Stochastic gravitational wave background from cold dark matter halos

The current knowledge of cosmological structure formation suggests that Cold Dark Matter (CDM) halos possess a nonspherical density profile, implying that cosmic structures can be potential sources of gravitational waves via power transfer from scalar perturbations to tensor metric modes in the nonlinear regime. By means of a previously developed mathematical formalism and a triaxial collapse model, we numerically estimate the stochastic gravitational-wave background generated by CDM halos during the fully nonlinear stage of their evolution. Our results suggest that the energy density associated with this background is comparable to that produced by primordial tensor modes at frequencies $\nu \approx {10}^{-18}–{10}^{-17}\mathrm{Hz}$ if the energy scale of inflation is $V^{1/4}\approx 1–2\times {10}^{15}\mathrm{GeV}$, and that these gravitational waves could give rise to several cosmological effects, including secondary CMB anisotropy and polarization.

Figure 1

Evolution of the principal-axis scale factors for the most probable ellipsoid of mass $M=5\times {10}^{15}{M}_{\odot }$ and initial overdensity $\delta (z_i=40)=6.4\times {10}^{-2}$, embedded in a flat $\Lambda \mathrm{CDM}$ universe, at distance $D=100\mathrm{Mpc}$ from the observer.

Figure 2

Two of the three nonvanishing traceless source components generated by the halo collapse of Fig. 1.

Figure 3

The total energy density ${\Omega }_{\mathrm{GW}}(\nu )$ associated with the stochastic GW background induced by CDM halos as a function of the proper frequency $\nu$ at observation.

Figure 4

Contribution to the total energy density ${\Omega }_{\mathrm{GW}}(\nu )$ by two most probable CDM halos of mass $5\times {10}^{15}{M}_{\odot }$ placed at redshifts $z=0.025$ and 0.075.