How Primordial Blackholes Forms From The Gauss-Bonnet-Corrected Single Field Inflation? (Cosmology)

Countless number of primordial blackholes formation scenarios have been already discussed by us on our website. Now, Shinsuke Kawai and Jinsu Kim proposed another interesting mechanism for the primordial blackhole formation. They considered a model in which a scalar field is coupled to the Gauss-Bonnet term, and showed that primordial blackholes may be seeded when a scalar potential term and the Gauss-Bonnet coupling term are nearly balanced. Large curvature perturbation in this model not only leads to the production of primordial blackholes but it also sources gravitational waves at the second order. Their study recently appeared in Arxiv.

Cosmic inflation provides a natural framework for the production of primordial blackholes. Single field inflation is capable of generating large primordial curvature perturbation in small scales compared to the scale of the cosmic microwave background. In the single field inflation models for which the primordial blackhole production and the secondary gravitational waves are studied, the gravity sector is usually assumed to be the Einstein gravity. The Einstein gravity however is by no means a complete theory. From the effective field theory viewpoint, for example, higher curvature terms are expected to arise. One such higher curvature term is the Gauss-Bonnet term,

which leads to a relatively well-behaved theory of higher curvature gravity.

Previously, Shinsuke Kawai and Jinsu Kim investigated a model in which a scalar field ϕ is coupled to the Gauss-Bonnet term and discussed the features of a de Sitter-like fixed point as an alternative to cosmic inflation; in the presence of the Gauss-Bonnet coupling term there may exist a nontrivial de Sitter-like fixed point where the scalar potential term is balanced with the higher curvature Gauss-Bonnet term. Near the nontrivial fixed point, the standard slow-roll approximation is invalid and the ultra-slow-roll regime of inflation naturally arises. Furthermore, they pointed out that the primordial curvature power spectrum may become enhanced near the nontrivial de Sitter-like fixed point, which potentially leads to production of primordial blackholes.

Now, they investigated the production of primordial blackholes and the scalar-induced second-order gravitational waves in such a setup.

FIG. 1. The curvature power spectrum is shown for their two benchmark parameter sets. The enhancement is observed as the inflaton enters the ultra-slow-roll regime near the non-trivial fixed point. Here k∗ = 0.05 Mpc¯1 © Kawai and Kim

By considering two benchmark parameter sets they showed that, a large enhancement occurs in the curvature power spectrum by numerically solving the equations of motion.

A mode with large enhancement of the curvature perturbation may experience gravitational collapse when reentering the horizon, thereby producing primordial blackholes. For their two benchmark sets, they computed the present abundance of primordial blackholes. One set accounts for the totality of the dark matter relic density today, while in the other case primordial blackholes constitute only a portion of the present dark matter relic abundance.

FIG. 2. The density parameter of the scalar-induced second-order gravitational waves is shown for their two benchmark sets. The gravitational wave signal of Set 1 is well within the reach of the sensitivity bound of future experiments such as LISA, DECIGO, and BBO. In the case of Set 2, the signal crosses the sensitivity bound of SKA as well. © Kawai and Kim

A large curvature perturbation that leads to the production of primordial blackholes inevitably source the scalar-induced second-order gravitational waves. They also obtained the present density parameter of the gravitational waves by utilizing the approximated analytical expression together with their numerical results of the curvature power spectrum. Both of their two benchmark sets are found to be within the sensitivity bounds of future gravitational wave experiments such as LISA, DECIGO, BBO, and SKA.

“While we focused on the scalar potential of the natural inflation model and assumed a smeared step function for the Gauss-Bonnet coupling function in this work, some of the features that we have found are generic. When there is a balance between a scalar potential term and a Gauss-Bonnet coupling term, a nontrivial fixed point may exist. Near the nontrivial fixed point the ultra-slow-roll inflation generically occurs, during which period a large enhancement of the curvature perturbation is guaranteed. We thus expect that the production of primordial blackholes and the secondary gravitational wave signals are natural in higher curvature gravity theories.”

— they concluded.

Reference: Shinsuke Kawai, Jinsu Kim, “Primordial blackholes from Gauss-Bonnet-corrected single field inflation”, Arxiv, pp. 1-9, 2021. https://arxiv.org/abs/2108.01340


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