Bouncing cosmology in f ( Q ) symmetric teleparallel gravity
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Bouncing cosmology in f ( Q) symmetric teleparallel gravity Francesco Bajardi1,2,a , Daniele Vernieri1,2,b , Salvatore Capozziello1,2,3,4,c 1 2 3 4
Department of Physics “E. Pancini”, University of Naples “Federico II”, Naples, Italy INFN Sez. di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, 80126 Naples, Italy Scuola Superiore Meridionale, Largo San Marcellino 10, 80138 Naples, Italy Tomsk State Pedagogical University, ul. Kievskaya, 60, Tomsk, Russia 634061
Received: 23 October 2020 / Accepted: 4 November 2020 © The Author(s) 2020
Abstract We consider f (Q) extended symmetric teleparallel cosmologies, where Q is the non-metricity scalar, and constrain its functional form through the order reduction method. By using this technique, we are able to reduce and integrate the field equations and thus to select the corresponding models giving rise to bouncing cosmology. The selected Lagrangian is then used to develop the Hamiltonian formalism and to obtain the Wave Function of the Universe which suggests that classical observable universes can be recovered according to the Hartle Criterion.
1 Introduction The gravitational interaction, described by Einstein’s General Relativity (GR), is the only fundamental force escaping a formulation according to Quantum Field Theory. After many attempts, the difficulty of quantizing gravity arose for several reasons. For instance, there are no techniques able to delete the divergences occurring in the two-loop effective action, so that the theory turns out to be renormalizable just up to one-loop level. In any case, there is also a lack in the quantum side because, in view of Quantum Gravity, the metric tensor should act both as a fundamental field and as the background. This makes the construction of a theory of Quantum Gravity very difficult starting from fundamental concepts. On the other hand, as widely demonstrated during the last decades, quantum corrections play a crucial role at infrared and ultraviolet scales, providing a fundamental contribution toward the explanation of late and early universe behavior. For example, the Big Bang theory suffers the initial singularity problem: spacetime should enucleate from “nothing” with deep conceptual issues related to this statement. Despite the lack of a final theory of Quantum Gravity, we can still fix some issues by considering the applications to cosmology. The approach consists in deriving dynamical quantum systems related to cosmological models and testable, in principle, by means of observations. This is not the full Quantum Gravity, but it is a workable scheme toward it. For example, from the Loop
a e-mail: [email protected] b e-mail: [email protected] c e-mail: [email protected] (corresponding author)
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Quantum Cosmology (LQC), it is possible to get bouncing solutions, according to which the universe might cyclically undergo an accelerated expansion followed by a contraction [1–6]. Specifically, the Big Bou
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