Quantum field theory in the de sitter universe

Bros, J.; Gazeau, Jean‐Pierre; Moschella, Ugo

doi:10.1103/physrevlett.73.1746

Cited by 141 publications

(259 citation statements)

References 13 publications

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“…The statistical functionF encodes the in- formation about the actual quantum state of the system. Having in mind an adiabatic switch-on of the interactions, 3 the initial data corresponding to the BunchDavies vacuum are given byF(p,…”

Section: General Setting In the P-representationmentioning

confidence: 99%

“…The maximally symmetric de Sitter space has attracted a great deal of attention both because of its direct relevance for inflationary physics and because it already exhibits the specific features of curved geometries as compared to the flat Minkowski space-time, arising, e.g., from gravitational redshift and particle creation [3][4][5][6][7][8][9][10][11]. Of particular interest is the case of light fields in units of the de Sitter radius, which have no analog in flat space and for which the limit of zero curvature is nonuniform due to nontrivial infrared effects.…”

Section: Introductionmentioning

confidence: 99%

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Infrared dynamics in de Sitter space from Schwinger–Dyson equations

Gautier

Serreau

2013

Physics Letters B

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We study the two-point correlator of an O(N) scalar field with quartic self-coupling in de Sitter space. For light fields in units of the expansion rate, perturbation theory is plagued by large logarithmic terms for superhorizon momenta. We show that a proper treatment of the infinite series of self-energy insertions through the Schwinger-Dyson equations resums these infrared logarithms into power laws. We provide an exact analytical solution of the Schwinger-Dyson equations for infrared momenta when the self-energy is computed at two-loop order. Our findings encompass previously obtained results using either stochastic or Euclidean approaches. The obtained correlator exhibits a rich structure with a superposition of free-field-like power laws. We extract mass and field-strength renormalization factors from the asymptotic infrared behavior. The latter are nonperturbative in the coupling in the case of a vanishing tree-level mass.

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Section: General Setting In the P-representationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Infrared dynamics in de Sitter space from Schwinger–Dyson equations

Gautier

Serreau

2013

Physics Letters B

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“…It is far less obvious that the 2-point function is positive, but this be shown using the following rather elegant and non-trivial representation due to [13,14] (assuming for simplicity a "principal series scalar field" characterized by…”

Section: A) Unruh Effectmentioning

confidence: 99%

Quantum fields in curved spacetime

2015

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We review the theory of quantum fields propagating in an arbitrary, classical, globally hyperbolic spacetime. Our review emphasizes the conceptual issues arising in the formulation of the theory and presents known results in a mathematically precise way. Particular attention is paid to the distributional nature of quantum fields, to their local and covariant character, and to microlocal spectrum conditions satisfied by physically reasonable states. We review the Unruh and Hawking effects for free fields, as well as the behavior of free fields in deSitter spacetime and FLRW spacetimes with an exponential phase of expansion. We review how nonlinear observables of a free field, such as the stress-energy tensor, are defined, as well as timeordered-products. The "renormalization ambiguities" involved in the definition of time-ordered products are fully characterized. Interacting fields are then perturbatively constructed. Our main focus is on the theory of a scalar field, but a brief discussion of gauge fields is included. We conclude with a brief discussion of a possible approach towards a nonperturbative formulation of quantum field theory in curved spacetime and some remarks on the formulation of quantum gravity. Quantum field theory in curved spacetime (QFTCS) is the theory of quantum fields propagating in a background, classical, curved spacetime (M , g). On account of its classical treatment of the metric, QFTCS cannot be a fundamental theory of nature. However, QFTCS is expected to provide an accurate description of quantum phenomena in a regime where the effects of curved spacetime may be significant, but effects of quantum gravity itself may be neglected. In particular, it is expected that QFTCS should be applicable to the description of quantum phenomena occurring in the early universe and near (and inside of) black holesprovided that one does not attempt to describe phenomena occurring so near to singularities that curvatures reach Planckian scales and the quantum nature of the spacetime metric would have to be taken into account.It should be possible to derive QFTCS by taking a suitable limit of a more fundamental theory wherein the spacetime metric is treated in accord with the principles of quantum theory. However, this has not been done-except in formal and/or heuristic ways-simply because no present quantum theory of gravity has been developed to the point where such a well defined limit can be taken. Rather, the framework of QFTCS that we shall describe in this review has been obtained by suitably merging basic principles of classical general relativity with the basic principles of quantum field theory in Minkowski spacetime. As we shall explain further below, the basic principles of classical general relativity are relatively easy to identify and adhere to, but it is far less clear what to identify as the "basic principles" of quantum field theory in Minkowski spacetime. Indeed, many of the concepts normally viewed as fundamental to quantum field theory in Minkowski spacetime, such as Poinca...

