Interaction of the generalized Duffin–Kemmer–Petiau equation with a non-minimal coupling under the cosmic rainbow gravity

Abstract

In this study, we survey the generalized Duffin–Kemmer–Petiau oscillator containing a non-minimal coupling interaction in the context of rainbow gravity in the presence of the cosmic topological defects in space-time. In this regard, we intend to investigate relativistic quantum dynamics of a spin-0 particle under the modification of the dispersion relation according to the Katanaev–Volovich geometric approach. Thus, based on the geometric model, we study the aforementioned bosonic system under the modified background by a few rainbow functions. In this way, by using an analytical method, we acquire energy eigenvalues and corresponding wave functions to each scenario. Regardless of rainbow gravity function selection, the energy eigenvalue can present symmetric, anti-symmetric, and symmetry breaking characteristics. Besides, one can see that the deficit angular parameter plays an important role in the solutions.

PDM KG-Coulombic particles in cosmic string rainbow gravity spacetime and a uniform magnetic field

“…Rainbow gravity (RG) has attracted research attention over the years [1][2][3][4][5] as a semi-classical extension of the deformed/doubly special relativity into general relativity (GR). It suggests that the energy of the probe particles affects the spacetime background, at the ultra-high energy regime, and the spacetime metric becomes energy-dependent [5][6][7][8][10][11][12][13][14][15][16][17][18]. That is, a cosmic string spacetime metric (in the natural units c = = G = 1)…”

PDM KG-oscillators in cosmic string rainbow gravity spacetime in a non-uniform magnetic field

“…In quantum gravity (QG), the semi-classical model of rainbow gravity (RG) (an extension of the deformed or doubly special relativity into a general relativity (GR) framework) has attracted research attention over the years [1][2][3][4][5]. Under the RG-model, the energy of the probe particles is assumed to affect the spacetime background, at the ultra-high energy regime, so that the spacetime metric become an energy-dependent one [5][6][7][8][9][10][11][12].…”

“…In quantum gravity (QG), the semi-classical model of rainbow gravity (RG) (an extension of the deformed or doubly special relativity into a general relativity (GR) framework) has attracted research attention over the years [1][2][3][4][5]. Under the RG-model, the energy of the probe particles is assumed to affect the spacetime background, at the ultra-high energy regime, so that the spacetime metric become an energy-dependent one [5][6][7][8][9][10][11][12]. Hereby, the Planck energy E p = c 5 /G plays the role of a threshold separating the classical description from the quantum mechanical one and introduces itself as another invariant energy scale alongside the speed of light.…”

“…For example, in a cosmic string spacetime background in rainbow gravity, Bezzerra et al [8] have studied Landau levels via Schrödinger and KG equations, Bakke and Mota [33] have studies the Dirac oscillator, they have also studied the Aharonov-Bohm effect [34]. Hosseinpour et al [5] have studied the DKP-particles,, Sogut et al [11] have studied the quantum dynamics of photon, and Kangal et al [12] have studied KG-particles in a topologically trivial Gödel-type spacetime in rainbow gravity. In the current proposal, however, we extend such studies to include position-dependent mass (PDM) settings.…”

“…with a constant α related to the deficit angle of the conical spacetime and defined as α = 1 − 4Gµ, where G is the Newton's constant and µ is the linear mass density of the cosmic string so that α < 1. This would suggest that the cosmic string metric (5) in the rainbow gravity takes the energy-dependent form…”