Does dark matter fall in the same way as standard model particles? A direct constraint of Euler's equation with cosmological data

TL;DR

The paper addresses whether dark matter obeys Euler's equation at cosmological scales by directly testing for non-gravitational interactions that would modify dark matter infall. It derives a direct relation $1+\Gamma(z)=\frac{2\hat{f}(z)}{3\hat{J}(z)}\left(1-\frac{d\ln\mathcal{H}(z)}{d\ln(1+z)}-\frac{d\ln\hat{f}(z)}{d\ln(1+z)}\right)$ in the linear regime to infer the fifth-force strength $\Gamma(z)$ from measurements of the growth rate $\hat{f}$ and Weyl-potential evolution $\hat{J}$, using data from galaxy velocities and DES lensing. Current observations show consistency with $\Gamma=0$, with a constant-amplitude constraint $\Gamma=-0.07\pm0.14$ (i.e., $[-0.21,0.07]$ at 1$\sigma$) and, when $\Gamma\ge0$ enforced, upper limits $\Gamma\le0.11$ (68%) and $\le0.24$ (95%). Forecasts for DESI and LSST indicate substantially improved sensitivity, potentially detecting departures at the $3-6\%$ level per redshift bin or constraining a constant $\Gamma$ to about $2\%$, thereby delivering a powerful, model-independent probe of non-gravitational dark matter interactions. The approach remains valid as long as general relativity holds and can be extended to test scale- and time-dependence with future data, including direct measurements of the time distortion $\Psi$.

Abstract

Since dark matter particles have never been directly detected, we do not know how they move, and in particular we do not know how they fall inside gravitational potential wells. Usually it is assumed that dark matter only interacts gravitationally with itself and with particles of the standard model, and therefore that its motion is governed by Euler's equation. In this paper, we test this assumption for the first time at cosmological scales, by combining measurements of galaxy velocities with measurements of gravitational potential wells, encoded in the Weyl potential. We find that current data are consistent with Euler's equation at redshifts $z\in [0.3,0.8]$, and we place constraints on the strength of a potential fifth force, which would alter the way dark matter particles fall. We find that a positive fifth force cannot exceed 7% of the gravitational interaction strength, while a negative fifth force is limited to 21%. The coming generation of surveys, including the Legacy Survey of Space and Time (LSST) of the Vera C. Rubin Observatory and the Dark Energy Spectroscopic Instrument (DESI) will drastically improve the constraints, allowing to constrain a departure from pure gravitational interaction at the level of 2%.

Figures (4)

• Figure 1: Left panel: The 22 measured data points of $\hat{f}$, from Table 1 of Ref. Grimm:2024fui (black points) and their spline reconstruction with 1$\sigma$ uncertainty (blue band), leading to the values of $\hat{f}$ at the four MagLim effective redshifts (red points). Right panel: Reconstruction of $\mathrm d \ln f(z)/\mathrm d\ln(1+z)$ based on the spline interpolation of $\hat{f}$. For both panels, the prediction assuming no fifth force and cosmological parameters from Planck Planck:2018vyg is shown as well (black line), being in agreement with the reconstruction at the $1\sigma$ level.
• Figure 2: We show the reconstructed values (in red) of the fifth force parameter $\Gamma$ together with the 1$\sigma$ uncertainties at the four effective redshifts of the DES MagLim sample. The measurements show no deviation from Euler's equation ($\Gamma=0$, black horizontal line). The green line with error bands shows the best-fit value and $1\sigma$ uncertainty assuming a constant value of $\Gamma$. We note that the measurements at different redshifts are correlated, as can be seen from the covariance matrix given in Appendix \ref{['app:convariance']}.
• Figure 3: Left panel: We show 17 values for $\hat{f}$ centered around the $\Lambda$CDM fiducial (black dots) and with 1$\sigma$ uncertainties achievable by DESI covering 14,000 square degrees (see Tables 2.3 and 2.5 of DESI:2016fyo). We also show the spline reconstruction (blue band), leading to the values of $\hat{f}$ at the nine effective redshifts of LSST (red dots). Right panel: Reconstruction of $\mathrm d \ln\hat{f(z)}/\mathrm d\ln(1+z)$ based on the spline interpolation of $\hat{f}$. For both panels, the prediction without a fifth force is shown as well (black line).
• Figure 4: Using forecast values of $\hat{f}$ from DESI DESI:2016fyo, we show the reconstructed values (in red) of the fifth force parameter $\Gamma$ together with the 1$\sigma$ uncertainties at the nine effective redshifts corresponding to the LSST forecast for $\hat{J}$Tutusaus:2022cab. Additionally, the blue band shows a forecast over the whole redshift range when interpolating the $\hat{J}$ data as well.