Inhomogeneous compact extra dimensions and de Sitter cosmology
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Regular Article - Theoretical Physics
Inhomogeneous compact extra dimensions and de Sitter cosmology Kirill A. Bronnikov1,2,3,a , Arkady A. Popov4,b , Sergey G. Rubin3,4,c 1
VNIIMS, Ozyornaya ul. 46, Moscow 119361, Russia Institute of Gravitation and Cosmology, RUDN University, ul. Miklukho-Maklaya 6, Moscow 117198, Russia 3 National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe shosse 31, Moscow 115409, Russia 4 N. I. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, Kremlevskaya Street 18, Kazan 420008, Russia
2
Received: 8 July 2020 / Accepted: 12 October 2020 © The Author(s) 2020
Abstract In the framework of multidimensional f (R) gravity, we study the possible metrics of compact extra dimensions assuming that our 4D space has the de Sitter metric. Manifolds described by such metrics could be formed at the inflationary and even higher energy scales. It is shown that in the presence of a scalar field, it is possible to obtain a variety of inhomogeneous metrics in the extra factor space M2 . Each of these metrics leads to a certain value of the 4D cosmological constant Λ4 , and in particular, it is possible to obtain Λ4 = 0, as is confirmed by numerically obtained solutions. A nontrivial scalar field distribution in the extra dimensions is an important feature of this family of metrics. The obtained solutions are shown to be stable under extradimensional perturbations.
1 Introduction The idea of extra dimensions is widely used for explanation of a variety of phenomena, such as the physics beyond the Standard Model, cosmological scenarios including inflationary models and the origin of the dark components of the Universe, etc. [1–4]. Sometimes extra dimensions are endowed with scalar fields and antisymmetric form fields to stabilize their metric. There are models where the Casimir effect is taken into account [5,6]. Thus inclusion of extra dimensions is a promising background for the physics below ∼ 10 TeV. At the same time, it is usually assumed that the Universe has been nucleated due to quantum processes at very high energies [7–10]. The metric of our Universe and the fields inside the horizon experience strong quantum fluctuations that could affect their dynamics and their final states at low energies [11,12], including the shape of extra dimensions. a e-mail:
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In this paper, we study the possible influence of a matter field on the metric of extra dimensions. Previous results concerning multidimensional gravity with 4D Minkowski factor space are published in [13–17], where the importance of inhomogeneous extra dimensions was discussed. In particular, the scalar field localization on deformed extra space. Here we extend the same idea to a more general case, the 4D de Sitter metric with an arbitrary Hubble parameter. Such a metric is approximately realized at the inflationary stage and can be valid up to Planck ener
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