The 6D Standing Wave Braneworld with Real Scalar Field
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PARTICLES AND FIELDS
The 6D Standing Wave Braneworld with Real Scalar Field Pavle Midodashvili1
· Levan Midodashvili2
Received: 15 June 2020 / Accepted: 7 September 2020 / Published online: 25 September 2020 © Sociedade Brasileira de F´ısica 2020
Abstract We introduce new non-static 6D braneworld model involving real 6D scalar field as the source of gravity. The brane is generated by the standing waves of gravity and real scalar field oscillating in the bulk. The oscillations are out of phase in time, so that the oscillation energy transfers back and forth between the standing waves of gravity and real scalar field. Underlying geometry of 6D spacetime has no horizons, the brane has one internal (on-brane) extra dimension which is compact and sufficiently small to describe our universe (hybrid compactification), and there is also one external to brane (off-brane) extra dimension, which is large or even infinite for the observers on the brane. We show that there are two different physical limits realizing the trapping of classical particles and light and also of massless scalar fields on the brane. In the first one, the amplitude of standing waves must be sufficiently large, while in the second one the amplitude of standing waves can be small enough. We show that in both cases particles and light, as well as massless scalar fields, are dynamically trapped on the brane by the pressure of bulk standing waves of gravity and real scalar field. Keywords Brane · Standing waves · Trapping of particles · Zero modes
1 Introduction Braneworld models with large extra dimensions [1–6] are very useful in addressing several insoluble problems in high energy physics (the hierarchy problem, the nature of flavor, etc.) (for reviews, see [7–10]). Most of the braneworlds are realized as static configurations, but there are also dynamical models, appearing mainly in cosmological studies, which involve time-dependent metrics and source matter fields, as well as branes with tensions varying in time [11–14]. One of the 5D braneworld models with non-stationary metric was proposed in [15–18] and was subsequently generalized to 6D in [19, 20]. In these models, the brane is generated by standing gravitational waves coupled to a phantom-like bulk scalar field, and rapid oscillations of these waves provide universal gravitational trapping of zero modes of all kinds of matter fields on the Pavle Midodashvili
[email protected] Levan Midodashvili [email protected] 1
Ilia State University, 3/5 Cholokashvili Ave., Tbilisi, Georgia
2
Gori State Teaching University, 53 Chavchavadze Ave., Gori, Georgia
brane [20–25]. Later in [26] it was introduced another nonstationary 5D anisotropic braneworld generated by standing waves of the gravitational and real scalar field, instead of the phantom-like scalar fields of [15–20]. The metric of this model has horizon in the bulk, and in the case of small amplitudes of standing waves matter is actually trapped on the brane of the width equal to the horizon size, while in the case of large amplitudes
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