Gravitational waves production during preheating within GB gravity with monomial coupling

Abstract

In this paper, we investigate the production of gravitational waves during the preheating era. To achieve this purpose, we consider Gauss-Bonnet inflation model with Power{\textendash}law potential, $V(φ)= V_0 φ^n$, and monomial Gauss-Bonnet coupling function, $ξ(φ)= ξ_0 φ^n$. We examine our model by comparing our findings with the current observational data. After that, we study the preheating stage by adopting an approach in which we establish a link between preheating duration, reheating phase and inflationary parameters. This step allows us to benefit from observational constraints imposed on inflation. Furthermore, we examine the production of gravitational waves during preheating epoch connecting the energy density to the preheating duration, $N_{pre}$, and then with the spectral index $n_s$. The generation of gravitational waves during preheating can satisfy observational constraints. In particular, the predicted present-day gravitational-wave energy density, expressed as a function of the scalar spectral index, is consistent with the Planck constraints for the choice of a dimensionless Gauss-Bonnet coupling parameter $α\equiv 4V_{0}ξ_{0}/3 = -1.5\times 10^{-6}$, an effective equation of state parameter $ω= 1/6$, and a preheating efficiency parameter $δ= 10^{5}$.

Figures (5)

• Figure 1: Tensor-to-scalar ratio, $r$, as a function of the spectral index $n_s$ considering three values of $\alpha$, for $n=1$ (left panel) and $n=2$ (right panel). The red and gray contours indicate $1\sigma$ and $2\sigma$ constraints from Planck, respectively.
• Figure 2: Preheating duration, $N_{pre}$, against the number of e-folds, $N_k$, considering three values of $\omega$, for $\alpha=-1.5\times10^{-6}$.
• Figure 3: Preheating duration $N_{pre}$ against the spectral index $n_s$ considering three values of $\omega$, for $\alpha=-1.5\times10^{-6}$ (left panel) and $\alpha=-2.5\times10^{-6}$ (right panel). The vertical light blue band represents the Planck constraints on the scalar spectral index, $n_s=0.9649\pm 0.0042$, whereas the dark blue band indicates the anticipated $10^{-3}$ precision expected from future experiments Amendola:2016saw.
• Figure 4: Variation of GW energy density versus the preheating duration, $N_{pre}$, for different values of the GW density spectra i.e. $4\times 10^{-3}$ (blue curve), $2\times 10^{-3}$ (orange curve), $10^{-3}$ (green curve) and $8\times 10^{-4}$ (red curve), with the coupling parameter $\alpha=-1.5\times10^{-6}$ and the equation of state $\omega=1/6$.
• Figure 5: Evolution of GW energy density as a function of the spectral index, $n_s$, for different values of the GW density spectra i.e. $4\times 10^{-3}$ (blue curve), $2\times 10^{-3}$ (orange curve), $10^{-3}$ (green curve) and $8\times 10^{-4}$ (red curve), considering two specific values of the coupling parameter $\alpha=-1.5\times10^{-6}$ (left plot) and $\alpha=-2.5\times10^{-6}$ (right plot). We take the equation of state $\omega=1/6$. The yellow vertical and blue horizontal regions indicate the Planck constraints on the spectral index, $n_s$, and the current GW energy density, $\Omega_{gw,0}h^2$, respectively.