Inflation without an Inflaton III: non-Gaussian signatures

Abstract

We investigate primordial non-Gaussianity in the Inflation without an Inflaton (IWI) framework, where scalar perturbations are generated at second order by primordial gravitational waves in Einstein gravity on an exact de Sitter (dS) background. Since scalar modes are produced nonlinearly from tensor modes, non-Gaussianity is an intrinsic prediction of the mechanism. We compute the corresponding scalar bispectrum, derive the relevant contribution to the three-point function of the scalar potential, and evaluate its shape numerically. We find that, unlike the scalar power spectrum, the bispectrum depends logarithmically on the ultraviolet cutoff set by the end of inflation, indicating a structural difference between the two- and three-point statistics in this scenario. Its shape is enhanced toward squeezed configurations, but its amplitude becomes strongly suppressed once the scalar power spectrum is normalized to the observed value. The resulting non-Gaussianity at CMB scales is therefore negligibly small, well below present observational sensitivity.

Figures (2)

• Figure 1: Dimensionless shape function $S_\phi(k_1,k_2,k_3)$ evaluated at fixed $k_3 = k_{\rm CMB} = 0.01\,\mathrm{Mpc}^{-1}$. The horizontal and vertical axes correspond to the ratios $k_1/k_3$ and $k_2/k_3$, restricted to the triangular domain $k_1 \le k_2 \le k_3$. The color scale indicates the amplitude of $S_\phi(k_1,k_2,k_3)$ in units of $10^{-16}$. The signal is enhanced toward squeezed configurations ($k_1 \ll k_2 \simeq k_3$).
• Figure 2: The negative value of the non-Gaussianity parameter, $f_{\rm NL}$, defined in Eq. \ref{['fnl_nobs']}, as a function of the cutoff parameter $N_{\rm obs}$. The shaded region, $N_{\rm obs}<30$, is displayed only as an extrapolation, whereas the physically relevant range is the non-shaded region. The figure shows that, once the scalar power spectrum is fixed to its observed amplitude, the bispectrum amplitude is rapidly suppressed as the cutoff is increased, following approximately an $e^{-3N_{\rm obs}/2}$ behaviour.