Semi-Analytical Solution of Dirac Equation in Schwarzschild-de Sitter Spacetime

In the present paper, we solve the radial parts of Dirac equation between the inner and the outer horizon in the Schwarzschild-de Sitter (SdS for short) geometry. Complete physical parameter space is divided into two regions depending on the height of the potential barrier and the energy of the incoming particle. In each region, we concentrate on two limiting cases. The first case is when the two horizons are close to each other and the second case is when the horizons are far apart. In each case, we give the semi-analytical solution by using WKB (Wentzel-Krames-Brillouin) approximation and show the instantaneous reflection and transmission coefficients as well as the radial wave functions graphically. PACS: 04.20.-q, 04.70.-s, 04.70.Dy, 95.30.Sf     

Separability of Dirac equation in higher dimensional Kerr–NUT–de Sitter spacetime

It is shown that the Dirac equations in general higher dimensional Kerr–NUT–de Sitter spacetimes are separated into ordinary differential equations.     

Surface vacuum energy and stresses for a brane in de Sitter spacetime

Vacuum expectation values of the surface energy–momentum tensor is investigated for a massless scalar field obeying mixed boundary condition on a brane in de Sitter bulk. To generate the corresponding vacuum surface densities we use the conformal relation between de Sitter and Rindler spacetimes.     

Dirac wave equation in the de Sitter universe

We present and discuss the Dirac wave equation in the de Sitter universe. This equation is obtained by factoring the second-order Casimir invariant operator associated to the Fantappié-de Sitter group.     

Dirac Fields in 3D de Sitter Spacetime

We show that the Dirac equation is separable in the circularly symmetric metric in three dimensions and when the background spacetime is de Sitter we find exact solutions to the radial equations. Using these results we show that the de Sitter horizon has a cross section equal to zero for the massless Dirac field, as in the case of the scalar field. Also, using the improved brick wall model we calculate the fermionic entropy associated with the de Sitter horizon and we compare it with some results previously published.     

Renormalized entropies in a de Sitter spacetime

The quantum entropies due to the scalar and Dirac fields are investigated in a pure de Sitter spacetime. The leading divergent terms in both cases are regularized by the Pauli-Villars scheme. It is shown that the explosive entropies can be renormalized according to the Bekenstein-Hawking formula.     

Gravitational waves generated during inflation from a 5D vacuum theory of gravity in a de Sitter expansion

In this Letter we study the generation of gravitational waves during inflation from a 5D vacuum theory of gravity. Within this formalism, on an effective 4D de Sitter background, we recover the typical results obtained with 4D inflationary theory in general relativity, for the amplitude of gravitational waves generated during inflation. We also obtain a range of values for the amplitude of tensor to scalar ratio which is in agreement with COBE observations.     

Dirac equation in curved spacetime with the metric in the Kerr-Schield form

The solution of the Dirac equation in the wave package form in a slightly curved spacetime (compared with the size of the wave package) was studied. For the metric in the Kerr-Schield form, a system of common differential equations describing spin conditions of massive neutral Dirac particles (neutrinos) was obtained. The effect of depolarization of the massive neutrinos in a gravitational field are discussed. This effect allows a considerable similarity between the theoretical and observed solar neutrino flows to be established if $m_{\nu _e } \geqslant 10^{ - 4} $ .     

Unification and hierarchy from 5D anti-de Sitter space

We show that perturbative high scale unification and a solution to the hierarchy problem are possible with extra dimensions in the context of the warped geometry of 5D anti-de Sitter space ( AdS(5)). This is possible because the couplings for bulk gauge bosons run logarithmically below the AdS(5) curvature scale. The calculation is done in five dimensions, rather than in the effective theory, which is strongly coupled above the TeV scale.     

Economic models for Dirac neutrinos in grand unified theories

It is shown that dimension five non-renormalizable interactions can produce light Dirac neutrinos in an extension of the minimal SU(5) GUT containing additional SU(5) singlets and global U(1) symmetries.     

Cosmological imprints of Dirac neutrinos in a keV-vacuum 2HDM

The Dirac neutrino masses could be simply generated by a neutrinophilic scalar doublet with a vacuum being dramatically different from the electroweak one. While the case with an eV-scale vacuum has been widely explored previously, we exploit in this work the desert where the scalar vacuum is of begin{document}$mathcal{O}(mathrm{keV})$end{document} scale. In this regime, there would be rare hope to probe the keV-vacuum neutrinophilic scalar model via the lepton-flavor-violating processes, which makes it distinguishable from the widely considered eV-scale vacuum. Although such a keV-vacuum scenario is inert in the low-energy flavor physics, we show that the baryogenesis realized via the lightest Dirac neutrino can be a natural candidate in explaining the baryon asymmetry of the Universe. Furthermore, the Dirac neutrinos with a keV-vacuum scalar can generate a shift of the effective neutrino number within the range begin{document}$0.097leqslant Delta N_{rm eff}leqslant 0.112$end{document}, which can be probed by the future Simons Observatory experiments. In particular, the model with a minimal value begin{document}$Delta N_{rm eff}=0.097$end{document} can already be falsified by the future CMB Stage-IV and Large Scale Structure surveys, providing consequently striking exploratory avenues in the cosmological regime for such a keV-vacuum scenario.     

Quintessential inflation from a variable cosmological constant in a 5D vacuum

We explore an effective 4D cosmological model for the universe where the variable cosmological constant governs its evolution and the pressure remains negative along all the expansion. This model is introduced from a 5D vacuum state where the (space-like) extra coordinate is considered as noncompact. The expansion is produced by the inflaton field, which is considered as nonminimally coupled to gravity. We conclude from experimental data that the coupling of the inflaton with gravity should be weak, but variable in different epochs of the evolution of the universe.