Limits on deviations from the inverse-square law on megaparsec scales

We present an attempt to constrain deviations from the gravitational inverse-square law on large-scale structure scales. A perturbed law modifies the Poisson equation, which implies a scale-dependent growth of overdensities in the linear regime and thus modifies the power spectrum shape. We use two large-scale structure surveys (the Sloan Digital Sky survey and the Anglo-Australian two-degree field galaxy redshift survey) to constrain the parameters of two simple modifications of the inverse-square law. We find no evidence for deviations from normal gravity on the scales probed by these surveys ($\sim {10}^{23}\mathrm{m}$).

Figure 1

$\widehat{d}(1/k\lambda )$ and $\widehat{d}(1/kR)$ for the Yukawa-like and PL models, respectively, at $a=1$ for a $\Lambda$CDM cosmological model (${\Omega }_m=0.27$ and ${\Omega }_{\Lambda }=0.73$).

Figure 2

Results from the first (Yukawa-like) model. Left: Likelihood as a function of $\alpha$ and $\lambda$ using data up to $k\sim 0.15\mathrm{h}/\mathrm{Mpc}$ using 2dF data. Contours denote one sigma marginalized (solid line), one sigma joint (dashed line), and two sigma joint (dashed-dotted line). Middle: Chi square as function of $\alpha$, marginalized over $\lambda$, using data up to $k\sim 0.15$. Right: Values of $\alpha$ corresponding to the maximum chi square with error bars denoting one sigma, as a function of the maximum $k$ included in the analysis.

Figure 3

Results from the PL model. Left: Likelihood as a function of $ϵ$ and $R$ using data up to $k\sim 0.15\mathrm{h}/\mathrm{Mpc}$ using SDSS data. Inner contours denote one sigma marginalized ($\sim \Delta {\chi }^2=1$ solid line), bottom contour denotes one sigma joint ($\sim \Delta {\chi }^2=2.3$ dashed line). Right: Chi square as function of $ϵ$, marginalized over $R$, using data up to $k\sim 0.15$.