Adiabatic instability in coupled dark energy-dark matter models

Abstract

We consider theories in which there exists a nontrivial coupling between the dark matter sector and the sector responsible for the acceleration of the universe. Such theories can possess an adiabatic regime in which the quintessence field always sits at the minimum of its effective potential, which is set by the local dark matter density. We show that if the coupling strength is much larger than gravitational, then the adiabatic regime is always subject to an instability. The instability, which can also be thought of as a type of Jeans instability, is characterized by a negative sound speed squared of an effective coupled dark matter/dark energy fluid, and results in the exponential growth of small scale modes. We discuss the role of the instability in specific coupled CDM and Mass Varying Neutrino (MaVaN) models of dark energy, and clarify for these theories the regimes in which the instability can be evaded due to non-adiabaticity or weak coupling.

Figures (2)

• Figure 1: [Bottom] The two component coupled dark energy (CDE) model, with exponential potential and coupling, with $\lambda =2$ and coupling $C=-20$ with $H_0=70 \, {\rm km} \, {\rm s}^{-1}\, {\rm Mpc}^{-1}$, $\Omega_{b}=0.05$, $\Omega_{c}=0.2$, $\Omega_{co}=0.05$, and $\Omega_{V}=0.70$. At late times the scalar field finds the adiabatic minimum with asymptotic equation of state, and sound speed $= -1/(1+\gamma) = -0.89$, able to reproduce a viable background evolution consistent with supernovae, CMB angular diameter distance and BBN expansion history constraints. The figure shows the evolution of the effective equation of state, $w_{eff} = P_{tot}/\rho_{tot}=(2/3) (d\ln t / d\ln a) -1,$ (black full line), the adiabatic speed of sound, $c_{a}^{2}=\dot{P}/\dot{\rho}$ for all components (blue long dashed line) and for the coupled components only (green dot long dashed line), and effective speed of sound for $c_s^2=\delta P/\delta\rho$ at $k=0.01/Mpc$ for all components (red dot-dashed line) and for the coupled components alone (magenta dotted line). The effective equation of state for a comparable $\Lambda$CDM model with $\Omega_{c}=0.25$, $\Omega_b=0.05$ and $\Omega_{\Lambda}=0.7$ is also shown (black dashed line). [Top] The growth of the fractional over-density $\delta=\delta\rho/\rho$ for $k=0.01/Mpc$ for the coupled CDM component, $\delta_{co}$, (red long dashed line) and uncoupled component, $\delta_{c}$, (black full line) in comparison to the growth for the $\Lambda$CDM model (black dashed line). At late times the adiabatic behavior triggers a dramatic increase in the rate of growth of both uncoupled and coupled components, leading to structure predictions inconsistent with observations.
• Figure 2: [Top panels] Evolution of $m_\nu(\phi)$ and neutrino temperature (left), and associated equation of state and adiabatic sound speed (right) for MaVaN model described in the text with $m_{\nu 0}=0.312eV$ and $\phi_*=1.8m_{\rm p}$. [Bottom left panel] Scalar field evolution in the MaVaN scenario, for 3 values of $\phi_*\sim 10^{-3}m_{\rm p}$, $0.3m_{\rm p}$ and $1.8m_{\rm p}$ (full lines) showing the $\tau^{0.5}$ attractor while the neutrino is relativistic allowing late time evolution to be independent of initial conditions. The vacuum expectation value of the scalar field, if the field becomes adiabatic, (dashed lines) is also shown. For $\phi_* \gtrsim 10^{-2}m_{\rm p}$ the scalar field does not enter an adiabatic era on cosmological scales before now, and growth of perturbations remains well-behaved. For smaller $\phi_*$, for example $\phi_*\sim 10^{-3}m_{\rm p}$ shown, the evolution is adiabatic at late times, similar to that discussed in Bjaelde:2007ki. [Bottom right panel] The resulting matter power spectrum from the coupled dark energy (CDE) model with $\phi_* = 1.8m_{\rm p}$ and $\Omega_\nu=0.02$ (full line) is very similar to that for $\Lambda$CDM (dashed line) with the same baryon fraction and $H_0$, $\Omega_m=0.3$, $\Omega_\nu=0.02$ when normalized at large scales.