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Self Regulation of Infrared Correlations for Massless Scalar Fields during Inflation
High Energy Physics - Theory · Submitted 2 May 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Since an interacting scalar field in de Sitter acquires a dynamical mass through these loop corrections, the infrared divergences of the two-point correlator are naturally self-regulated.
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The abstract, sentence by sentence
Self-energies of a minimally coupled scalar field with quartic and trilinear interactions are calculated in a de Sitter background, using a position space propagator. For quartic interactions, we recover earlier results for the seagull diagram, namely that it contributes an effective mass for the scalar field at leading order in the infrared enhancement in a steady-state de Sitter background. We further show that the sunset diagram also contributes to this effective mass and argue that these two contributions are sufficient in order to determine a self-consistent dynamical mass. In addition, trilinear interactions also induce a dynamical mass for the scalar field which we calculate. Since an interacting scalar field in de Sitter acquires a dynamical mass through these loop corrections, the infrared divergences of the two-point correlator are naturally self-regulated.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Self-energies of a minimally coupled scalar field with quartic and trilinear interactions are calculated in a de Sitter background, using a position space propagator. | method 0.50 | 0.93 | 0.04 | asserted 1.00 |
| s1 | For quartic interactions, we recover earlier results for the seagull diagram, namely that it contributes an effective mass for the scalar field at leading order in the infrared enhancement in a steady-state de Sitter background. | result 0.93 | 0.50 | 0.10 | asserted 1.00 |
| s2 | We further show that the sunset diagram also contributes to this effective mass and argue that these two contributions are sufficient in order to determine a self-consistent dynamical mass. | result 0.81 | 0.94 | 0.20 | asserted 0.95 |
| s3 | In addition, trilinear interactions also induce a dynamical mass for the scalar field which we calculate. | result 0.90 | 0.94 | 0.09 | asserted 1.00 |
| s4 | Since an interacting scalar field in de Sitter acquires a dynamical mass through these loop corrections, the infrared divergences of the two-point correlator are naturally self-regulated. | interpretation 0.97 | 0.75 | 0.75 | asserted 1.00 |
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The paper
Original abstract
Self-energies of a minimally coupled scalar field with quartic and trilinear interactions are calculated in a de Sitter background, using a position space propagator. For quartic interactions, we recover earlier results for the seagull diagram, namely that it contributes an effective mass for the scalar field at leading order in the infrared enhancement in a steady-state de Sitter background. We further show that the sunset diagram also contributes to this effective mass and argue that these two contributions are sufficient in order to determine a self-consistent dynamical mass. In addition, trilinear interactions also induce a dynamical mass for the scalar field which we calculate. Since an interacting scalar field in de Sitter acquires a dynamical mass through these loop corrections, the infrared divergences of the two-point correlator are naturally self-regulated.
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References
How the literature uses it
32 arXiv papers cite this in 55 sentences
Papers citing it · 30 sentences without a confident label
Builds on it 1 paper
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The resulting self-mass is given by ([ref]), which generalizes de Sitter results in [ref] (see also [ref] ) to quasi-de Sitter case and the 1PI results in [ref] to leading order in 2PI.
Quantum corrections to scalar field dynamics in a slow-roll space-time · Conclusions · 0.97
Uses its method or tool 1 paper
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We now return to the approaches pursued in [ref] which are based on evaluations of the scalar-field self-energy and the Schwinger-Dyson equation [equation] We project this equation on the zero-mode component by integrating over $x^'$ and using the identity [equation] which follows from ([ref]).
On "dynamical mass" generation in Euclidean de Sitter space · 4 Schwinger-Dyson equation · 0.84
Uses its data or values 1 paper
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Stochastic approximations imply that the light Higgs field develops a mass $μ_eff^2≈0.3534λ^1/2H^2$ [ref] .
Gravitational corrections to Higgs potentials · The effective potential and stability · 0.81
Compares with it 2 papers
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In terms of $z$, the “dynamical mass” is given by [equation] Keeping only the one-loop tadpole diagram in ([ref]), which corresponds to truncation after the quadratic term, we obtain $z=√(2)$ and $m_dyn^2 = √(3λ) H^2/(4 π)$ (in $d=4$), which coincides with the mean-field result [ref] and the one-loop result in Lorentzian de Sitter space [ref] .
