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Dark Matter with Time-Dependent Mass

Greg W. Anderson, Sean M. Carroll

TL;DR

The paper addresses the age discrepancy in flat CDM by introducing dark matter whose rest mass grows with the scale factor, realized through m_ψ = λ ⟨φ⟩ with a density-dependent potential U(φ). The coupled φ–ψ system yields an effective potential V(φ)=u_0 φ^{−p}+λ n_ψ φ, leading to ⟨φ⟩=(p u_0 /(λ n_ψ))^{1/(1+p)} and an energy component ρ_V that scales as ρ_V ∝ a^{−3p/(1+p)} with equation of state w=−1/(1+p); thus ρ_V redshifts more slowly than ordinary matter (ρ_M ∝ a^{−3}). Consequently, the total energy density evolves to yield an older universe, with t0 ≈ (2/3)H0^{−1}(1+1/p) in the Ω_M0=0 limit; a minimal realization with p=1 and Ω_V0 ≈ 0.96 predicts vamp equality at z_{VM} ≈ 7 and t0 ≈ 17 Gyr for H0 ≈ 70 km s^{−1} Mpc^{−1}. The authors discuss observational tests (SNe Ia, lensing, CMB) and the impact on perturbation growth, highlighting competing effects: a negative-pressure drive that enhances growth and ψ free streaming that damps it, necessitating detailed Boltzmann treatment. They also consider possible particle-physics origins for φ and constraints from variations of Standard Model parameters.

Abstract

We propose a simple model in which the cosmological dark matter consists of particles whose mass increases with the scale factor of the universe. The particle mass is generated by the expectation value of a scalar field which does not have a stable vacuum state, but which is effectively stabilized by the rest energy of the ambient particles. As the universe expands, the density of particles decreases, leading to an increase in the vacuum expectation value of the scalar (and hence the mass of the particle). The energy density of the coupled system of variable-mass particles (``vamps'') redshifts more slowly than that of ordinary matter. Consequently, the age of the universe is larger than in conventional scenarios.

Dark Matter with Time-Dependent Mass

TL;DR

The paper addresses the age discrepancy in flat CDM by introducing dark matter whose rest mass grows with the scale factor, realized through m_ψ = λ ⟨φ⟩ with a density-dependent potential U(φ). The coupled φ–ψ system yields an effective potential V(φ)=u_0 φ^{−p}+λ n_ψ φ, leading to ⟨φ⟩=(p u_0 /(λ n_ψ))^{1/(1+p)} and an energy component ρ_V that scales as ρ_V ∝ a^{−3p/(1+p)} with equation of state w=−1/(1+p); thus ρ_V redshifts more slowly than ordinary matter (ρ_M ∝ a^{−3}). Consequently, the total energy density evolves to yield an older universe, with t0 ≈ (2/3)H0^{−1}(1+1/p) in the Ω_M0=0 limit; a minimal realization with p=1 and Ω_V0 ≈ 0.96 predicts vamp equality at z_{VM} ≈ 7 and t0 ≈ 17 Gyr for H0 ≈ 70 km s^{−1} Mpc^{−1}. The authors discuss observational tests (SNe Ia, lensing, CMB) and the impact on perturbation growth, highlighting competing effects: a negative-pressure drive that enhances growth and ψ free streaming that damps it, necessitating detailed Boltzmann treatment. They also consider possible particle-physics origins for φ and constraints from variations of Standard Model parameters.

Abstract

We propose a simple model in which the cosmological dark matter consists of particles whose mass increases with the scale factor of the universe. The particle mass is generated by the expectation value of a scalar field which does not have a stable vacuum state, but which is effectively stabilized by the rest energy of the ambient particles. As the universe expands, the density of particles decreases, leading to an increase in the vacuum expectation value of the scalar (and hence the mass of the particle). The energy density of the coupled system of variable-mass particles (``vamps'') redshifts more slowly than that of ordinary matter. Consequently, the age of the universe is larger than in conventional scenarios.

Paper Structure

This paper contains 4 sections, 30 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Scale factor and age of the universe
  3. Particle parameters and abundances
  4. Further consequences

Figures (2)

  • Figure 1: Effective potential for $\phi$. The light solid curve is the bare potential $U(\phi)\propto \phi^{-1}$. The effective potential at finite density, given by the solid curves, is obtained by adding a contribution linear in $\phi$ and proportional to the number density $n_\psi$. This is plotted for two different values of $n_\psi$, corresponding to two different stages in the evolution of the universe. As the universe expands, $n_\psi$ decreases, and the equilibrium value of $\phi$ increases.
  • Figure 2: Age of the universe in billions of years. The values in this plot are computed for flat universes consisting of only vamps and nonrelativistic matter, with $p=1$.