From Cavendish to PLANCK: Constraining Newton’s gravitational constant with CMB temperature and polarization anisotropy

We present new constraints on cosmic variations of Newton’s gravitational constant by making use of the latest CMB data from WMAP, BOOMERANG, CBI and ACBAR experiments and independent constraints coming from big bang nucleosynthesis. We found that current CMB data provide constraints at the $\sim 10\%$ level, that can be improved to $\sim 3\%$ by including big bang nucleosynthesis data. We show that future data expected from the Planck satellite could constrain $G$ at the $\sim 1.5\%$ level while an ultimate, cosmic variance limited, CMB experiment could reach a precision of about 0.4%, competitive with current laboratory measurements.

Figure 1

Ionization fraction in function of redshift for different values of ${\lambda }_G$.

Figure 2

From Top to Bottom: Temperature, Polarization and cross Temperature-Polarization power spectra in function of variations in ${\lambda }_G$.

Figure 3

Temperature power spectrum when the gravitational constant varies such that ${\lambda }_G=0.9$. The graph shows the effects of the smooth transition parametrization described in Eq. (5) (green line) and of the Heaviside parametrization of Eq. (6) for different redshifts of transition $z_T$ between 0.1 and 2.

Figure 4

68% and 95% likelihood contour plots on the ${\lambda }_G$-$n_S$ plane using present CMB data with and without BBN constraints.

Figure 5

68% and 95% likelihood contour plots on the ${\lambda }_G$-${\omega }_b$ plane using present CMB data with and without BBN constraints.

Figure 6

68% and 95% likelihood contour plots on the ${\lambda }_G$-$z_T$ plane using present CMB data.

Figure 7

Dependence on variation from the fine structure constant $\alpha$ of the temperature anisotropy angular spectra.