Damping of gravitational waves in matter and Λ−dominated era

Neutrinos as a probe of curvature

“…The homogeneous solution of tensor mode in matter dominated is j 1 (u) or sin u u 2 which for nonzero f v (0), the solutions approach 0.9861 sin u u 2 and 0.626 sin u u 2 with high accuracy for flat and closed spacetime, respectively [21]. The point is GWs decays as 1 u from radiation to matter era, where…”

“…Also, a numerical solution of Eq. (21) shows that D n (u) follows the f v (0) solution pretty accurately until u ≈ 1 when the perturbation enters the horizon [as compared with the solution sin u u for f v (0)]. Thereafter, the Therefore, the effect of neutrino damping reduces the tensor amplitude by the factor of 0.5664 in the open cosmology, while in the flat and closed cases, the factor is 0.8026 and 0.4910, respectively [19,20].…”

“…It was thought that the interaction of these modes with matter and radiation could be negligible [18], but Steven Weinberg showed far outside the horizon at the temperature ≈ 10 10 0 K tensor modes can be affected by anisotropic inertia which contain free streaming neutrinos and antineutrinos [19]. This issue was explored in the spatially closed spacetime and extended to the Λ-dominated era [20,21]. Here, in addition to the above reports, we will use the neutrinos effect on gravitational waves damping as a tool to show the difference between spatially closed and open universe.…”

Gravitational waves with dark energy

“…However, it is shown that at the temperature of ≈ 10 10 ( 0 K), the tensor modes can be affected by anisotropic inertia, which contains free streaming neutrinos and antineutrinos [3]. This issue has been explored in the spatially curved spacetime and extended to the Λ-dominated era [4][5][6]. Here, we study the effect of dark energy on GWs.…”

Gravitational Waves in a Closed Spacetime via Deviation Equation

“…In addition, Planck 2018 CMB lensing [9] and baryon acoustic oscillations [10][11][12] suggest a flat universe are quantitatively inconsistent at 2.5 to 3σ with CMB data. Hence, by choosing the maximally extended de-Sitter metric (K = 1) as the unperturbed background, we studied the propagation of gravitational waves [13] and its damping by neutrinos in closed spacetime [14,15]. As before, many authors have considered the de Sitter background to study GWs; M.Shibata et al investigated the dynamical evolution of axisymmetric gravitational waves in asymptotically de-Sitter spacetime [16] and found that, if the mass of gravitational waves is larger than the critical value, M crit, = (3 √ Λ) −1 the formation of black holes will be prevented, even in the presence of highly non-linear and localized gravitational waves.…”