Origin of the red spectral tilt in Inflation without an Inflaton
Abstract
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 ns−1=2nT, since it contains four tensor mode functions. The scalar spectral tilt ns≃0.9649 at CMB scales therefore gives nT≃−0.0175, independent of the tensor-to-scalar ratio r, hence different from the standard single-field slow-roll prediction nT=−r/8. A full time-dependent calculation of ϕ2 in exact dS leads to an almost scale-invariant scalar power spectrum, with a small blue infrared residual on the order of ns−1≃+4×10−4. In order to account for the observed red tilt, we introduce a slow drift in the Hubble rate, parametrized by ε=−Ḣ/H2. The tensor tilt is then given by nT=−2ε, implying ns−1≃−4ε, at leading order. The observed tilt requires ε∗≃0.0088, far exceeding the drift that can be sustained by the classical graviton backreaction, for which we find |εself|≲10−11. Therefore, we investigate the quantum break-time of dS as the origin of the background evolution. In this picture, the scalar tilt becomes ns−1=−4CqNsp(H/mpl)2, where Cq is an order-one depletion coefficient, and the tilt is directly connected to the particle content of dS, Nsp. The evolution of the drift itself further predicts a positive running of αs=+1/2(1−ns)2≃+6×10−4. These results conclude the distinctive observational predictions of the IWI scenario, establishing it as a falsifiable alternative to standard inflaton-driven models.
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BibTeX
@misc{jimenez2026origin,
title = {{Origin of the red spectral tilt in Inflation without an Inflaton}},
author = {Raul Jimenez and Daniele Bertacca and Mariam Abdelaziz and Sabino Matarrese and Angelo Ricciardone and Marisol Traforetti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20378},
eprint = {2610.20378},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20378},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Origin of the red spectral tilt in Inflation without an Inflaton
AU - Raul Jimenez
AU - Daniele Bertacca
AU - Mariam Abdelaziz
AU - Sabino Matarrese
AU - Angelo Ricciardone
AU - Marisol Traforetti
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20378
UR - https://arxiv.org/abs/2610.20378
AB - 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≃0.9649 at CMB scales therefore gives n_T≃−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≃+4×10^−4. In order to account for the observed red tilt, we introduce a slow drift in the Hubble rate, parametrized by ε=−Ḣ/H^2. The tensor tilt is then given by n_T=−2ε, implying n_s−1≃−4ε, at leading order. The observed tilt requires ε_∗≃0.0088, far exceeding the drift that can be sustained by the classical graviton backreaction, for which we find |ε_self|≲10^−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=+1/2(1−n_s)^2≃+6×10^−4. These results conclude the distinctive observational predictions of the IWI scenario, establishing it as a falsifiable alternative to standard inflaton-driven models.
ER -