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    Inflation without an inflaton. II. Observational predictions

    Marisol Traforetti1,*, Mariam Abdelaziz2,3,4,†, Daniele Bertacca5,6,7,‡, Raul Jimenez1,8,§, Sabino Matarrese5,6,7,9,∥, and Angelo Ricciardone10,11,¶

    • *Contact author: marisol.traforetti@icc.ub.edu
    • †Contact author: mariamtarekmohamed.abdelaziz-ssm@unina.it
    • ‡Contact author: daniele.bertacca@pd.infn.it
    • §Contact author: raul.jimenez@icc.ub.edu
    • ∥Contact author: sabino.matarrese@pd.infn.it
    • Contact author: angelo.ricciardone@unipi.it

    Phys. Rev. D 113, 023553 – Published 30 January, 2026

    DOI: https://doi.org/10.1103/cfg4-5p3s

    Abstract

    We present a complete computation of the scalar power spectrum in the inflation without inflaton (IWI) framework, where the inflationary expansion is driven solely by a de Sitter (dS) background and scalar fluctuations arise as second-order effects sourced by tensor perturbations. By explicitly deriving and numerically integrating the full second-order kernel of the Einstein equations, we obtain a scale-invariant scalar spectrum without invoking a fundamental scalar field. In this framework, the amplitude of the scalar fluctuations is directly linked to the scale of inflation. More precisely, we show that matching the observed level of scalar fluctuations Δϕ2(k*)≈10−9 at cosmic microwave background scales fixes the inflationary energy scale Hinf as a function of the number of observed e-folds Nobs. For Nobs≃30–60, we find Hinf≃5×1013  GeV–2×1010  GeV, corresponding to a tensor-to-scalar ratio r≃0.01–5×10−9. In particular, requiring consistency with instantaneous reheating, we predict a number of e-foldings O(50) and an inflationary scale Hinf≃1011  GeV. We also incorporate in our framework the quantum break time of the dS state, and we show that it imposes an upper bound on the number of particle species. Specifically, using laboratory constraints on the number of species limits the duration of inflation to Nobs≲126 e-folds. These results establish the IWI scenario as a predictive and falsifiable alternative to standard inflaton-driven models, linking the observed amplitude of primordial fluctuations directly to the quantum nature and finite lifetime of dS space.

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    See Also

    Inflation without an inflaton. III. Non-Gaussian signatures

    Mariam Abdelaziz, Marisol Traforetti, Daniele Bertacca, Raul Jimenez, Sabino Matarrese, and Angelo Ricciardone
    Phys. Rev. D 114, 023517 (2026)

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