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“…These are made trivial in the Minkowski case by the use of momentum-space, but this is not so in the de Sitter space. We restrict at first our attention to the principal series and start by deriving a new general formula expressing the decay probability of a particle which applies to both Minkowski and de Sitter spacetimes in dimension d, where the de Sitter manifold is identified with the hyperboloid {x ∈ R A Klein-Gordon neutral scalar field φ with mass m ≥ 0 is characterized by its two-point vacuum expectation value w m (x, y) = (Ω, φ(x) φ(y)Ω) which is uniquely specified up to a constant factor by requiring invariance, locality, and a suitable spectral condition (having a thermodynamical physical interpretation in the dS case [9,10]). w m allows for the reconstruction of the Fock space of the theory and of a representation of the invariance group whose restriction to the one-particle subspace is irreducible and labeled by m. In the dS case m can be related to a dimensionless parameter ν as follows…”

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confidence: 99%

“…The identification of a conserved energy among these quantities has proven to be useful in classical field theory [15]. The same quantity remains exactly conserved also at the quantum level although it becomes an operator whose spectrum is not positive [9] even when restricted to the region where the corresponding classical expression is positive [15]; the thermodynamical properties of dS fields arise precisely in this restriction [9]. Energy is conserved also in the decay processes that violate mass subadditivity, once the adiabatic limit has been performed.…”

mentioning

confidence: 99%

The lifetime of a massive particle in a de Sitter universe

Bros

Epstein

Moschella³

2008

J. Cosmol. Astropart. Phys.

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We study particle decay in de Sitter space-time as given by first order perturbation theory in an interacting quantum field theory. We show that for fields with masses above a critical mass mc there is no such thing as particle stability, so that decays forbidden in flat space-time do occur there. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is comparable with de Sitter radius. Particles with lower mass are even stranger: The masses of their decay products must obey quantification rules, and their lifetime is zero.Some important progress in the astronomical observations of the last ten years [1,2] have led to the surprising conclusion that the recent universe is dominated by a "dark" exotic form of energy density that acts repulsively at large scales. The simplest and best known candidate for the "dark energy" is the cosmological constant, and the de Sitter geometry, which is the homogeneous and isotropic solution of the cosmological Einstein equations in vacuo, appears to take the double role of reference geometry of the universe, namely the geometry of spacetime deprived of its matter and radiation content and of the geometry that the universe will approach asymptotically.One might think that the presence of a cosmological constant, while having a huge impact on our understanding of the universe as a whole, would not influence microphysics in its quantum aspects. This is also the viewpoint taken in the context of inflationary models [3], where the effective cosmological constant is many orders of magnitude larger than the one observed today. However this conclusion may have to be reassessed. Indeed, in presence of a cosmological constant, however small, it is the notion of elementary particle itself which has to be reconsidered, since the usual asymptotic theory is based on concepts which refer closely to Minkowski spacetime and to its Fourier representation, and do not apply to the de Sitter universe which is not asymptotically flat; in fact a true asymptotic theory does not exist at present for de Sitter space. A possible basic approach is perturbation theory; unfortunately, calculations of perturbative amplitudes which in the Minkowskian case would be simple or even trivial become rapidly prohibitive or impossible in the de Sitter case: this in spite of the fact that one is dealing with a maximally symmetric manifold.In this letter we have tackled one such calculation, namely that of the mean lifetime of dS unstable scalar particles. The results exhibit significant differences compared to the Minkowski case and decay processes which are normally forbidden become possible (as exhibited by Nachtmann [4] in a special case) and vice versa, processes that are normally possible are now forbidden. The maximal symmetry of the dS universe allows for the introduction of a global mass operator, one of the two Casimir operators of the dS group SO(1, d) (see e.g. [5]); this quantity is conserved for dS invariant field theories and it still makes sense to follow Wign...

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Quantum field theory in the de sitter universe

Cited by 141 publications

References 13 publications

Infrared dynamics in de Sitter space from Schwinger–Dyson equations

Infrared dynamics in de Sitter space from Schwinger–Dyson equations

Quantum fields in curved spacetime

The lifetime of a massive particle in a de Sitter universe

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