Cosmology with a Non-minimally Coupled Dark Matter Fluid I. Background Evolution

TL;DR

The paper investigates cosmology with a non-minimally coupled dark matter fluid, introducing a coupling term $ε L^2 G_{μν} T^{μν}_{DM}$ that modifies gravity while keeping the standard matter content. It derives the modified Friedmann and Raychaudhuri equations and shows that, at early times when $χ ≡ 8π G L^2 ρ_{DM} \ge 1$, the DM-curvature coupling drives an accelerated expansion that can address the horizon and flatness problems without introducing new fields, and that a cosmological bounce is possible for negative spatial curvature. The analysis reveals that standard ΛCDM is recovered at late times as $χ$ decays, with the fiducial length scale $L$ fixed to ensure subdominant DM interactions relative to SM forces. The work also notes caveats regarding perturbations and the validity of the fluid description in the high-energy regime, indicating that a full perturbative analysis is needed and will be presented in a follow-up study. The proposed NMC-DM framework offers a potential unified approach to tackling early-universe singularities and fine-tuning while remaining compatible with current observations at late times.

Abstract

We explore a cosmological model in which dark matter is non-minimally coupled to gravity at the fluid level. While typically subdominant compared to Standard Model forces, such couplings may dominate dark matter dynamics. We show that this interaction modifies the early-time Friedmann equations, driving a phase of accelerated expansion that can resolve the horizon and flatness problems without introducing additional fields. At even earlier times, the coupling to spatial curvature may give rise to a cosmological bounce, replacing the initial singularity of standard cosmology. These results suggest that non-minimally coupled dark matter could offer a unified framework for addressing both the singularity and fine-tuning problems.

Figures (3)

• Figure 1: Evolution of the density parameters as a function of redshift $1+z \equiv a^{-1}$. Solid lines represent the solution in the present non-minimal coupling model, while the dotted lines show the corresponding ones in the $\Lambda \rm CDM$ model. The vertical dotted grey lines represent matter-radiation equality at $\log\left(1+z_{\rm eq}\right) \simeq 3.54$, the onset of the NMC at redshift $\log\left(1+z_{\rm NMC}\right)\simeq 11.08$, and the beginning of the curvature era (or the redshift of the bounce), at redshift $\log\left(1+z_{k}\right) \simeq 32.20$.
• Figure 2: The dynamical state parameter $w$ as a function of redshift. The solid, dashed and dotted-dashed lines are the behavior in the presence of NMC with negative, null, or positive curvature respectively, while the dotted line is the one in $\Lambda$CDM. The vertical dotted grey lines represent matter-radiation equality at $\log\left(1+z_{\rm eq}\right) \simeq 3.54$, the onset of the NMC at redshift $\log\left(1+z_{\rm NMC}\right)\simeq 11.08$, and the beginning of the curvature era (or the redshift of the bounce), at redshift $\log\left(1+z_{k}\right) \simeq 32.20$.
• Figure 3: The comoving Hubble horizon as a function of redshift. The solid, dashed and dotted-dashed lines are the behavior in the presence of NMC with negative, null, or positive curvature respectively, while the dotted line is the one in $\Lambda$CDM. The vertical dotted grey lines represent matter-radiation equality at $\log\left(1+z_{\rm eq}\right) \simeq 3.54$, the onset of the NMC at redshift $\log\left(1+z_{\rm NMC}\right)\simeq 11.08$, and the beginning of the curvature era (or the redshift of the bounce), at redshift $\log\left(1+z_{k}\right) \simeq 32.20$. The horizontal dashed line shows the value of the horizon at the epoch of recombination at $\log\left(1+z_{\rm CMB}\right) \simeq 3.04$. The line further intersects the horizon at $\log\left(1+z_{\rm end}\right) \simeq 26.36$.