A preliminary study about gravitational wave radiation and cosmic heat death

We study the role of gravitational waves (GW) in the heat death of the universe. Due to the GW emission, in a very long period, dynamical systems in the universe suffer from persistent mechanical energy dissipation, evolving to a state of universal rest and death. With N-body simulations, we adopt a simple yet representative scheme to calculate the energy loss due to the GW emission. For current dark matter systems with mass $\sim10^{12}-10^{15} M_\odot$, we estimate their GW emission timescale as $\sim10^{19}-10^{25}$ years. This timescale is significantly larger than any baryon processes in the universe, but still $\sim10^{80}$ times shorter than that of the Hawking radiation. We stress that our analysis could be invalid due to many unknowns such as the dynamical chaos, the quadrupole momentum of halos, the angular momentum loss, the dynamic friction, the central black hole accretion, the dark matter decays or annihilations, the property of dark energy and the future evolution of the universe.