Precision gravity constraints on large dark sectors

A bstract General relativity, treated as a low-energy effective field theory, predicts quantum corrections to Newton’s law of gravitation arising from loops of matter and graviton fields. While these corrections are utterly negligible for the Standard Model particle content, the situation changes dramatically in the presence of a hidden or dark sector containing a very large number of light degrees of freedom. In such cases, loop-induced modifications to the Newtonian potential can accumulate to levels testable in laboratory and astrophysical probes of gravity at short distances. In this work we systematically derive and constrain the impact of large dark sectors on precision tests of Newton’s law, translating effective-field-theory predictions into the experimental language of Yukawa-type deviations and inverse-square-law deformations. By mapping precision fifth-force constraints onto bounds on species multiplicities and masses, we show that current and forthcoming experiments already impose nontrivial constraints on the size and structure of hidden sectors coupled only gravitationally. For truly massless hidden states, present data still permit multiplicities as large as $$ \mathcal{O}\left({10}^{61}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>61</mml:mn> </mml:msup> </mml:mfenced> </mml:math> , with modest spin dependence; for finite masses the constraints reduce to the familiar short-range Yukawa parameterization. Our results provide a model-independent framework for confronting dark-sector scenarios with precision gravity data and clarify how non-minimal scalar couplings, potential higher-derivative poles at large species number, and Kaluza-Klein towers fit within this picture. The approach is complementary to cosmological probes: Big Bang Nucleosynthesis and the Cosmic Microwave Background constrain relic abundances under specified production histories, whereas laboratory tests constrain the spectrum of light states irrespective of their cosmological population.