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     

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.     

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.     

5D Dirac Equation in Induced-Matter Theory

According to an induced-matter approach, Liu and Wesson obtained the rest mass of a typical particle from the reduction of a 5D Klein–Gordon equation to a 4D one. Introducing an extra-dimension momentum operator identified with the rest mass eigenvalue operator, we consider a way to generalize the 4D Dirac equation to 5D. An analogous normal Dirac equation is gained when the generalization reduces to 4D. We find the rest mass of a particle in curved space varies with spacetime coordinates and check this for the case of exact solitonic and cosmological solution of the 5D vacuum gravitational field equations.     

Super-exponential inflation from a dynamical foliation of a 5D vacuum state

We introduce super-exponential inflation (ω<−1) from a 5D Riemann-flat canonical metric on which we make a dynamical foliation. The resulting metric describes a super accelerated expansion for the early universe well known as super-exponential inflation that, for very large times, tends to an asymptotic de Sitter (vacuum dominated) expansion. The scalar field fluctuations are analyzed. The important result here obtained is that the spectral index for energy density fluctuations is not scale invariant, and for cosmological scales becomes ns(k<k_?)?1. However, for astrophysical scales this spectrum changes to negative values ns(k>k_?)<0.