrum as a function of gravitational coupling strength set by the Brans-Dicke parameter $\omega$ and for different values of the exponent of the chameleon field potential $\alpha$. The constraints are compared to upper bounds inferred from Solar System [32], astrophysical distance indicator [24], and cosmological (cluster) observations [25] (cf. Ref. [28]). For a range of chameleon model parameters, clipping can provide the strongest constraints.