Gauss–Bonnet inflation with a constant rate of roll

Abstract

In the model of the inflaton nonminimal coupling to the Gauss–Bonnet term, we discuss the constant-roll inflation with constant $$\epsilon _1$$ ϵ 1 , constant $$\epsilon _2$$ ϵ 2 and constant $$\eta _H$$ η H , respectively, with the additional assumption that $$\delta _1$$ δ 1 is a constant. Using the Bessel function approximation, we get the analytical expressions for the scalar and tensor power spectrum and derive the scalar spectral index $$n_{\mathcal {R}}$$ n R and the tensor to scalar ratio r to the first order of $$\epsilon _1$$ ϵ 1 . By using the Planck 2018 observations constraint on $$n_{\mathcal {R}}$$ n R and r, we obtain some feasible parameter space and show the result on the $$n_{\mathcal {R}}-r$$ n R - r region. The scalar potential is also reconstructed in some special cases.

Cosmic Evolution of the Logarithmic f(R) Model and the dS Swampland Conjecture

“…If ∂V ∂φ is retained for a long time, the second example refers to an ultra-slow-roll model. In agreement with the above equations, Einstein-Hilbert action is investigated using a canonical scalar field as used in previous works [12,102,103]. Similarly, in f (R), gravitational models are a natural generalization of the constant-roll condition,…”

Primordial Black Holes in Scalar Field Inflation Coupled to the Gauss–Bonnet Term with Fractional Power-law Potentials

“…We consider the Einstein-GB action as follows (Guo & Dominik 2010;Jiang et al 2013;Koh et al 2014;Gao 2020;Odintsov et al 2020aOdintsov et al , 2020bPozdeeva et al 2020;Rashidi & Nozari 2020;Azizi et al 2022;Khan 2022;Shahraeini et al 2022;Gangopadhyay & Khan 2023;Nojiri et al 2023;Odintsov et al 2023Odintsov et al , 2023Nojiri & Odintsov 2024):…”

“…where a is the scale factor. The Friedmann equations and the equation of motion can be derived by taking variation of the action (1) with respect to the metric g μ ν and the scalar field f, respectively as follows (Guo & Dominik 2010;Jiang et al 2013;Koh et al 2014;Gao 2020;Odintsov et al 2020aOdintsov et al , 2020bPozdeeva et al 2020;Khan 2022;Gangopadhyay & Khan 2023;Nojiri et al 2023;Odintsov et al 2023Odintsov et al , 2023:…”

“…where H a a º  is the Hubble parameter, the dot denotes the time derivative, and the subscript (,f) demonstrates the derivative with respect to f. In GB gravity, the slow-roll parameters are defined as follows (Guo & Dominik 2010;Jiang et al 2013;Koh et al 2014;Gao 2020;Odintsov et al 2020a):…”

Anisotropic constant-roll inflation for the Dirac–Born–Infeld model

“…Consequently, the constant-roll inflation has been investigated extensively in Refs. [115][116][117][118][119][120][121][122][123][124][125][126][127][128][129][130][131][132][133]. It appears that the constant-roll condition has been applied to a number of cosmological models such as the non-minimal Coleman-Weinberg [119], F(R) gravity [120][121][122][123], scalar-tensor gravity [124], k-inflation [125], non-canonical scalar field [126], DBI [127], Palatini-R 2 gravity [128], Gauss-Bonnet gravity [129,130], multi scalar fields [131], non-commutative gravity [132], and f (φ)R gravity [133] models to figure out either novel (exact) inflationary solutions or cosmological consequences.…”