Leading bounds on micro- to picometer fifth forces from neutron star cooling

The equivalence principle and the inverse-square law of gravity could be violated at short distances ($10^{-6}$ to $10^{-12}$ meters) by scalars sporting a coupling $g_N$ to nucleons and mass $\mathrm{eV}\lesssim m_\phi\lesssim\rm MeV$. We show for the first time that stringent bounds on the existence of these scalars can be derived from the observed cooling of nearby isolated neutron stars (NSs). Although NSs can only be used to set limits comparable to the classic SN 1987A cooling bound in the case of pseudoscalars such as the QCD axion, the shallow temperature dependence of the scalar emissivity results in a huge enhancement in the effect of $\phi$ on the cooling of cold NSs. As we do not find evidence of exotic energy losses, we can exclude couplings down to $g_N\lesssim 5 \times 10^{-14}$. Our new bound supersedes all existing limits on scalars across six orders of magnitude in $m_\phi$. These conclusions also extend to Higgs-portal models, for which the bound on the scalar-Higgs mixing angle is $\sin\theta\lesssim 6\times 10^{-11}$.