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arXiv · 2608.06071

Integrable models of inflation beyond slow-roll

M. Bianchi·G. Dibitetto·J. F. Morales·V. Zevola
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Abstract

We propose a novel analytic approach to the study of multi-component FLRW cosmologies and their perturbations. The dynamics is triggered by a single scalar field with a scalar potential codifying the energy density and pressure of the multi-component fluid. This description unifies standard Big Bang cosmologies, models of inflation and dark energy under a unique framework. The key to integrability is to express the scalar potential in terms of the Hubble function $H(\phi)$ that plays the role of a fake superpotential, turning the dynamics into a first order problem, that may be analytically solved in a suitable time coordinate. In this framework, we propose integrable inflationary models with similar properties to the ones analysed in the literature and compatible with observations. Finally, we study scalar and tensor cosmological perturbations in each model by integrating Mukhanov-Sasaki equations via numerical and (semi-)analytic techniques. This allow us to compute the power spectrum, the spectral indices and the tensor-to-scalar ratio beyond the slow-roll approximation and compare our general results {against} the currently available observations and the theoretical predictions based on the slow-roll approximation.

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M. Bianchi, G. Dibitetto, J. F. Morales, V. Zevola. 2026-08-06. Integrable models of inflation beyond slow-roll. https://arxiv.org/abs/2608.06071

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