Topology and Dark Energy: Testing Gravity in Voids

Modified gravity has garnered interest as a backstop against dark matter and dark energy (DE). As one possible modification, the graviton can become massive, which introduces a new scalar field—here with a Galileon-type symmetry. The field can lead to a nontrivial equation of state of DE which is density and scale dependent. Tension between type Ia supernovae and Planck could be reduced. In voids, the scalar field dramatically alters the equation of state of DE, induces a soon-observable gravitational slip between the two metric potentials, and develops a topological defect (domain wall) due to a nontrivial vacuum structure for the field.

Figure 1

Plot of $f$ with ${\pi }^{\prime }/r=f(\Delta ){\Lambda }^3$, where $\Delta =\delta {\rho }_m/{\rho }_{m0}$ is the difference between the mean density inside of a radius $r$ and the mean density today normalized by the mean density today. The vertical dashed black lines indicate the domain wall region. The wiggly dashed red line is meant to indicate that a field transition between branches takes place within the region.

Figure 2

Plot of the EOS of DE $w_{\mathrm{DE}}$, where $⟨{\rho }_m⟩/{\rho }_{\mathrm{m}0}$ is the mean density of matter interior to a radius $r$ over the mean density today ${\rho }_{m0}$. The dashed blue line represents case one, and the solid black line represents case two.