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

TL;DR

This work tests potential deviations from the gravitational inverse-square law on megaparsec scales by modeling two perturbations to gravity — a Yukawa-like term and a power-law-like term — and evolving the matter power spectrum within linear and mildly non-linear regimes. Using a ΛCDM background and marginalizing over the power-spectrum amplitude and primordial slope, the authors compare predictions to SDSS and 2dFGRS measurements of the present-day power spectrum. They also derive the corresponding bispectrum corrections, though a full bispectrum analysis is deferred to future work. The results show no evidence for deviations from Newtonian gravity on the scales probed ($\sim 10^{23}$ m), placing constraints on $\alpha$ and $\epsilon$ that are statistically consistent with zero; the study also highlights how future weak-lensing data could further tighten these bounds.

Abstract

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 (~ 10^(23) m.)

Figures (3)

• Figure 1: $\hat{d}(\frac{1}{k \lambda})$ and $\hat{d}(\frac{1}{k R})$ 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 $k \sim 0.15$ h/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 $\epsilon$ and $R$ using data up to $k \sim 0.15$ h/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 $\epsilon$, marginalized over $R$, using data up to $k \sim 0.15$.