Abstract
We present the holographic predictions for cosmological 3-point correlators, involving both scalar and tensor modes, for a universe which started in a non-geometric holographic phase. Holographic formulae relate the cosmological 3-point functions to stress tensor correlation functions of a holographically dual three-dimensional non-gravitational QFT. We compute these correlators at 1-loop order for a theory containing massless scalars, fermions and gauge fields, and present an extensive analysis of the constraints due to Ward identities showing that they uniquely determine the correlators up to a few constants. We define shapes for all cosmological bispectra and compare the holographic shapes to the slow-roll ones, finding that some are distinguishable while others, perhaps surprisingly, are not. In particular, for three gravitons, we are able to recover the slow-roll shapes exactly.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. McFadden and K. Skenderis, Holography for Cosmology, Phys. Rev. D 81 (2010) 021301 [arXiv:0907.5542] [INSPIRE].
P. McFadden and K. Skenderis, The Holographic Universe, J. Phys. Conf. Ser. 222 (2010) 012007 [arXiv:1001.2007] [INSPIRE].
P. McFadden and K. Skenderis, Observational signatures of holographic models of inflation, arXiv:1010.0244 [INSPIRE].
P. McFadden and K. Skenderis, Holographic Non-Gaussianity, JCAP 05 (2011) 013 [arXiv:1011.0452] [INSPIRE].
R. Easther, R. Flauger, P. McFadden and K. Skenderis, Constraining holographic inflation with WMAP, JCAP 09 (2011) 030 [arXiv:1104.2040] [INSPIRE].
P. McFadden and K. Skenderis, Cosmological 3-point correlators from holography, JCAP 06 (2011) 030 [arXiv:1104.3894] [INSPIRE].
J.M. Maldacena and G.L. Pimentel, On graviton non-Gaussianities during inflation, JHEP 09 (2011) 045 [arXiv:1104.2846] [INSPIRE].
J. Soda, H. Kodama and M. Nozawa, Parity Violation in Graviton Non-Gaussianity, JHEP 08 (2011) 067 [arXiv:1106.3228] [INSPIRE].
M. Shiraishi, D. Nitta and S. Yokoyama, Parity Violation of Gravitons in the CMB Bispectrum, Prog. Theor. Phys. 126 (2011) 937 [arXiv:1108.0175] [INSPIRE].
X. Gao, T. Kobayashi, M. Yamaguchi and J. Yokoyama, Primordial non-Gaussianities of gravitational waves in the most general single-field inflation model, Phys. Rev. Lett. 107 (2011) 211301 [arXiv:1108.3513] [INSPIRE].
A. Jevicki, Y. Kazama and T. Yoneya, Generalized conformal symmetry in D-brane matrix models, Phys. Rev. D 59 (1999) 066001 [hep-th/9810146] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Precision holography for non-conformal branes, JHEP 09 (2008) 094 [arXiv:0807.3324] [INSPIRE].
P. Creminelli, A. Nicolis, L. Senatore, M. Tegmark and M. Zaldarriaga, Limits on non-Gaussianities from wmap data, JCAP 05 (2006) 004 [astro-ph/0509029] [INSPIRE].
H. Osborn and A. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].
I. Antoniadis, P.O. Mazur and E. Mottola, Conformal Invariance, Dark Energy and CMB Non-Gaussianity, arXiv:1103.4164 [INSPIRE].
P. Creminelli, Conformal invariance of scalar perturbations in inflation, Phys. Rev. D 85 (2012) 041302 [arXiv:1108.0874] [INSPIRE].
D. Anninos, T. Hartman and A. Strominger, Higher Spin Realization of the dS/CFT Correspondence, arXiv:1108.5735 [INSPIRE].
H. Boonstra, K. Skenderis and P. Townsend, The domain wall/QFT correspondence, JHEP 01 (1999) 003 [hep-th/9807137] [INSPIRE].
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
T. Hertog and J. Hartle, Holographic No-Boundary Measure, arXiv:1111.6090 [INSPIRE].
S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
M. Henningson and K. Skenderis, The Holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
M. Henningson and K. Skenderis, Holography and the Weyl anomaly, Fortsch. Phys. 48 (2000) 125 [hep-th/9812032] [INSPIRE].
S. Giombi, S. Prakash and X. Yin, A Note on CFT Correlators in Three Dimensions, arXiv:1104.4317 [INSPIRE].
P. Di Francesco, P. Mathieu and D. Senechal, Conformal field theory, Springer, New York, U.S.A. (1997).
L. Senatore, K.M. Smith and M. Zaldarriaga, Non-Gaussianities in Single Field Inflation and their Optimal Limits from the WMAP 5-year Data, JCAP 01 (2010) 028 [arXiv:0905.3746] [INSPIRE].
J. Fergusson and E. Shellard, The shape of primordial non-Gaussianity and the CMB bispectrum, Phys. Rev. D 80 (2009) 043510 [arXiv:0812.3413] [INSPIRE].
D. Babich, P. Creminelli and M. Zaldarriaga, The Shape of non-Gaussianities, JCAP 08 (2004) 009 [astro-ph/0405356] [INSPIRE].
S. Weinberg, Cosmology, Oxford University Press (2008).
A.I. Davydychev, A Simple formula for reducing Feynman diagrams to scalar integrals, Phys. Lett. B 263 (1991) 107 [INSPIRE].
A.I. Davydychev, Recursive algorithm of evaluating vertex type Feynman integrals, J. Phys. A 25 (1992) 5587 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1112.1967
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Bzowski, A., McFadden, P. & Skenderis, K. Holographic predictions for cosmological 3-point functions. J. High Energ. Phys. 2012, 91 (2012). https://doi.org/10.1007/JHEP03(2012)091
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2012)091