On "dynamical mass" generation in Euclidean de Sitter space · 4 Schwinger-Dyson equation · 0.98
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[ref] , which agree with the result ([ref]) in the limit $ϵ→0$.
Quantum corrections to scalar field dynamics in a slow-roll space-time · 2PI Gap equation · 0.92
Cites it as support 3 papers
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What these methods reveal is that in de Sitter space interactions lead to the generation a non-zero variance $⟨ϕ̂^2⟩$ giving rise to an effective mass, which will regulate the infrared behaviour of the theory [ref] .
Light scalars on cosmological backgrounds · Introduction · 0.96
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A variety of approaches, many using stochastic methods, are converging to this conclusion [ref] which is strongly supported by the results of this work.
Thermal Interpretation of Infrared Dynamics in de Sitter · Discussion · 0.96
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Different approaches also suggest that such infrared divergences can indeed tamed in de Sitter and physically interpreted [ref] .
Fluctuation-dissipation and equilibrium for scalar fields in de Sitter · Discussion · 0.97
Cites it as background 13 papers
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This semi-classical approach to quantum corrections in curved space-time has a very long history, and provides an hugely popular formalism to compute corrections to the effective potential (such as recently in [ref] ), to the inflaton equation of motion (see for instance [ref] ), and to the Friedman equations (for instance [ref] ), by treating gravity as a classical background to a quantum field (for standard texts see [ref] ).
Quantum corrections to inflaton dynamics, the semi-classical approach and the semi-classical limit · Introduction · 0.94
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This kind of fields have been considered by several authors in different frameworks; for instance, in the stochastic approach [ref] , in the context of Euclidean de Sitter space [ref] , using dynamical renormalization group resummations [ref] , or other nonperturbative approximation schemes [ref] .
The Hartree approximation in curved spacetimes revisited I: the effective potential in de Sitter · Introduction · 0.94
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Motivated by the inflationary cosmology, the interpretation and treatment of the infrared divergence has become of interest in recent years [ref] .
Effective potential and Goldstone bosons in de Sitter space · Introduction · 0.80
What it cites · 11 sentences without a confident label
Compares with 3 papers
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Using this propagator, we avoid appealing to stochastic arguments and the Fokker-Planck equation for the calculation of the IR-enhancement effects as it is done in Ref. [ref] .
On Resumming Inflationary Perturbations beyond One-loop · Introduction · 0.83
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This perhaps explains differences between the cases of a quartic and a trilinear self-interaction, that have been observed in Ref. [ref] when using functional renormalisation group methods.
Super-Hubble de Sitter Fluctuations and the Dynamical RG · Discussion and Conclusions · 0.83
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The approximation strategies employed in the present work appear related to those of Ref. [ref] for a scalar field on a four-dimensional sphere.
On the proper treatment of massless fields in Euclidean de Sitter space · Discussion and Conclusions · 0.91
Cites as support 2 papers
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To our knowledge, the viability of this idea has been demonstrated for a $ϕ^4$ theory using three different approaches: stochastic inflation [ref] , Schwinger-Dyson equations [ref] and the functional renormalisation group [ref] .
On Resumming Inflationary Perturbations beyond One-loop · Introduction · 0.96
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To our knowledge, the viability of this idea has been demonstrated for a $ϕ^4$ theory using three different approaches: stochastic inflation [ref] , Schwinger-Dyson equations [ref] and the functional renormalisation group [ref] .
Super-Hubble de Sitter Fluctuations and the Dynamical RG · Introduction · 0.96
Cites as background 2 papers
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A related approach has been developed for Euclidean de Sitter space, which is compact and therefore the IR divergence can be isolated in the discrete zero mode [ref] .
On the proper treatment of massless fields in Euclidean de Sitter space · Introduction · 0.83
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Ref. [ref] , where this and other matters are reviewed.) Under certain circumstances, this may lead to problems for models of the inflationary stage of cosmic expansion, where the space-time is approximately de Sitter.
Infrared effects in inflationary correlation functions · Introduction · 0.98
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