In this paper we consider the Dirac oscillator in the context of Doubly General Relativity or Gravity's Rainbow. In order to obtain the energy levels of the Dirac oscillator, we solve the Dirac equation in the cosmic string spacetime modified by gravity's rainbow scenarios described by two rainbow functions. We then obtain that, as a consequence of the modification of the cosmic string line element by the two rainbow functions, the energy levels of the Dirac oscillator are appreciable altered. The results are plotted and compared with the standard case, without gravity's rainbow effects. * Electronic address: kbakke@fisica.ufpb.br † Electronic address: hmota@fisica.ufpb.br arXiv:1802.08711v2 [gr-qc]

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In this paper, we analyse the bosonic current densities induced by a magnetic flux running along an idealized cosmic string in a high-dimensional spacetime, admitting that the coordinate along the string's axis is compactified. Additionally we admit the presence of an magnetic flux enclosed by the compactification axis. In order to develop this analysis we calculate the complete set of normalized bosonic wave-functions obeying a quasiperiodicity condition, with arbitrary phase β, along the compactified dimension. In this context, only azimuthal and axial currents densities take place. As to the azimuthal current, two contributions appear. The first contribution corresponds to the standard azimuthal current in a cosmic string spacetime without compactification, while the second contribution is a new one, induced by the compactification itself. The latter is an even function of the magnetic flux enclosed by the string axis and is an odd function of the magnetic flux along its core with period equal to quantum flux, Φ 0 = 2π/e. On the other hand, the nonzero axial current density is an even function of the magnetic flux along the core of the string and an odd function of the magnetic flux enclosed by it. We also find that the axial current density vanishes for untwisted and twisted bosonic fields in the absence of the magnetic flux enclosed by the string axis. Some asymptotic expressions for the current density are provided for specific limiting cases of the physical parameter of the model.

In the present paper we investigate the effects caused by the modification of the dispersion relation obtained by solving the Klein-Gordon equation in the closed Einstein's universe in the context of rainbow's gravity models. Thus, we analyse how the quantum vacuum fluctuations of the scalar field are modified when compared with the results obtained in the usual General Relativity scenario. The regularization, and consequently the renormalization, of the vacuum energy is performed adopting the Epstein-Hurwitz and Riemann's zeta functions.

We calculate the total internal energy, total energy density and pressure, and the free energy for the neutrino and electromagnetic fields in Einstein and closed Friedmann cosmological models.The Casimir contributions to all these quantities are separated. The asymptotic expressions for both the total internal energy and free energy, and for the Casimir contributions to them are found in the limiting cases of low and high temperatures. It is shown that the neutrino field does not possess a classical limit at high temperature. As for the electromagnetic field, we demonstrate that the total internal energy has the classical contribution and the Casimir internal energy goes to the classical limit at high temperature. The respective Casimir free energy contains both linear and logarithmic terms with respect to the temperature. The total and Casimir entropies for the neutrino and electromagnetic fields at low temperature are also calculated and shown to be in agreement with the Nernst heat theorem.