Global existence of the scalar field in de Sitter spacetime

Yagdjian, Karen

doi:10.1016/j.jmaa.2012.06.020

Cited by 54 publications

(46 citation statements)

References 26 publications

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“…On the other hand, the important case of n = 3 and the quadratic nonlinearity is not covered. We note here that their results as well as Theorem 0.2 of the present paper, neither prove nor disprove the following conjecture from the article [34].…”

Section: Condition (L)contrasting

confidence: 69%

“…In [32]- [34] a global existence of small data solutions of the Cauchy problem for the semilinear Klein-Gordon equation and systems of equations in the de Sitter space-time with flat time slices, that is, σ ij (x) = δ ij , is proved. The nonlinearity F was assumed Lipschitz continuous with exponent α ≥ 0 (see definition below).…”

Section: ])mentioning

confidence: 99%

“…For n = 3 the mass m interval (0, √ 2) is called the Higuchi bound in quantum field theory [18]. The proof of the global existence in [32]- [34] is based on the special integral representations (see Section 1) and L p − L q estimates.…”

Section: ])mentioning

confidence: 99%

“…In the present paper we are going to extend the small data global existence result of [34] for the spatially flat de Sitter space-time to the de Sitter space-time with the time slices being Riemannian manifolds.…”

Section: ])mentioning

confidence: 99%

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Global in time existence of self-interacting scalar field in de Sitter spacetimes

Galstian

Yagdjian

2017

Nonlinear Analysis: Real World Applications

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We prove the existence of a global in time solution of the semilinear Klein-Gordon equation in the de Sitter space-time. The coefficients of the equation depend on spatial variables as well, that make results applicable to the space-time with the time slices being Riemannian manifolds. IntroductionIn this paper we prove the existence of a global in time solution of the semilinear Klein-Gordon equation in the de Sitter space-time. The coefficients of the equation depend on spatial variables as well, that make results applicable to the space-time with the time slices being Riemannian manifolds. In the spatially flat de Sitter model, these slices are R 3 , while in the spatially closed and spatially open cases these slices can be the three-sphere S 3 and the three-hyperboloid H 3 , respectively (see, e.g., [12, p.113]).The metric g in the de Sitter space-time is defined as follows, g 00 = g 00 = −1, g 0j = g 0j = 0, g ij (x, t) = e 2t σ ij (x), i, j = 1, 2, . . . , n, where n j=1 σ ij (x)σ jk (x) = δ ik , and δ ij is Kronecker's delta. The metric σ ij (x) describes the time slices. In the quantum field theory the matter fields are described by a function ψ that must satisfy equations of motion. In the case of a massive scalar field, the equation of motion is the semilinear Klein-Gordon equation generated by the metric g:Here m is a physical mass of the particle. In physical terms this equation describes a local selfinteraction for a scalar particle. A typical example of a potential function would be V (ψ) = ψ 4 . The semilinear equations are also commonly used models for general nonlinear problems.The covariant Klein-Gordon equation in the de Sitter space-time in the coordinates is

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Section: Condition (L)contrasting

confidence: 69%

Section: ])mentioning

confidence: 99%

Section: ])mentioning

confidence: 99%

Section: ])mentioning

confidence: 99%

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Global in time existence of self-interacting scalar field in de Sitter spacetimes

Galstian

Yagdjian

2017

Nonlinear Analysis: Real World Applications

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“…Turning back to the initial value problem (1), the small data global existence result is proved by Yagdjian [8] in Sobolev space…”

Section: Introductionmentioning

confidence: 99%

Approximate solutions to the nonlinear Klein-Gordon equation in de Sitter spacetime

Yazici

Şengül

2016

Open Physics

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Numerical results for the Klein‐Gordon equation in de Sitter spacetime

Selvi̇topi̇

Yazici

2018

Math Methods in App Sciences

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We consider the initial value problem for the Klein‐Gordon equation in de Sitter spacetime. We use the central difference scheme on the temporal discretization. We also discretize the spatial variable using the finite element method with implicit and the Crank‐Nicolson schemes for the numerical solution of the initial value problem. In order to show the accuracy for the results of the solutions, we also examine the finite difference methods. We observe that the numerical results obtained by using these methods are compatible.

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Global existence of the scalar field in de Sitter spacetime

Cited by 54 publications

References 26 publications

Global in time existence of self-interacting scalar field in de Sitter spacetimes

Global in time existence of self-interacting scalar field in de Sitter spacetimes

Approximate solutions to the nonlinear Klein-Gordon equation in de Sitter spacetime

Numerical results for the Klein‐Gordon equation in de Sitter spacetime

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