Abstract
It is shown that the squeezed limit of inflationary expectation values follows from reparametrization invariance of the wavefunction of the universe. This translates into a constraint on the longitudinal modes of functional derivatives of the wavefunction. Thus, the local non-Gaussianity induced by single field inflation is purely a gauge artifact. We focus on Einstein gravity in de Sitter space and single field inflation, although the formalism only relies on the diffeomorphism invariance of the theory, and thus applies to any theory of gravity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
P. Creminelli and M. Zaldarriaga, Single field consistency relation for the 3-point function, JCAP 10 (2004) 006 [astro-ph/0407059] [INSPIRE].
X. Chen, M.-x. Huang, S. Kachru and G. Shiu, Observational signatures and non-Gaussianities of general single field inflation, JCAP 01 (2007) 002 [hep-th/0605045] [INSPIRE].
C. Cheung, A.L. Fitzpatrick, J. Kaplan and L. Senatore, On the consistency relation of the 3-point function in single field inflation, JCAP 02 (2008) 021 [arXiv:0709.0295] [INSPIRE].
D. Seery, M.S. Sloth and F. Vernizzi, Inflationary trispectrum from graviton exchange, JCAP 03 (2009) 018 [arXiv:0811.3934] [INSPIRE].
P. Creminelli, G. D’Amico, M. Musso and J. Norena, The (not so) squeezed limit of the primordial 3-point function, JCAP 11 (2011) 038 [arXiv:1106.1462] [INSPIRE].
P. Creminelli, J. Norena and M. Simonovic, Conformal consistency relations for single-field inflation, JCAP 07 (2012) 052 [arXiv:1203.4595] [INSPIRE].
L. Leblond and E. Pajer, Resonant Trispectrum and a Dozen More Primordial N-point functions, JCAP 01 (2011) 035 [arXiv:1010.4565] [INSPIRE].
L. Senatore and M. Zaldarriaga, A Note on the Consistency Condition of Primordial Fluctuations, JCAP 08 (2012) 001 [arXiv:1203.6884] [INSPIRE].
V. Assassi, D. Baumann and D. Green, On Soft Limits of Inflationary Correlation Functions, JCAP 11 (2012) 047 [arXiv:1204.4207] [INSPIRE].
W.D. Goldberger, L. Hui and A. Nicolis, One-particle-irreducible consistency relations for cosmological perturbations, Phys. Rev. D 87 (2013) 103520 [arXiv:1303.1193] [INSPIRE].
B.S. DeWitt, Quantum Theory of Gravity. 1. The Canonical Theory, Phys. Rev. 160 (1967) 1113 [INSPIRE].
E. Pajer, F. Schmidt and M. Zaldarriaga, The Observed Squeezed Limit of Cosmological Three-Point Functions, arXiv:1305.0824 [INSPIRE].
K. Hinterbichler, L. Hui and J. Khoury, An Infinite Set of Ward Identities for Adiabatic Modes in Cosmology, JCAP 01 (2014) 039 [arXiv:1304.5527] [INSPIRE].
P. Creminelli, A. Perko, L. Senatore, M. Simonović and G. Trevisan, The Physical Squeezed Limit: Consistency Relations at Order q 2, JCAP 11 (2013) 015 [arXiv:1307.0503] [INSPIRE].
J. de Boer, E.P. Verlinde and H.L. Verlinde, On the holographic renormalization group, JHEP 08 (2000) 003 [hep-th/9912012] [INSPIRE].
F. Larsen and R. McNees, Inflation and de Sitter holography, JHEP 07 (2003) 051 [hep-th/0307026] [INSPIRE].
F. Larsen and R. McNees, Holography, diffeomorphisms and scaling violations in the CMB, JHEP 07 (2004) 062 [hep-th/0402050] [INSPIRE].
F. Larsen, J.P. van der Schaar and R.G. Leigh, de Sitter holography and the cosmic microwave background, JHEP 04 (2002) 047 [hep-th/0202127] [INSPIRE].
D.S. Salopek and J.R. Bond, Nonlinear evolution of long wavelength metric fluctuations in inflationary models, Phys. Rev. D 42 (1990) 3936 [INSPIRE].
J.B. Hartle and S.W. Hawking, Wave Function of the Universe, Phys. Rev. D 28 (1983) 2960 [INSPIRE].
J.M. Maldacena and G.L. Pimentel, On graviton non-Gaussianities during inflation, JHEP 09 (2011) 045 [arXiv:1104.2846] [INSPIRE].
E. Witten, Quantum gravity in de Sitter space, hep-th/0106109 [INSPIRE].
A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE].
H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].
L. Berezhiani and J. Khoury, Slavnov-Taylor Identities for Primordial Perturbations, arXiv:1309.4461 [INSPIRE].
A. Rouet and R. Stora, Ward identities and trace identities for the stress-energy tensor, Lett. Nuovo Cim. 4S2 (1972) 136 [INSPIRE].
P. Mansfield, Continuum strong coupling expansion of Yang-Mills theory: Quark confinement and infrared slavery, Nucl. Phys. B 418 (1994) 113 [hep-th/9308116] [INSPIRE].
L. Senatore and M. Zaldarriaga, On Loops in Inflation, JHEP 12 (2010) 008 [arXiv:0912.2734] [INSPIRE].
L. Senatore and M. Zaldarriaga, On Loops in Inflation II: IR Effects in Single Clock Inflation, JHEP 01 (2013) 109 [arXiv:1203.6354] [INSPIRE].
G.L. Pimentel, L. Senatore and M. Zaldarriaga, On Loops in Inflation III: Time Independence of zeta in Single Clock Inflation, JHEP 07 (2012) 166 [arXiv:1203.6651] [INSPIRE].
L. Senatore and M. Zaldarriaga, The constancy of ζ in single-clock Inflation at all loops, JHEP 09 (2013) 148 [arXiv:1210.6048] [INSPIRE].
S. Weinberg, Quantum contributions to cosmological correlations, Phys. Rev. D 72 (2005) 043514 [hep-th/0506236] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1309.1793
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Pimentel, G.L. Inflationary consistency conditions from a wavefunctional perspective. J. High Energ. Phys. 2014, 124 (2014). https://doi.org/10.1007/JHEP02(2014)124
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2014)124