Interacting dark sector from intrinsic entropy couplings

Abstract

We introduce a new class of interacting dark sector models that couple the intrinsic entropy of dark matter to scalar field dark energy. Using the Lagrangian formulation for relativistic perfect fluids, we construct consistent covariant actions that incorporate algebraic and derivative entropy couplings. These interactions leave the expansion history unchanged, rendering the background cosmology indistinguishable from $Λ$CDM or uncoupled quintessence. At the level of cosmological perturbations, the entropy couplings generate scale-dependent modifications to the dark matter Euler equation, while the continuity equation remains unaltered at linear order. The resulting interactions correspond to a pure-momentum exchange within the dark sector. We show that intrinsic entropy perturbations can carry primordial scale dependence, and non-minimal couplings can lead to a scale-dependent suppression or enhancement of structure growth. Finally, we demonstrate that these models are generically compatible with current Cosmic Microwave Background observations, while inducing distinctive signatures in large-scale structure. The framework provides a theoretically well-motivated and observationally viable extension to the standard cosmological model, opening new directions to explore novel interactions in the dark sector.

Figures (4)

• Figure 1: Comparison of the entropy-induced source terms entering the dark matter growth equation in the quasi-static limit, \ref{['eq:deltacpp']}, for the derivative coupling (left) and algebraic coupling (right), according to the definition in \ref{['eq:models']}. We show the Euler-source contribution $k^2|Q_s|$ (rose) and the effective density contribution $4\pi G a^2 |\Delta \rho_s|$ (green) for three representative modes, $k=10^{-4}h\,{\rm Mpc}^{-1}$ (solid), $k=10^{-2}h\,{\rm Mpc}^{-1}$ (dashed), and $k=10^{-1}h\,{\rm Mpc}^{-1}$ (dotted). The vertical lines mark horizon crossing, $k=aH$, for each mode. The effective density source is scale independent for most of the evolution, except for the largest scales ($k=10^{-4}h\,{\rm Mpc}^{-1}$) upon horizon entry.
• Figure 2: Relative deviations of the entropic-CDM perturbations and clustering amplitude with respect to $\Lambda$CDM and as a function of redshift $z$ for $k_8=0.125\,h\,{\rm Mpc}^{-1}$. The top and middle panels show the fractional changes in the dark matter density contrast $\delta_c$ and velocity divergence $\theta_c$, while the bottom panels show the relative change in $\sigma_8$. The entropy perturbation $\delta s$ is parameterised as in \ref{['eq:deltas_def']}. The left panels show the derivative coupling for different values of $h_0$, while the right panels depict the algebraic coupling with varying $g_0$, as defined in \ref{['eq:models']}. In both cases the effects remain negligible at early times and grow only at late times, when the entropy coupling becomes dynamically relevant. The largest deviations occur in $\theta_c$, reflecting the fact that the interaction enters directly through the Euler equation, \ref{['Eul1']}, while the impact on $\delta_c$ and $\sigma_8$ is induced indirectly through the changes to the $\theta_c$ and the metric potentials.
• Figure 3: Relative deviations in the matter power spectrum $P(k)$ (top panels), the CMB spectrum of temperature anisotropies $C_\ell^{TT}$ (middle panels), and the CMB lensing potential spectrum $C_\ell^{\phi\phi}$ (bottom panels), with respect to $\Lambda$CDM. The left panels show the derivative case and the right panels the algebraic case, as specified in \ref{['eq:models']}. The coupling parameters are varied as indicated in each panel, while the entropy perturbation $\delta s$ is defined according to \ref{['eq:deltas_def']}. The matter power spectrum exhibits the largest deviations, with the strongest departures on small scales driven by the entropy-induced source term in the dark matter Euler equation, while on large scales the deviations are associated with the modified evolution of the metric potentials. In contrast, the primary CMB temperature spectrum is only very weakly affected, with visible changes mainly confined to the low-multipole late integrated Sachs-Wolfe regime. The CMB lensing potential exhibits small departures arising from the line-of-sight integration of the late-time modifications of the metric potentials, effectively probing the effects of the entropy coupling.
• Figure 4: Early-time scaling of the numerical solutions for $\delta_c$, $\theta_c$, $\delta\phi$, and $\delta\phi'$ at $k=10^{-4}\,\mathrm{Mpc}^{-1}$. All quantities are normalised to their expected leading-order super-horizon adiabatic initial conditions, showing agreement with the analytic expansion derived in \ref{['sec:initial']}. The entropy perturbation $\delta s$ is parameterised as in \ref{['eq:deltas_def']}. The left panel corresponds to the derivative case with $h_0=0.01$, and the right panel to the algebraic case with $g_0=0.001$, as defined in \ref{['eq:models']}.