Dark forces suppress structure growth

TL;DR

The paper investigates whether a scalar-mediated long-range force in the dark sector can enhance cosmic structure growth. Using a kinetic-theory framework with a linearly coupled, massless mediator, it shows that absolute density perturbations do not grow faster than in ΛCDM because background evolution cancels the enhanced clustering, and primary CMB measurements tightly constrain early DM density, leading to a suppressed late-time growth when θs is fixed. It then analyzes predictions for low-redshift observables, finding that CMB calibration drives a net suppression of lensing and distances, and discusses how nonminimal models might reverse this trend, though nonlinear modeling would be required to test such scenarios. The results clarify the interplay between expansion history and structure formation in dark-force models, constrain interpretations of neutrino-mass limits, and highlight the need for nonlinear developments to explore any potential structure-enhancing extensions.

Abstract

No experimental test precludes the possibility that the dark matter experiences forces beyond general relativity -- in fact, a variety of cosmic microwave background observations suggest greater late-time structure than predicted in the standard $Λ$ cold dark matter model. We show that minimal models of scalar-mediated forces between dark matter particles do not enhance the growth of unbiased tracers of structure: weak lensing observables depend on the total density perturbation, for which the enhanced growth of the density contrast in the matter era is cancelled by the more rapid dilution of the background dark matter density. Moreover, the same background-level effects imply that scenarios compatible with CMB temperature and polarization anisotropies in fact suppress structure growth, as fixing the distance to last scattering requires a substantially increased density of dark energy. Though massive mediators undo these effects upon oscillating, they suppress structure even further because their gravitational impact as nonclustering subcomponents of matter outweighs the enhanced clustering strength of dark matter. We support these findings with analytic insight that clarifies the physical impact of dark forces and explains how primary CMB measurements calibrate the model's predictions for low-redshift observables. We discuss implications for neutrino mass limits and other cosmological anomalies, and we also consider how nonminimal extensions of the model might be engineered to enhance structure.

Figures (12)

