Primordial black holes in SB SUSY Gauss-Bonnet inflation

TL;DR

The paper addresses PBH formation from enhanced curvature perturbations in a Gauss-Bonnet inflation framework with a low-scale SB SUSY potential. It implements a two-part Gauss-Bonnet coupling to induce a brief ultra-slow-roll phase, solving the Mukhanov-Sasaki equations numerically to obtain the scalar and tensor power spectra while satisfying Planck constraints. The study demonstrates PBHs spanning ${\cal O}(10^{-13})M_\odot$ to ${\cal O}(14)M_\odot$ with corresponding abundances and predicts secondary gravitational waves that lie within the reach of upcoming detectors, including a nano-Hz signal compatible with NANOGrav 15-year data. It also shows compatibility with swampland criteria and highlights observationally testable predictions across multiple GW observatories, making the SB SUSY potential viable in GB inflation.

Abstract

Here, we explore the formation of primordial black holes (PBHs) within a scalar field inflationary model coupled to the Gauss-Bonnet (GB) term, incorporating the low-scale spontaneously broken supersymmetric (SB SUSY) potential. The coupling function amplifies the curvature perturbations, consequently leading to the formation of PBHs and detectable secondary gravitational waves (GWs). Through the adjustment of the model parameters, the inflaton can be decelerated during an ultra-slow-roll (USR) phase, thereby augmenting curvature perturbations. Beside the observational constraints, the swampland criteria are investigated. Our computations forecast the formation of PBHs with masses around ${\cal O}(10)M_{\odot}$, aligning with the observational data of LIGO-Virgo, and PBHs with masses ${\cal O}(10^{-6})M_{\odot}$ as potential explanation for the ultrashort-timescale microlensing events recorded in the OGLE data. Additionally, our proposed mechanism can generate PBHs with masses around ${\cal O}(10^{-13})M_{\odot}$, constituting roughly 99$\%$ of the dark matter. The density parameters of the produced GWs ($Ω_{\rm GW_0}$) intersect with the sensitivity curves of GW detectors. Two cases of our model fall within the nano-Hz frequency regime. One of them satisfies the power-law scaling as $Ω_{\rm{GW}}(f) \sim f^{5-γ}$, with the $γ= 3.51$, which is consistent with the data of NANOGrav 15-year.

Figures (8)

• Figure 1: Evolution of (a) the scalar filed $\phi$, (b) the Hubble parameter, (c) the first slow-roll parameter $\epsilon_1$, (d) the second slow-roll parameter $\epsilon_2$, (e) $c_s^{2}$, (f) $c_t^{2}$ versus the $e$-folds number $N$ for cases of Table \ref{['tab1']}. The cases A, B, C, and D are respectively shown by blue, green, red and purple lines.
• Figure 2: Evolution of the second slow-roll parameter $\epsilon_2$ with respect to the $e$-fold number $N$ for case A of the model with $\xi(\phi)=\xi_{\rm I}(\phi)$ (black curve) and $\xi(\phi)=\xi_{\rm I}(\phi)[1+\xi_{\rm II}(\phi)]$ (blue curve).
• Figure 3: The effective potential, Eq. (\ref{['veff']}), with respect to the scalar field for all cases of the model in the Einstein frame.
• Figure 4: Validity of the swampland criteria for our model for (a) $\Delta\phi= \phi(N) - \phi(N_{\rm end})$, (b) $M_{\rm Pl}|V_{,\phi}/V|$, and (c) $M_{\rm Pl}^2|V_{,\phi\phi}/V|$ versus the $e$-fold number $N$. The cases A, B, C, and D are, respectively, depicted by blue, green, red and purple lines.
• Figure 5: The scalar power spectrum ${\cal P}_{s}$ as a function of the wavenumber $k$ for each parameter set of Table \ref{['tab1']}. The cases A, B, C, and D are respectively shown by blue, green, red and purple curves. The CMB observations exclude the light-green shaded region akrami:2020. The orange region shows the $\mu$-distortion of CMB Fixsen:1996. The cyan area represents the effect on the ratio between neutron and proton during the big bang nucleosynthesis (BBN) Inomata:2016. The EPTA observations constrain the yellow area Inomata:2019-a.