CMB from a Gauss-Bonnet-induced de Sitter fixed point

Abstract

In gravitational effective theories including higher curvature terms, cosmological solutions can have nontrivial de Sitter fixed points. We study phenomenological implications of such points, focusing on a theory in which a massive scalar field is nonminimally coupled to the Euler density.We first analyze the phase portrait of the dynamical system, and show that the fixed point can be a sink or a saddle, depending on the strength of the coupling. Then we compute the perturbation spectra generated in the vicinity of the fixed point in order to investigate whether the fixed point may be considered as cosmic inflation. We find parameter regions that are consistent with the cosmological data, given that the anisotropies in the cosmic microwave background are seeded by the fluctuations generated near the fixed point. Future observation may be used to further constrain the coupling function of this model. We also comment briefly on the swampland conjecture.

Primordial blackholes from Gauss-Bonnet-corrected single field inflation

“…As pointed out in Ref. [107], due to the ultra-slowroll regime, we see a large enhancement in the curvature power spectrum. Finally we compute the spectral index n s and the tensor-to-scalar ratio r by using Eq.…”

“…Thus, the nontrivial fixed point becomes a saddle point, as pointed out in Ref. [107]. Near the nontrivial fixed point, Eq.…”

“…( 5) is approximated as φ + 3H φ ≈ 0, indicating an ultra-slow-roll regime. An inflaton trajectory that passes near the nontrivial fixed point will enter an ultra-slow-roll regime and experiences an enhancement in the curvature power spectrum [107].…”

“…In Ref. [107], we investigated a model in which a scalar field ϕ is coupled to the Gauss-Bonnet term and discussed the features of a de Sitterlike 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.…”

Primordial black holes and scalar induced gravitational waves from the $E$ model with a Gauss-Bonnet term

“…which means the inflaton evolves into an instant ultra slow roll (USR) phase, which is an efficient way to enhance the curvature perturbations. In fact, this critical value φ c is a nontrivial fixed point [68]. So, this provides a way to adjust the parameters to realize a USR phase in different energy scales, which corresponds to produce power spectrum with a large peak at different scales.…”