Inflationary gravitational waves in consistent $D\to 4$ Einstein-Gauss-Bonnet gravity

Abstract

We study the slow-roll single field inflation in the context of the consistent $D\to 4$ Einstein-Gauss-Bonnet gravity that was recently proposed in \cite{Aoki:2020lig}. In addition to the standard attractor regime, we find a new attractor regime which we call the Gauss-Bonnet attractor as the dominant contribution comes from the Gauss-Bonnet term. Around this attractor solution, we find power spectra and spectral tilts for the curvature perturbations and gravitational waves (GWs) and also a model-independent consistency relation among observable quantities. The Gauss-Bonnet term provides a nonlinear $k^4$ term to the GWs dispersion relation which has the same order as the standard linear $k^2$ term at the time of horizon crossing around the Gauss-Bonnet attractor. The Gauss-Bonnet attractor regime thus provides a new scenario for the primordial GWs which can be tested by observations. Finally, we study non-Gaussianity of GWs in this model and estimate the nonlinear parameters $f_{\mathrm{NL},\mathrm{sq}}^{s_1{s}_2{s}_3}$ and $f_{\mathrm{NL},\mathrm{eq}}^{s_1{s}_2{s}_3}$ by fitting the computed GWs bispectra with the local-type and equilateral-type templates respectively at the squeezed limit and at the equilateral shape. For helicities $(+++)$ and $(--)$, $f_{\mathrm{NL},\mathrm{sq}}^{s_1{s}_2{s}_3}$ is larger while $f_{\mathrm{NL},\mathrm{eq}}^{s_1{s}_2{s}_3}$ is larger for helicities $(++-)$ and $(--+)$.

arXiv comment30 pages, 4 figures, observational bound is corrected

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