Particle dark energy

We explore the physics of a gas of particles interacting with a condensate that spontaneously breaks Lorentz invariance. The equation of state of this gas varies from $1/3$ to less than $-1$ and can lead to the observed cosmic acceleration without requiring a vacuum energy. The particles are always stable. In our particular class of models these particles are fermions with a chiral coupling to the condensate. They may behave as relativistic matter at early times, produce a brief period where they dominate the expansion with $w<0$ today, and behave as matter at late time. There are no small parameters in our models, which generically lead to dark energy clustering and, depending on the choice of parameters, smoothing of small scale power.

Figure 1

The equation of state as a function of spatial momentum for a positive (solid line) and negative (dashed line) helicity gas with $\delta$-function distribution, and for a blackbody centered on $k$ for a positive helicity gas (dotted line), for the case $m=b/10$. The blackbody solution is a “smoothed” version of the $\delta$-function case.

Figure 2

The group velocity, $v_g$, for positive helicity (solid line) and negative helicity (dotted line) particles, for the case $m=b/10$. At the point $k=b$, where $w=0$ (matterlike), the sound speed is very large, in contrast to ordinary matter, and this prevents significant clustering.

Figure 3

A series of snapshots of the particle distribution, $n(k)$ (solid lines) for the case $m=1$, $b=10$. The dashed line is the dispersion relation, $\omega (k)$. Reading the solid lines chronologically from right to left, this figure shows how a high-temperature Fermi-Dirac distribution cools, and particles clump in the well of the dispersion relation at $k=b$ and then redshift after decoupling.

Figure 4

The equation of state of the entire universe (i.e., including all components) as a function of scale factor in a $\Psi$CDM scenario (solid line.) Here we have taken the decoupling to happen between $0.20\lesssim z\lesssim 0.62$, we have taken the ${\Omega }_{\psi ,i}=0.08$ at $z>1$, and $b=M^2/F=400m$. The $d_{\mathrm{LSS}}$, $h$ and $q_0$ for this model agree with that of a fiducial $\Lambda$CDM model, plotted for reference as a dashed line.

Figure 5

The equation of state of the entire universe as a function of scale factor in a D$\Psi$CDM scenario (solid line.) Here we have taken $\tau =2t_0$ and $b=45m$. The $d_{\mathrm{LSS}}$ and $h$ for both models agree with that of the $\Lambda$CDM model, plotted for reference as a dashed line.