de Sitter spacetime: effects of metric perturbations on geodesic motion

Bini, Donato; Esposito, Giampiero; Geralico, Andrea

doi:10.1007/s10714-011-1287-2

Cited by 7 publications

(6 citation statements)

References 32 publications

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“…Einstein's equations are thus linearized about the chosen background. However, the standard cosmological model is formulated in terms of a Friedmann flat metric equipped with a positive cosmological constant Λ. Gravitational wave perturbation equations have been obtained and solved in [10] by using Fourier transform in the static patch of a de Sitter universe. Their equations show that effects due to Λ on these equations are negligible.…”

Section: Introductionmentioning

confidence: 99%

“…From the reasonings above, the necessity is thus evident for a deep understanding of the features of gravitational waves in a cosmological context. The usual approach [3][4][5][6][7][8][9][10] in terms of tensorial spherical harmonics has proved very succesful for studying perturbations of static and stationary spherical stars and black holes and studying the spectrum of frequencies of quasi-normal modes in terms of the famous Regge-Wheeler and Zerilli master equations. In a cosmological context [18,19], in order to study the spectrum of primordial inflation, the interest mainly focused on cosmological perturbations.…”

Section: Introductionmentioning

confidence: 99%

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Axial and polar gravitational wave equations in a de Sitter expanding universe by Laplace transform

Viaggiu

2017

Class. Quantum Grav.

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In this paper we study the propagation in a de Sitter universe of gravitational waves generated by perturbating some unspecified spherical astrophysical object in the frequencies domain. We obtain the axial and polar perturbation equations in a cosmological de Sitter universe in the usual comoving coordinates, the coordinates we occupy in our galaxy. We write down the relevant equations in terms of Laplace transform with respect to the comoving time t instead of the usual Fourier one that is no longer available in a cosmological context. Both axial and polar perturbation equations are expressed in terms of a non trivial mixture of retarded-advanced metric coefficients with respect to the Laplace parameter s (complex translation). The axial case is studied in more detail. In particular, the axial perturbations can be reduced to a master linear second-order differential equation in terms of the Regge-Wheeler function Z where a coupling with a retarded Z with respect to the cosmological time t is present. It is shown that a de Sitter expanding universe can change the frequency ω of a gravitational wave as perceived by a comoving observer. The polar equations are much more involved. Nevertheless, we show that also the polar perturbations can be expressed in terms of four independent integrable differential equations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Axial and polar gravitational wave equations in a de Sitter expanding universe by Laplace transform

Viaggiu

2017

Class. Quantum Grav.

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“…Closed-form (i.e. the so-called Liouvillian) solutions of the radial equation were discussed in [7] by means of the Kovacic algorithm [16].…”

Section: Singular Polynomial Solutions To the Radial Equationmentioning

confidence: 99%

“…4 Three-term recurrence relation and the radial eigenvalue problemIn this section we present analytic solution to the radial equation on 0 ≤ r ≤ r H . By the substitutionR(r) = Q − s+1 2 Y (r),(4.16)one can convert the radial equation into the normal Schrödinger form[7]…”

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confidence: 99%

Analytic solutions of the Teukolsky equation for massless perturbations of any spin in de Sitter background

Zhang

2020

Preprint

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We present analytic solutions to the Teukolsky equation for massless perturbations of any spin in the 4-dimensional de Sitter background. The angular part of the equation fixes the separation constant to a discrete set and its solution is given by hypergeometric polynomials. For the radial part, we derive analytic power series solution which is regular at the poles and determine a transcendental function whose zeros give the characteristic values of the wave frequency. We study the existence of explicit polynomial solutions to the radial equation and obtain two classes of singular closed-form solutions, one with discrete wave frequencies and the other with continuous frequency spectra.

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“…The background is de-Sitter spacetime in slicing such that the spatial section is a 3-sphere. In the previous works mostly the case K = 0 wre investigated extensively [1][2][3][4][5]. Even though in some works K is not fixed for demonstrating the general field equations, but for solving them usually K = 0 is imposed [6,7].…”

Section: Introductionmentioning

confidence: 99%