Cold Dark Matter and Dark Energy Based on an Analogy with Superconductivity

TL;DR

The paper develops a Nambu–Jona-Lasinio–like framework with a chiral asymmetry that forms fermion Cooper pairs, yielding a cold dark matter candidate via a second-order phase transition to a massive condensate. The approach uses Hubbard–Stratonovich fields and finite-temperature field theory to derive an effective potential, a thermal history with a rapid κ-dominated epoch, and a low-energy dispersion that suppresses dark-matter velocities on cosmological scales. A parallel massive-fermion branch provides a metastable vacuum that can mimic dark energy with a slowly evolving equation of state wΔ evolving from 1/3 to 1 and finally toward −1. The model makes distinctive predictions for the CMB and LSS, including a slightly faster CDM decay and a time-varying wΔ, and links the small scales set by the gap Δ0 to the observed dark energy density and baryon asymmetry through an exponential suppression mechanism.

Abstract

We present a novel candidate for cold dark matter consisting of condensed Cooper pairs in a theory of interacting fermions with broken chiral symmetry. Establishing the thermal history from the early radiation era to the present, the fermions are shown to behave like standard radiation at high temperatures, but then experience a critical era decaying faster than radiation, akin to freeze-out that sets the relic abundance. Through a second-order phase transition, fermion - antifermion pairs condense and the system asymptotes towards zero temperature and pressure. By the present era, the non-relativistic, massive condensate decays slightly faster than in the standard scenario -- a unique prediction that may be tested by combined measurements of the cosmic microwave background and large scale structure. We also show that in the case of massive fermions, the phase transition is frustrated, and freeze-out instead leaves a residual, long-lived

Figures (6)

• Figure 1: Effective potential $V(\Delta,T)$ versus $\Delta$ for the massless theory at $T=2 T_c$ (blue), $T=T_c$ (black, dashed), and $T=0$ (red). The parameters are $(\kappa,\,\Lambda_{UV},\,M)=(0.56, 1.1, 1.2)$ TeV, for the cold dark matter scenario. For illustrative purposes, the $T\neq 0$ curves have been artificially shifted vertically to match the $T=0$ curve at $\Delta=0$.
• Figure 2: Finite temperature corrections to the zero temperature $\xi_{00}$. Corrections are exponentially suppressed for large $\Delta_0/T$. Fitted by $e^{-x}x^2\ln(x)$, where $x=\beta\Delta$.
• Figure 3: Cosmic energy density $\rho^{1/4}$ vs. redshift, $z$. Standard Model radiation (red), $\Delta$ field with $\Omega_{\rm CDM}=0.25$ (blue), cosmological constant dark energy with $\Omega_{\rm DE}=0.7$ (black dashed), and baryons with $\Omega_{\rm B}=0.05$ (black dotted). Same parameters for CDM are used as in Fig.(\ref{['fig:phase-transition']}). The proposed, metastable dark energy model is also shown (green, dot-dashed).
• Figure 4: Equation of state $w_\Delta$ versus redshift, $z$. There are four distinct eras: Radiation, $w_\Delta=1/3$; $\kappa$-domination, $w_\Delta = 1$; Phase Transition, at $z\sim 10^{12}$; Pressureless matter, at $z\lesssim 10^{12}$. Same parameters are used as in Fig.\ref{['fig:phase-transition']}.
• Figure 5: Effective Potential in the Massive Case. As before, $V(\Delta_{\rm min})=0$. Notice that $V(0)-V(\Delta_{\rm min})$ is tiny compared to the barrier height $10^{-6}$eV$^4$ and width $\sim 10^{-4}$eV, exponentially suppressing the tunneling probability to $\Delta_{\rm min}$.