Cosmological constraints on Newton’s constant

We present cosmological constraints on deviations of Newton’s constant at large scales without specifying a model, analyzing latest cosmic microwave background (CMB) anisotropies and primordial abundances of light elements synthesized by big bang nucleosynthesis (BBN). BBN limits the possible deviation at typical scales of BBN epoch, say at ${10}^8–{10}^{12}\mathrm{m}$, to lie between $-5\%$ and $+1\%$ of the experimental value, and CMB restricts the deviation at larger scales ${10}^2–{10}^9\mathrm{pc}$ to be between $-26\%$ and $+66\%$ at the $2\sigma$ confidence level. The cosmological constraints are compared with the astronomical one from the evolution of isochrone of globular clusters.

Figure 1

Predicted BBN light-element abundances vs the baryon-to-photon ratio ${\eta }_{10}$. ${}^4\mathrm{He}$, D, and ${}^7\mathrm{Li}$ abundances are shown in the top, center, and bottom panels, respectively. They are compared with the observationally inferred primordial abundances (horizontal lines). Plotted are models with $\xi =1.01$ (solid lines) and $\xi =0.95$ (dashed lines). In our analysis, neutron lifetime is taken to be the average value of ${\tau }_n=878.5\sec$ [27] and ${\tau }_n=885.7\sec$ [29].

Figure 2

Constraints from the primordial abundances (lines) and CMB (contours) on ${\eta }_{10}$ and $\xi$. The shaded region denotes parameters allowed by BBN. The contours show the marginalized $1,2\sigma$ limits on this parameter plane from fits to the CMB power spectrum. The solid and dashed contours correspond to the limits from WMAP data alone, and those from WMAP, CBI, and ACBAR data sets, respectively.

Figure 3

CMB power spectrum with and without the variation of $\xi$. Higher peaks are more severely damped as $\xi$ increases, while the height of the first peak is almost unchanged.

Figure 4

Marginalized probability distribution of $\xi$. The solid and dashed lines correspond to the probability distributions obtained by WMAP data alone and by WMAP, CBI, and ACBAR data sets, respectively.

Figure 5

Limits on the variation of $\xi$ from various observations. Limit from Sloan Digital Sky Survey is taken from 6.