Minimal targets for dilaton direct detection

Fifth force and equivalence principle tests search for new interactions by precisely measuring forces between macroscopic collections of atoms and molecules and their properties under free fall. In contrast, the early Universe plasma probes these interactions at a more fundamental level. In this paper, we consider the case of a scalar mediating a fifth force, and show that the effects of dimensional transmutation, spontaneous symmetry breaking, and the running of the gauge couplings cause the scalar's low-energy interactions to mix, leading to nearly universal dynamics at early times. We use known expressions for the pressure of the Standard Model during its various epochs to compute the scalar effective potential, and find that the cosmological dynamics of this scalar are very sensitive to the reheat temperature of the Universe. Given the unknown reheat temperature, we show that scalar couplings to matter larger than $\sim 10^{-6}(m_\phi/{\rm eV})^{-1/4}$ relative to gravity produce the correct dark matter abundance, motivating new physics searches in this part of parameter space.