Constraining a possible time variation of the gravitational constantGwith terrestrial nuclear laboratory data

Abstract

Testing the constancy of the gravitational constant $G$ is a longstanding fundamental question in natural science. As first suggested by Jofr\'e, Reisenegger, and Fern\'andez (2006, Phys. Rev. Lett. 97, 131102), Dirac's hypothesis of a decreasing gravitational constant $G$ with time caused by the expansion of the Universe would induce changes in the composition of neutron stars, causing dissipation and internal heating. Eventually, neutron stars reach their quasistationary states where cooling, as a result of neutrino and photon emissions, balances the internal heating. The correlation of surface temperatures and radii of some old neutron stars may thus carry useful information about the rate of change of $G$. Using the density dependence of the nuclear symmetry energy, constrained by recent terrestrial laboratory data on isospin diffusion in heavy-ion reactions at intermediate energies, and the size of neutron skin in $^{208}\mathrm{Pb}$, within the gravitochemical heating formalism developed by Jofr\'e et al. (2006, Phys. Rev. Lett. 97, 131102), we obtain an upper limit for the relative time variation $|\stackrel{\ifmmode\cdot\else\textperiodcentered\fi{}}{G}/G|$ in the range ($4.5\text{\ensuremath{-}}21)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ yr${}^{\ensuremath{-}1}$.