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Supersymmetric Q-balls as dark matter

Alexander Kusenko, Mikhail Shaposhnikov

TL;DR

This paper shows that supersymmetric extensions of the Standard Model naturally host stable non-topological solitons called Q-balls, which carry baryon or lepton number. In flat potentials, Q-balls have $m_Q \sim Q^{3/4}$, so for sufficiently large charge the energy per unit charge drops below fermionic masses, making them effectively stable; B-balls with $Q \gtrsim 10^8$ can be entirely stable, while L-balls require $Q \gtrsim 10^{32}$ to survive. The authors demonstrate that large relic Q-balls can form in the early universe via instabilities of a scalar condensate and via solitosynthesis/mergers, with fragmentation potentially producing Q-balls of charges $Q \sim 10^{16}-10^{20}$ or larger. Surviving Q-balls could thus constitute dark matter and may also address the cosmological moduli problem by entrapping moduli inside slowly evaporating Q-balls, though observational prospects favor smaller, more abundant B-balls due to their higher expected number density.

Abstract

Supersymmetric extensions of the standard model generically contain stable non-topological solitons, Q-balls, which carry baryon or lepton number. We show that large Q-balls can be copiously produced in the early universe, can survive until the present time, and can contribute to dark matter.

Supersymmetric Q-balls as dark matter

TL;DR

This paper shows that supersymmetric extensions of the Standard Model naturally host stable non-topological solitons called Q-balls, which carry baryon or lepton number. In flat potentials, Q-balls have , so for sufficiently large charge the energy per unit charge drops below fermionic masses, making them effectively stable; B-balls with can be entirely stable, while L-balls require to survive. The authors demonstrate that large relic Q-balls can form in the early universe via instabilities of a scalar condensate and via solitosynthesis/mergers, with fragmentation potentially producing Q-balls of charges or larger. Surviving Q-balls could thus constitute dark matter and may also address the cosmological moduli problem by entrapping moduli inside slowly evaporating Q-balls, though observational prospects favor smaller, more abundant B-balls due to their higher expected number density.

Abstract

Supersymmetric extensions of the standard model generically contain stable non-topological solitons, Q-balls, which carry baryon or lepton number. We show that large Q-balls can be copiously produced in the early universe, can survive until the present time, and can contribute to dark matter.

Paper Structure

This paper contains 4 sections, 21 equations, 3 figures.

Table of Contents

  1. Lifetime of Q-balls
  2. Solitosynthesis and collisions
  3. Instability and pattern formation in the motion of a scalar condensate
  4. Surviving Q-balls as dark matter

Figures (3)

  • Figure 1: At early times $\omega$ changes at, roughly, the same rate as the expansion of the universe. All modes of instability are red-shifted before they can grow sufficiently. However, at later times $\omega$ approaches a constant value $\sim m_{_S}$ and the instabilities develop. The size of a domain is determined by the fastest-growing mode at the time when the rate of change in $\omega$ becomes different from $1/t$.
  • Figure 2: The amplification $S(k)= \int_{t_0}^{t_{max}} \alpha(k,t) dt$ of growing modes is computed numerically for different values of $k$. The fastest-growing mode has the wave number $k \sim 10^2 H$ at the time when the instability develops. An individual Q-ball gathers charge from, roughly, $10^{-2}$ of the size of the horizon.
  • Figure 3: The charge density per comoving volume in (1+1) dimensions for a sample potential analyzed numerically during the period when the spatially homogeneous condensate breaks up into high- and low-density domains. Two domains with high charge density are expected to form Q-balls.