Cosmological supersymmetric model of dark energy

Recently, a supersymmetric model of dark energy coupled to cold dark matter, the supersymmetron, has been proposed. In the absence of cold dark matter, the supersymmetron field converges to a supersymmetric minimum with a vanishing cosmological constant. When cold dark matter is present, the supersymmetron evolves to a matter-dependent minimum where its energy density does not vanish and could lead to the present acceleration of the Universe. The supersymmetron generates a short-ranged fifth force which evades gravitational tests. It could lead to observable signatures on structure formation due to a very strong coupling to dark matter. We investigate the cosmological evolution of the field, focusing on the linear perturbations and the spherical collapse and find that observable modifications in structure formation can indeed exist. Unfortunately, we find that when the growth rate of perturbations is in agreement with observations, an additional cosmological constant is required to account for dark energy. In this case, effects on large-scale structures are still present at the nonlinear level which are investigated using the spherical collapse approach.

Figure 1

The cosmological evolution of ${\phi }_{\rho }$ (above) and $m_{\phi }$ (below) as function of redshift. The dashed line shows the analytical approximation Eq. (32) (above) and Eq. (35) (below). The supersymmetron parameters are $z_{\infty }=1.0$, $\beta =1$, and $n=0.5$. $x$ and $m_{\infty }$ do not have any influence on the evolution of the minimum and do therefore not need to be specified here.

Figure 2

The equation of state for the supersymmetron as function of redshift for four different values of $f=\frac{{\Omega }_{\phi }}{{\Omega }_{\phi }+{\Omega }_{\mathrm{CC}}}$: the fraction of dark energy in the supersymmetron to the total dark energy density today. The horizontal dotted line shows the analytical approximation ${\omega }_{\phi }=-\frac{1}{n+1}$. The supersymmetron parameters are $z_{\infty }=1.0$, $\beta =1$, $n=0.5$ and $x$ is fixed to give the desired $f$ in each case.

Figure 3

$r(a)$ as a function of the scale factor $a$ for $R=\frac{r_i}{a_i}=0.1$, 1, 10, $100\mathrm{Mpc}/h$ (from left to right) compared with the behavior for $r$ in usual $\Lambda \mathrm{CDM}$ (solid line). The initial density contrast is the same in all runs and is fixed such as to give collapse today for $\Lambda \mathrm{CDM}$. The supersymmetron parameters are $z_{\infty }=0.0$, $\beta =n=1$, $x={10}^{-43}$, and $m_{\infty }={10}^5\mathrm{eV}$.

Figure 4

The strength of the fifth force at the surface of the spherical overdensity during the collapse as a function of the scale factor $a$ for $R=\frac{r_i}{a_i}=0.1$, 1, 10, $100\mathrm{Mpc}/h$ (from top to bottom). The parameters are the same as in Fig. 1.

Figure 5

The $\Lambda \mathrm{CDM}$-lineary-extrapolated critical density contrast for collapse for the supersymmetron as a function of the halo mass. The dashed line shows the $\Lambda \mathrm{CDM}$ prediction ${\delta }_c\approx 1.67$. The supersymmetron parameters are $z_{\infty }=0.0$, $\beta =n=1$, $x={10}^{-43}$, and $m_{\infty }={10}^5\mathrm{eV}$.

Figure 6

The fractional difference in the supersymmetron mass function compared to $\Lambda \mathrm{CDM}$ at $z=0$. The symmetron parameters are $m_{\infty }={10}^5\mathrm{eV}$, $z_{\infty }=0.0$, $x={10}^{-43}$, and $\beta =n=1$. The supersymmetron converges to $\Lambda \mathrm{CDM}$ for large halo masses.