Cosmological Scenarios with Bounce and Genesis in Horndeski Theory and Beyond
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ibution for the JETP special issue in honor of I. M. Khalatnikov’s 100th anniversary
Cosmological Scenarios with Bounce and Genesis in Horndeski Theory and Beyond V. E. Volkovaa,*, S. A. Mironova,b,c,**, and V. A. Rubakova,d,*** a
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, 117312 Russia Institute for Theoretical and Mathematical Physics, Moscow State University, Moscow, 119991 Russia c Alikhanov Institute for Theoretical and Experimental Physics, Moscow, 117218 Russia d Physics Faculty, Moscow State University, Moscow, 119991 Russia *e-mail: [email protected] **e-mail: [email protected] ***e-mail: [email protected]
b
Received June 4, 2019; revised June 7, 2019; accepted June 8, 2019
Abstract—This essay is a brief review of the recent studies of non-singular cosmological scenarios with bounce and Genesis and their stability in a subclass of scalar–tensor theories with higher derivatives—beyond Horndeski theories. We discuss the general results of stability analysis of the nonsingular cosmological solutions in beyond Horndeski theories, as well as other closely related topics: 1) the no-go theorem, which is valid in the general Horndeski theories but not in their extensions, 2) singularities in disformal transformations relating beyond Horndeski theories with general ones, 3) healthy behavior of the scalar sector in the unitary gauge despite divergencies of coefficients in the quadratic action for perturbations (“γ-crossing”). We describe several specific examples of bouncing cosmologies and models with Genesis epoch which have neither ghosts nor gradient instabilities among the linearized perturbations about the homogeneous isotropic background during entire evolution. DOI: 10.1134/S1063776119100236
1. INTRODUCTION Cosmological scenarios with the bouncing or Genesis stage serve as possible extensions of the standard hot Big Bang theory. In both of these scenarios, spacetime has vanishing 4D curvature at early times, i.e., the Hubble parameter and its time derivatives take on small values. The bouncing model implies that the Universe undergoes a contracting stage at early times, which terminates at some moment of time (the bounce) and the Universe transits to the expansion epoch (see [1–3] for reviews). The Genesis scenario describes the accelerated expansion of the Universe from the asymptotically empty Minkowski space: the energy density of exotic matter, which drives the evolution during the Genesis epoch, grows in time, and so does the expansion rate (the Hubble parameter); at some stage, when the energy density and Hubble parameter have grown sufficiently large, the energy of the exotic matter gets transformed into heat, so that the Universe transits to the standard hot stage [4, 5]. The specific feature of both scenarios is the absence of initial singularity, whose inevitable pres-
ence in the hot Big Bang theory has not been overcome even with the invention of inflation [6, 7]. In fact, non-singular cosmologies with bounce or Genesis may be equally
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