Domain walls coupled to matter: The symmetron example

We study properties of domain walls in the symmetron model, in which the scalar gravitational degree of freedom decouples from matter in regions of high density and exhibits a spontaneously broken $Z_2$ symmetry at low densities. The nonminimal coupling of the scalar to matter leads to a host of interesting properties of the domain walls that are not present in minimally coupled theories. We estimate the cosmological energy fraction in domain walls and find that this leads to an upper bound on the redshift of the symmetry breaking. We also show that a spherical symmetron wall can remain stable if it is “pinned” on matter halos and derive a criterion for the stability. In addition, we present results of numerical simulations of representative interactions between domain walls and matter overdensities.

Figure 1

Physical thickness of symmetron domain walls as a function of redshift for three different sets of model parameters. The curves that increase with redshift correspond to the walls in the symmetron model, while the horizontal straight lines are the values for “conventional” domain walls, when $\rho =0$.

Figure 2

The ratio, ${\mathrm{\Omega }}_{\mathrm{DW}}$, of the DW energy density and that of matter for a set of parallel domain walls separated by a comoving distance $D$. The thin and thick lines correspond to $z_{\mathrm{SSB}}=10$ and $z_{\mathrm{SSB}}=1000$, respectively. The continuous, dashed, and dotted-dashed lines corresponds to values of $D$ of 100, 10, and $1\mathrm{Mpc}/\mathrm{h}$, respectively.

Figure 3

The ratio, ${\mathrm{\Omega }}_{\mathrm{DW}}$, of the DW energy density and that of matter given by Eq. (35) using the distance between walls given by Eq. (42). Different thicknesses of the lines correspond to different values of $z_{\mathrm{SSB}}$.

Figure 4

Scalar field corresponding to a halo and a domain wall. Left: the wall is inside the halo. Right: the wall has moved to the left. See the text for explanation.

Figure 5

Snapshots of a 2D simulation of the interaction of a DW with a set of filaments. The color coding corresponds to the scalar field $\chi$. The upper-left panel is the initial condition, and time runs from top left to bottom right. This is an example of a wall getting trapped by the filaments.

Figure 6

Snapshots of a 2D simulation of unpinnned DW moving away from a filament. The color coding corresponds to the scalar field $\chi$. The upper-left panel is the initial condition.