Real scalar field scattering in the nearly extremal Schwarzschildben de Sitter space

Reasonable approximations are introduced to investigate the real scalar field scattering in the nearly extremal Schwarzschild--de Sitter (SdS) space. The approximations naturally lead to the invertible x(r) and the global replacement of the true potential by a P?shl--Teller one. Meanwhile, the Schr?dinger-like wave equation is transformed into a solvable form. Our numerical solutions to the wave equation show that the wave is characteristically similar to the harmonic under the tortoise coordinate x, while the wave piles up near the two horizons and the wavelength tends to its maximum as the potential approaches to the peak under the radial coordinate r.     

A new vacuum state in de Sitter space

We present a new vacuum state which can be defined in a region of de Sitter space. This region corresponds to a K=?1 Robertson-Walker coordinatization of de Sitter space. The renormalized expectation value of the stress tensor for the conformally invariant massless scalar field in this vacuum is evaluated, and is found to differ from the corresponding result in the usual de Sitter-invariant vacuum by the absence of a pure radiation term. We also indicate that this can be accounted for by regarding the de Sitter-invariant vacuum as a thermal state relative to the new vacuum.     

On the stability of a self-similar spherical bubble of a scalar Higgs field in de Sitter space

An exact generalized discontinuous solution of the spherical-bubble type is obtained for a scalar Higgs field in de Sitter space. It is shown that the radius of such a generalized bubble evolves in accordance with one of the exact solutions to a dynamical problem considered previously for the bubble radius in the thin-wall approximation, where the bubble-wall thickness is negligible in relation to the bubble radius. Both the generalized solution and the self-similar bubble-type solution that was obtained earlier for the Higgs field in de Sitter space are studied for stability: it is shown that the former is stable, while the latter is unstable in this space. A physical interpretation of the reasons for the instability of the self-similar solution is given.     

Scalar massless field in de Sitter space

A method for quantizing a scalar massless field in the de Sitter space is demonstrated; the method is based on the conformai invariance of the field equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 19–24, July, 1972.The author would like to thank Professor N. A. Chernikov for his aid and É. A. Tagirov for helpful criticism.     

CPT groups for spinor field in de Sitter space

A group structure of the discrete transformations (parity, time reversal and charge conjugation) for spinor field in de Sitter space are studied in terms of extraspecial finite groups. Two CPT groups are introduced, the first group from an analysis of the de Sitter–Dirac wave equation for spinor field, and the second group from a purely algebraic approach based on the automorphism set of Clifford algebras. It is shown that both groups are isomorphic to each other.     

de Sitter branes with a bulk scalar

We propose new brane world models arising from a scalar field in the bulk. In these examples, the induced on-brane line element is de Sitter (or anti de Sitter) and the bulk (five dimensional) Einstein equations can be exactly solved to obtain warped spacetimes. The solutions thus derived are single and two-brane models—one with thin branes while the other one of the thick variety. The field profiles and the potentials are obtained and analysed for each case. We note that for the thick brane scenario the field profile resembles a kink, whereas for one or more thin branes, it is finite and bounded in the domain of the extra dimension. We have also addressed the localisation of gravity and other matter fields on the brane for these braneworld models.     

Real scalar field scattering in the nearly extremal Schwarzschild de Sitter space

Reasonable approximations are introduced to investigate the real scalar field scattering in the nearly extremal Schwarzschild-de Sitter (SdS) space.The approximations naturally lead to the invertible x(r) and the global replacement of the true potential by a Pshl-Teller one.Meanwhile,the Schrdinger-like wave equation is transformed into a solvable form.Our numerical solutions to the wave equation show that the wave is characteristically similar to the harmonic under the tortoise coordinate x,while the wave piles up near the two horizons and the wavelength tends to its maximum as the potential approaches to the peak under the radial coordinate r.     

Effective potential for quantum scalar fields in a de Sitter geometry

We study the quantum theory of an O(N) scalar field on de Sitter geometry at leading order in a nonperturbative 1/N expansion. This resums the infinite series of so-called superdaisy loop diagrams. We obtain the de Sitter symmetric solutions of the corresponding, properly renormalized, dynamical field equations and compute the complete effective potential. Because of its self-interactions, the field acquires a strictly positive square mass which screens potential infrared divergences. Moreover, strongly enhanced ultralong-wavelength fluctuations prevent the existence of a spontaneously broken symmetry state in any dimension.     

Adiabatic regularization and Green's function of a scalar field in de Sitter space: Positive energy spectrum and no trace anomaly

In the conventional adiabatic regularization the vacuum ultraviolet divergences of a quantum field in curved spacetime are removed by subtracting the k-mode of the stress tensor to the 4 th-order.For a scalar field in de Sitter space,we find that the4 th-order regularized spectral energy density is negative.Moreover,the 2 nd-order regularization for minimal coupling(ξ=0)and the 0 th-order regularization for conformal coupling(ξ=1/6) yield a positive and UV-convergent spectral energy density and power spectrum.The regularized stress tensor in the vacuum is maximally symmetric and can drive inflation,while its k-modes representing the primordial fluctuations are nonuniformly distributed.Conventional regularization of a Green's function in position space is generally plagued by a log IR divergence.Only in the massless case with ξ=0 or 1/6,we can directly regularize the Green's functions and obtain vanishing results that agree with the adiabatic regularization results.In this case,the regularized power spectrum and stress tensor are both zero,and no trace anomaly exists.To overcome the log IR divergence problem in the massive cases with ξ=0 and 1/6,we perform Fourier transformation of the regularized power spectra and obtain the regularized analytical Green's functions which are IR-and UV-convergent.     

Adiabatic invariants and scalar fields in a de Sitter space-time

The method of adiabatic invariants for time dependent Hamiltonians is applied to a massive scalar field in a de Sitter space-time. The scalar field ground state, its Fock space and coherent states are constructed and related to the particle states. Diverse quantities of physical interest are illustrated and compared with previous results.     

Gaupta-Bleuler triplet for massless spin-3/2 field in de Sitter space

Physicists have been interested in quantization of spinor and vector free fields in 4-dimensional de Sitter space-time,in ambient space notation.The Gupta-Bleuler formalism has been extensively applied to the quantization of gauge invariant theories.The field equation of the massless spin-3/2 fields is gauge invariant in de Sitter space.In this paper,we study the quantization of massless spin-3/2 gauge fields in de Sitter space-time by the Gupta-Bleuler formalism.This triplet carries an indecomposable representation of the de Sitter group.     

Possible types of the evolution of vacuum shells around the de Sitter space

All possible evolution scenarios of a thin vacuum shell surrounding the spherically symmetric de Sitter space have been determined and the corresponding global geometries have been constructed. Such configurations can appear at the final stage of the cosmological phase transition, when isolated regions (islands) of the old vacuum remain. The islands of the old vacuum are absorbed by the new vacuum, expand unlimitedly, or form black holes and wormholes depending on the sizes of the islands as well as on the density and velocity of the shells surrounding the islands.