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Register a new userGlobal in Time Existence of Self-Interacting Scalar Field in De Sitter Spacetimes
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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.
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We present a condition on the self-interaction term that guaranties the existence of the global in time solution of the Cauchy problem for the semilinear Klein-Gordon equation in the Friedmann-Lama$hat{i}$tre-Robertson-Walker model of the contracting universe. For the Klein-Gordon equation with the Higgs potential we give a lower estimate for the lifespan of solution.
We investigate the dynamical behavior of a scalar field non-minimally coupled to Einsteins tensor and Ricci scalar in geometries of asymptotically de Sitter spacetimes. We show that the quasinormal modes remain unaffected if the scalar field is massless and the black hole is electrically chargeless. In the massive case, the coupling of both parameters produces a region of instability in the spacetime determined by the geometry and field parameters. In the Schwarzschild case, every solution for the equations of motion with $ell>0$ has a range of values of the coupling constant that produces unstable modes. The case $ell=0$ is the most unstable one, with a threshold value for stability in the coupling. For the charged black hole, the existence of a range of instability in $eta$ is strongly related to geometry parameters presenting a region of stability independent of the chosen parameter.
In this paper, we compute the effective action of both a scalar field and a Dirac spinor field in the global de Sitter space of any dimension $d$ using the in-/out-state formalism. We show that there is particle production in even dimensions for both scalar field and spinor field. The in-out vacuum amplitude $Z_{in/out}$ is divergent at late times. By using dimensional regularization, we extract the finite part of $log Z_{in/out}$ for $d$ even and the logarithmically divergent part of $log Z_{in/out}$ for $d$ odd. We also find that the regularized in-out vacuum amplitude equals the ratio of determinants associated with different quantizations in $AdS_d$ upon the identification of certain parameters in the two theories.
In a recent work the first named author, Levitin and Vassiliev have constructed the wave propagator on a closed Riemannian manifold $M$ as a single oscillatory integral global both in space and in time with a distinguished complex-valued phase function. In this paper, first we give a natural reinterpretation of the underlying algorithmic construction in the language of ultrastatic Lorentzian manifolds. Subsequently we show that the construction carries over to the case of static backgrounds thanks to a suitable reduction to the ultrastatic scenario. Finally we prove that the overall procedure can be generalised to any globally hyperbolic spacetime with compact Cauchy surfaces. As an application, we discuss how, from our procedure, one can recover the local Hadamard expansion which plays a key role in all applications in quantum field theory on curved backgrounds.
Inertial observers in de Sitter are surrounded by a horizon and see thermal fluctuations. To them, a massless scalar field appears to follow a random motion but any attractive potential, no matter how weak, will eventually stabilize the field. We study this thermalization process in the static patch (the spacetime region accessible to an individual observer) via a truncation to the low frequency spectrum. We focus on the distribution of the field averaged over a subhorizon region. At timescales much longer than the inverse temperature and to leading order in the coupling, we find the evolution to be Markovian, governed by the same Fokker-Planck equation that arises when the theory is studied in the inflationary setup.
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