Bimetric structure formation: Non-Gaussian predictions

The minimal bimetric theory employing a disformal transformation between matter and gravity metrics is known to produce exactly scale-invariant fluctuations. It has a purely equilateral non-Gaussian signal, with an amplitude smaller than that of Dirac Born Infeld inflation (with opposite sign) but larger than standard inflation. We consider nonminimal bimetric models, where the coupling $B$ appearing in the disformal transformation ${\widehat{g}}_{\mu \nu }=g_{\mu \nu }-B{\partial }_{\mu }\varphi {\partial }_{\nu }\varphi$ can run with $\varphi$. For power-law $B(\varphi )$ these models predict tilted spectra. For each value of the spectral index, a distinctive distortion to the equilateral property can be found. The constraint between this distortion and the spectral index can be seen as a “consistency relation” for nonminimal bimetric models.

Figure 1

We plot the non-Gaussian amplitude from Eq. (4.15) $-\mathcal{A}(1,x_2,x_3)/(x_2{x}_3)$ for $n_s=1$ (left) and $n_s=0.96$ (right).