Gravitational collapse, primordial black hole, and gravitational wave in Einstein--Gauss-Bonnet theory with two scalar fields

In this paper, we investigate the gravitational collapse to form the black hole in the acceleratingly expanding universe in the frame of Einstein--Gauss-Bonnet theory having two scalar fields and we study the propagation of the gravitational wave (GW). This may describe the creation of the primordial black holes in the early stages of the universe and the impact of their creation on the propagation of primordial gravitational waves. The collapsing spacetime can be obtained by using the formulation of the ``reconstruction'', that is, we find a model that realises the desired or given geometry. In the reconstructed models, ghosts often appear, which could be eliminated by imposing constraints. We show that the standard cosmological solutions or self-gravitating objects such as a planet, the Sun, various types of stars, etc., in Einstein's gravity, are also solutions in this model. Using the dynamical value of the Gauss-Bonnet coupling, the propagation of the high-frequency GW is investigated. The propagating speed changes due to the coupling during the period of the black hole formation. The speed of the GW propagation going into the black hole is different from that of the wave going out.