Note on the reheating temperature in Starobinsky-type potentials
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Note on the reheating temperature in Starobinsky-type potentials Jaume Haro1 · Llibert Aresté Saló2 Received: 23 July 2020 / Accepted: 18 November 2020 © The Author(s) 2020
Abstract The relation between the reheating temperature, the number of e-folds and the spectral index is shown for the Starobinsky model and some of its descendants through a very detailed calculation of these three quantities. The conclusion is that for viable temperatures between 1 MeV and 109 GeV the corresponding values of the spectral index enter perfectly in its 2σ C.L., which shows the viability of this kind of models. Keywords Reheating · Number of e-folds · Starobinsky model
Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The number of e-folds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Different models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Case n = 1: the exact Starobinsky model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Case n = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 The particular case wr e = 1/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Llibert Aresté Saló [email protected] Jaume Haro [email protected]
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Departament de Matemàtiques, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain
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School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK 0123456789().: V,-vol
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J. Haro, L. Aresté Saló
1 Introduction The Starobinsky model based on R 2 -gravity in the Jordan frame [1], which was extensively studied in the literature (see for instance [2–5] and [6] for a detailed dynamical analysis), is one of the most promising scenarios to explain the inflationary paradigm proposed by A. Guth in [7] because it provides theoretical data about the power spectrum of perturbations, which matches very well with the recent observational data obtained by the Planck team [8]. In addition, contrary to the Guth’s paper, in [1] the author briefly details a successfully reheating mechanism based on the production of particles named scalarons whose decay products reheat the universe (see [3,9,10] for a detailed discussion of this mechanism), obtaining a reheating temperature around 109 GeV [11] (see also [2] for the derivation of this reheating temperature when the decay products are massless and minimally coupled with gravity). Working in the Einstein frame, R 2 -gravity leads to the well-known Starobinsky potential [2], which has been recently studied as an inflationary potential, and the reheating temperature provided by the model is related to its correspondi
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