Cosmological Solutions in the Tensor-Multi-Scalar Theory of Gravity with the Higgs Potential
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Cosmological Solutions in the Tensor-Multi-Scalar Theory of Gravity with the Higgs Potential K. A. Bolshakova1 and S. V. Chervon1, 2, 3* 1
Laboratory of Gravitation, Cosmology and Astrophysics, Ulyanovsk State Pedagogical University, pl. Lenina 4/5, Ulyanovsk, 432071, Russia 2 Department of Physics, N. Bauman Moscow State Technical University, 2nd Baymanskaya ul. 5, str. 1, Moscow, 105005, Russia 3 Institute of Physics, Kazan Federal University, Kremlyovskaya ul. 18, Kazan, 420008, Russia Received February 9, 2020; revised February 19, 2020; accepted February 26, 2020
Abstract—We consider a generalization of Higgs inflation, based on cosmology of general relativity (GR), to the case of a two-field model of the tensor-multiscalar theory of gravity (TMS TG). Cosmological solutions are found in the case where a scalar field with the Higgs potential, as a source of TMS TG is in the slow-rolling mode. Solutions with power and exponential-power-law evolution of the scale factor are obtained for various limiting forms of the Higgs potential. DOI: 10.1134/S0202289320020048
1. INTRODUCTION An important role in the development of modern cosmology belongs to the inflationary stage in the early epoch of the Universe evolution, which has become a necessary feature of the Big Bang model, which leads to a solution of many problems of the Friedmannian standard cosmology, including the problems of the horizon, flatness and large scale structure formation. The models of cosmological inflation are usually based on the consideration of Einstein’s gravity, minimally coupled to a self-interacting scalar field [1]. The field characteristics, including its mass and the shape of its potential, determine the type of the phenomenological model that must necessarily lead to agreement with the observational data. However, quite often the questions of the shape of the potential and the physical essence of the scalar field itself do not receive a sufficient justification from the standpoint of fundamental physics. An important exception is the nonminimal Higgs inflation proposed by Bezrukov and Shaposhnikov [2] in 2008. For many researchers, this work has served as a starting point for further extensions of the model, such as Higgs inflation with a dilaton [3, 4], hybrid Higgs inflation [5], brane inflation with a Higgs potential [6], Higgs inflation with a scalar [7]. It should be noted that the concept of a “scalaron” was introduced in the Starobinsky model [8] (reliably consistent with *
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the observational data) in his scenario in the framework of modified R + R2 gravity. Thus we notice a tendency to introduce additional scalar fields into consideration, which is connected with the necessity to eliminate the contradiction with experiments on the electroweak interactions [9, 10]. The inclusion of additional fields into consideration leads to the idea to investigate the multi-field theory of gravity [11] (or the chiral cosmological model [12]), which is similar to the tensor-multiscalar theory of gravity. One should note the possi
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