Unveiling dark fifth forces with linear cosmology

TL;DR

This work investigates dark fifth forces acting exclusively on Dark Matter, introducing a light scalar mediator with $m_\varphi \lesssim H_0$ that induces an effective Equivalence Principle violation on cosmological scales. The authors develop a comprehensive framework linking particle-level interactions to fluid and field descriptions, and they analyze both the background evolution and linear perturbations in two scenarios: a pure fifth-force (5F) and a coupled dark energy (CDE) case. They derive and solve the modified cosmological equations, showing that even a small $\beta$ can produce measurable effects on DM growth and DM–baryon relative perturbations, with distinctive imprints on the CMB and the matter power spectrum. By performing MCMC fits to Planck CMB and BAO data, they obtain the strongest cosmological bounds to date on the dark fifth-force coupling ($\beta \lesssim 0.005$–$0.01$ depending on the scenario), and discuss implications for the Hubble tension and possible connections to visible-sector EP tests. The results demonstrate that linear cosmology is a powerful probe of long-range DM interactions and lay the groundwork for exploring nonlinear effects and broader mediator models.

Abstract

We initiate the exploration of the cosmology of dark fifth forces: new forces acting solely on Dark Matter. We focus on long range interactions which lead to an effective violation of the Equivalence Principle on cosmological scales today. At the microscopic level, the dark fifth force can be realized by a light scalar with mass smaller than the Hubble constant today ($\lesssim 10^{-33}\,\text{eV}$) coupled to Dark Matter. We study the behavior of the background cosmology and linear perturbations in such a Universe. At the background level, the new force modifies the evolution of the Dark Matter energy density and thus the Hubble flow. At linear order, it modifies the growth of matter perturbations and generates relative density and velocity perturbations between Dark Matter and baryons that grow over time. We derive constraints from current CMB and BAO data, bounding the strength of the dark fifth force to be less than a percent of gravity. These are the strongest constraints to date. We present potential implications of this scenario for the Hubble tension and discuss how our results are modified if the light scalar mediator accounts for the observed density of the Dark Energy. Finally, we comment on the interplay between our constraints and searches for violations of the Equivalence Principle in the visible sector.

Figures (15)

• Figure 1: (Left) The time evolution of $\bar{s}$ in a pure 5th force scenario, assuming $\beta = 0.005$. In the analytical solution for the MD epoch, Eq. \ref{['eq:s_MD']}, we have set $\bar{s}_{\rm eq} = \bar{s}_{\rm ini}\,$. (Right) The same as in the left panel, but now assuming $s$ is a Coupled Dark Energy field. The vertical dot-dashed line corresponds to the redshift at which the $s$ equation of state parameter crosses zero as it transitions from $w_s = +1$ to $w_s = -1$, derived analytically in Eq. \ref{['eq:crossing']}.
• Figure 2: (Left) In the top panel, the time evolution of the energy density of the different species in a pure 5th force scenario, assuming $\beta = 0.005$. The bottom panel shows the fractional contributions. For the scalar field $s$, the light orange dotted line shows the analytical estimate of $\bar{\rho}_s/\bar{\rho}_{\rm tot}$ during early MD, as found in Eq. \ref{['eq:rhos_MD']}. In both panels, light orange dashed curves show the scalar field evolution starting from initial values of $\bar{s}'$ different from the natural expectation determined by Eq. \ref{['eq:s_RD']}: from bottom to top, $\bar{s}^\prime_{\rm ini} = \{0, 10^2, 10^4\} (\bar{s}_{\rm ini}^\prime)_{\rm natural}\,$. (Right) The same as in the left panels, but now assuming $s$ is a Coupled Dark Energy field.
• Figure 3: Same as Fig. \ref{['fig:s_bkg_beta0p005']}, but for $\beta = 0.02$.
• Figure 4: Same as Fig. \ref{['fig:rho_bkg_beta0p005']}, but for $\beta = 0.02$.
• Figure 5: (Left) From top to bottom: Hubble normalized to $\Lambda$CDM, equation of state parameter for the 5th force field, DM density $\omega_\chi$ normalized to CDM, and comoving distance normalized to $\Lambda$CDM, for $\beta = 0.005$. We focus on the time evolution from matter-radiation equality onwards. Dashed and dot-dashed lines correspond to analytical approximations discussed in the text. (Right) Same as in the left panels, but for $\beta = 0.02$.