• Figure 1: Sensitivity of the growth rate $\mathrm{d} \ln X / \mathrm{d} \ln a$ to the strength of a long-range force acting on dark matter, with $X$ the density contrast $\delta_{\chi b}$ (left) or the total density perturbation $\delta \rho_{\chi b}$ (right) in baryons and dark matter. The sensitivity is quoted as the response coefficient multiplying $\beta f_\chi^2$, the combination of the LRF strength relative to gravity, $\beta = \left( \partial \ln m_\chi / \partial \varphi \right)^2$, and the dark matter fraction, $f_\chi$, that parametrizes the effects; it is computed via the relative difference for $k = 10~\mathrm{Mpc}^{-1}$ modes between a cosmology with a force strength relative to gravity of $\beta = 10^{-2}$ and $\Lambda$CDM divided by $\beta f_\chi^2$. Horizontal lines mark the analytic, matter-era results eqn:delta-growth-rate, eqn:Phi-growth-rate; the vertical line marks matter-radiation equality. The results labeled "background/perturbations only" isolate the LRF effects in the equations of motion for the background and linear perturbations as described in the main body; all effects combine to yield zero net sensitivity of $\delta \rho_{\chi b}$ (and therefore of metric potentials) to the LRF in matter domination. Inset panels enlarge the matter-era dynamics. Dashed and solid lines respectively fix the dark energy density to zero (to better illustrate the effects in a pure-matter Universe) and the angular extent of the photon sound horizon at last scattering $\theta_s$; the latter incurs a strong suppression of the growth rate that is explained in sec:suppression.
• Figure 2: Sensitivity of unlensed CMB temperature (left) and polarization (right) anisotropies to a scalar-mediated long-range force acting on dark matter, fixing the early-time dark matter density $\omega_\chi(a \to 0)$ and angular size of the sound horizon $\theta_s$. Each panel depicts the relative residual between a cosmology with a force strength relative to gravity of $\beta = 10^{-2}$ and $\Lambda$CDM divided by $\beta f_\chi^2$, i.e., an approximation to $\partial \ln C_\ell / \partial \ln (1 + \beta f_\chi^2)$. For comparison, transparent, dashed lines depict the sensitivity of the the amplitude of dark matter density perturbations, evaluated at peak visibility ($a_\star$) and at the comoving scales $k = \ell / D_{M, \star}$ that predominantly contribute to each $\ell$. Each panel depicts results that consistently implement the model (black) and artificially disable the mediator's impact on the evolution of the dark matter's background (red) or perturbations (blue), following fig:growth-deviation. As elaborated in the main text, these results evidence the gravitational decoupling of plasma and dark-matter perturbations on small scales $500 \lesssim \ell \lesssim 5000$; the dark force therefore only impacts the generation of small-scale anisotropies at last scattering via the expansion history, largely by modifying diffusion damping (see fig:cmb-sensitivity-undamped).
• Figure 3: Calibration of the dark matter density near last scattering by CMB temperature and polarization data. Under a massless, linearly coupled mediator, dark matter begins redshifting faster than CDM around matter-radiation equality. Since the shape of the temperature and polarization spectra are most sensitive to the background evolution of dark matter in the epoch leading up to when CMB photons last scatter (vertical grey band), CMB data most strongly constrain the dark matter abundance at this time (top panel). Indeed, the dark matter matter abundance shortly before recombination is constrained with the same precision as is standard CDM (thin horizontal lines). Moreover, its correlation coefficient with the long-range force strength $\beta$ (bottom panel) vanishes at the same moment.
• Figure 4: Sensitivity of lensed CMB temperature anisotropies (left) and the CMB lensing spectrum (right) to a scalar-mediated long-range force acting on dark matter, measured as described in fig:cmb-sensitivity. The inset panel displays the impact of the ISW effect for lower multipoles on different axes scales. All results fix the angular size of the sound horizon $\theta_s$ and either the dark matter density at last scattering (opaque lines), as motivated by fig:early-calibration, or the early-time dark matter density $\omega_\chi(a \to 0)$ (transparent lines), for comparison with fig:cmb-sensitivity. Lensing is suppressed on all observationally relevant scales in the latter case; the CMB's calibration of $\omega_\mathrm{DM}(a_\mathrm{CMB})$ alters the shape of the transfer function such that small-scale lensing is marginally enhanced by $< 2 \beta f_\chi^2$, deriving from changes to the background evolution. These scales are not those for which current data exhibit an excess and are also nonnegligibly impacted by nonlinear structure formation (not accounted for here given its lack of study under additional long-range forces); see fig:lensing-spaghetti. Like fig:cmb-sensitivity, red, blue, and black lines respectively depict results when modifying the dynamics of perturbations, the background, or both, demonstrating the substantial cancellation between the two effects.
• Figure 5: Residuals of the CMB lensing convergence relative to the $\Lambda$CDM best fit (to all Planck PR3 temperature and polarization data) for samples from posteriors for $\Lambda$CDM (left) and for the dark force model (middle and right), each calibrated to PR3 temperature data at $\ell \leq 1000$ and polarization and the cross spectrum at $\ell \leq 600$. This subset is essentially insensitive to lensing; the comparison to the best fit to all PR3 data indicates the degree to which each model, calibrated to the unlensed CMB, underpredicts the lensing amplitude preferred by the full dataset. Curves in the left and middle panels are colored by the comoving dark matter density at recombination, $a_\mathrm{CMB}^3 \omega_\mathrm{DM}(a_\mathrm{CMB})$, which reduces to $\omega_c$ in $\Lambda$CDM; the right panel colors by the LRF strength relative to gravity, $\beta$. Joint CMB lensing reconstruction data (which are not included in the fits) are displayed in red Carron:2022eygACT:2023douACT:2023douSPT-3G:2024atgSPT-3G:2025zuh. Solid black lines show the residual for the reference $\Lambda$CDM cosmology when modeling nonlinear structure growth, which indicates the error made by neglecting it (i.e., because we presently lack a nonlinear model that accounts for the dark force).