Path integral for multi-field inflation

Gong, Jinn Ouk; Seo, Min-Seok; Shiu, Gary

doi:10.1007/jhep07(2016)099

Cited by 16 publications

(11 citation statements)

References 69 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[10][11][12][13][14][15][16]). See also [17][18][19][20] for introductions to this approach in cosmology. However, it seems that the convenience and advantage of diagrammatic calculation are not widely appreciated in previous studies.…”

Section: Introductionmentioning

confidence: 99%

Schwinger-Keldysh diagrammatics for primordial perturbations

Chen

Wang

Xianyu

2017

J. Cosmol. Astropart. Phys.

123

208

View full text Add to dashboard Cite

We present a systematic introduction to the diagrammatic method for practical calculations in inflationary cosmology, based on Schwinger-Keldysh path integral formalism. We show in particular that the diagrammatic rules can be derived directly from a classical Lagrangian even in the presence of derivative couplings. Furthermore, we use a quasi-single-field inflation model as an example to show how this formalism, combined with the trick of mixed propagator, can significantly simplify the calculation of some in-in correlation functions. The resulting bispectrum includes the lighter scalar case (m < 3H/2) that has been previously studied, and the heavier scalar case (m > 3H/2) that has not been explicitly computed for this model. The latter provides a concrete example of quantum primordial standard clocks, in which the clock signals can be observably large. *

show abstract

Section: Introductionmentioning

confidence: 99%

Schwinger-Keldysh diagrammatics for primordial perturbations

Chen

Wang

Xianyu

2017

J. Cosmol. Astropart. Phys.

123

208

View full text Add to dashboard Cite

show abstract

“…[109] for a review and Refs. [90,92,[110][111][112][113][114][115][116][117][118][119][120][121] for its application to cosmology). There, the path integral is defined along the time path C from the sufficient past τ −∞ to the sufficient future τ ∞ and then again back to τ −∞ .…”

Section: Cubic Action and The Feynman Rulementioning

confidence: 99%

Squeezed bispectrum and one-loop corrections in transient constant-roll inflation

Motohashi¹,

Tada²

2023

Preprint

View full text Add to dashboard Cite

In canonical single-field inflation, the production of primordial black holes (PBH) requires a transient violation of the slow-roll condition. The transient ultra slow-roll inflation is an example of such scenario, and more generally, one can consider the transient constantroll inflation. We investigate the squeezed bispectrum in the transient constant-roll inflation, and find that the Maldacena's consistency relation holds for a sufficiently long-wavelength mode, whereas it is violated for modes around the peak scale for the non-attractor case. We also demonstrate how the one-loop corrections are modified compared to the case of the transient ultra slow-roll inflation, focusing on representative one-loop terms orgiginating from a time derivative of the second slow-roll parameter in the cubic action. We find that the perturbativity requirement on those terms does not rule out the production of PBH from the transient constant-roll inflation. Therefore, it is a simple counterexample of the recently claimed no-go theorem of PBH production from single-field inflation.

show abstract

“…This approach is commonly used to calculate the non-Gaussianities during inflation [9,[15][16][17]. The Schwinger-Keldysh formalism uses the path-integral approach for this time evolution and permits a diagrammatic representation, [18][19][20]. Although these diagrammatics provide an excellent way of organizing perturbation theory, this does not simplify the calculations significantly and the Schwinger-Keldysh formalism results in somewhat the same expression as the in-in formalism [21].…”

Section: Introductionmentioning

confidence: 99%

Derivative Interactions during Inflation: A Systematic Approach

Abolhasani,

Goodhew

2022

Preprint

View full text Add to dashboard Cite

We present a systematic prescription for calculating cosmological correlation for models with derivative interactions through the wavefunction of the universe and compare this result with the "in-in" formalism-canonical approach. The key step in this procedure is to perform the path integral over conjugate momenta after which a straightforward generalisation of Feynman's Rules can be applied. We show that this integral recovers the classical action plus some additional divergent contributions which are necessary to cancel other divergences that arise due to loop diagrams involving time derivatives. As a side project, for the first time, we introduce the "off-shell" version of the in-in formalism that is sometimes more straightforward, especially for the models with derivative coupling. To examine our prescription, as a specific example, we work out the trispectra of the scalar fluctuation in the model with the λ φ3 derivative coupling. Contents 1 Introduction 1 2 Outline 2 3 In-in Calculations: A Review 3 3.1 Interaction potential 4 3.2 λφ ′ 3 Trispectrum: the Canonical Approach 7 4 Wavefunctional of the universe 8 4.1 Canonical to functional formulation 9 4.2 φ ′ 3 Wavefunction 11 4.3 φ ′ 3 interaction: Trispectrum 13 4.4 Divergent Corrections: Position Space 15 5 Conclusions and Outlook 18 A Path Integral Formulation: Transition Probability Amplitude 18 B φ ′ 3 interaction: Feynman Rules 21 B.1 Wavefunction of the Universe: λφ ′ 3 23 B.2 N-point functions 24 C Propagator and its derivatives 25 C.1 Time order product & Equal time commutation relation 25 C.2 Analytical Continuation 26 C.3 Minkowski Space 26 C.4 On-shell vs Off-shell calculations 27 C.4.1 Off-shell propagator 28 C.4.2 On-shell propagator 29 D Propagators in the inflationary background 29 E Divergent Corrections: Momentum Space 31

show abstract

Path integral for multi-field inflation

Cited by 16 publications

References 69 publications

Schwinger-Keldysh diagrammatics for primordial perturbations

Schwinger-Keldysh diagrammatics for primordial perturbations

Squeezed bispectrum and one-loop corrections in transient constant-roll inflation

Derivative Interactions during Inflation: A Systematic Approach

Contact Info

Product

Resources

About