Origin of the red spectral tilt in Inflation without an Inflaton
In Inflation without an Inflaton (IWI), a de Sitter (dS) background drives inflation, and the graviton bilinear generates scalar perturbations at second order, with no inflaton or additional fundamental scalar field. We investigate how this scenario can account for the observed scalar spectral tilt. The tensor-mode dependence of the scalar power spectrum gives the consistency relation $n_s-1=2n_T$, since it contains four tensor mode functions. The scalar spectral tilt $n_s\simeq0.9649$ at CMB scales therefore gives $n_T\simeq-0.0175$, independent of the tensor-to-scalar ratio $r$, hence different from the standard single-field slow-roll prediction $n_T=-r/8$. A full time-dependent calculation of $ϕ_2$ in exact dS leads to an almost scale-invariant scalar power spectrum, with a small blue infrared residual on the order of $n_s-1\simeq+4\times10^{-4}$. In order to account for the observed red tilt, we introduce a slow drift in the Hubble rate, parametrized by $\varepsilon=-\dot H/H^2$. The tensor tilt is then given by $n_T=-2\varepsilon$, implying $n_s-1\simeq-4\varepsilon$, at leading order. The observed tilt requires $\varepsilon_\ast\simeq0.0088$, far exceeding the drift that can be sustained by the classical graviton backreaction, for which we find $|\varepsilon_{\rm self}|\lesssim10^{-11}$. Therefore, we investigate the quantum break-time of dS as the origin of the background evolution. In this picture, the scalar tilt becomes $n_s-1=-4C_qN_{sp}(H/m_{pl})^2$, where $C_q$ is an order-one depletion coefficient, and the tilt is directly connected to the particle content of dS, $N_{sp}$. The evolution of the drift itself further predicts a positive running of $α_s=+\tfrac12(1-n_s)^2\simeq+6\times10^{-4}$. These results conclude the distinctive observational predictions of the IWI scenario, establishing it as a falsifiable alternative to standard inflaton-driven models.