Revisiting non-Gaussianity in multifield inflation with curved field space
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Springer
Received: August 21, 2019 Accepted: December 19, 2019 Published: January 14, 2020
Sebastian Garcia-Saenz, Lucas Pinol and S´ ebastien Renaux-Petel Institut d’Astrophysique de Paris, GReCO, UMR 7095 du CNRS et de Sorbonne Universit´e, 98bis boulevard Arago, 75014 Paris, France
E-mail: [email protected], [email protected], [email protected] Abstract: Recent studies of inflation with multiple scalar fields have highlighted the importance of non-canonical kinetic terms in novel types of inflationary solutions. This motivates a thorough analysis of non-Gaussianities in this context, which we revisit here by studying the primordial bispectrum in a general two-field model. Our main result is the complete cubic action for inflationary fluctuations written in comoving gauge, i.e. in terms of the curvature perturbation and the entropic mode. Although full expressions for the cubic action have already been derived in terms of fields fluctuations in the flat gauge, their applicability is mostly restricted to numerical evaluations. Our form of the action is instead amenable to several analytical approximations, as our calculation in terms of the directly observable quantity makes manifest the scaling of every operator in terms of the slow-roll parameters, what is essentially a generalization of Maldacena’s single-field result to non-canonical two-field models. As an important application we derive the single-field effective field theory that is valid when the entropic mode is heavy and may be integrated out, underlining the observable effects that derive from a curved field space. Keywords: Cosmology of Theories beyond the SM, Effective Field Theories, Sigma Models ArXiv ePrint: 1907.10403
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)073
JHEP01(2020)073
Revisiting non-Gaussianity in multifield inflation with curved field space
Contents 1 Introduction
1
2 Generalities 2.1 Background 2.2 Covariant field fluctuations and gauge choice 2.3 Quadratic action and linear equations of motion
3 4 4 6 7 8 9 10
4 Single-field effective theories 4.1 Generalities and regime of validity 4.2 Single-field effective theory of fluctuations 4.3 When full fields can be integrated out
12 12 15 20
5 Conclusions
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A Two-field cubic action A.1 First building blocks A.2 Manipulations of the cubic action (3) A.2.1 Manipulations of Lini (ζ, θ) A.2.2 Manipulating the interactions involving entropic perturbations and total cubic action
23 23 23 24
B Boundary terms and field redefinitions
28
1
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Introduction
Primordial non-Gaussianities are arguably the most promising probe of the physics of the early universe (see [1] for the most recent observational constraints and e.g. [2–6] for reviews). In the context of inflation, they offer a unique observational window into energy scales even above the Hubble scale — very likely the highest scales that we may ever hope to indirectly probe. In this setting, non-Gaussianities are predominantly due to the threepoint interactions of the s
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