Abstract
In holographic models of cosmology based on the (A)dS/CFT correspondence, conformal symmetry is implicit in the dual description of the Universe. Generically, however, one cannot expect the (broken) conformal invariance in the cosmic fluctuations as only the scale invariance is manifest in experiments. Also, in order for the prediction of the holographic models to make sense, the conformal symmetry needs to be broken as the scalar mode of the metric fluctuations becomes pure gauge in the conformal limit. We discuss the improvement ambiguity of the energy-momentum tensor in this context and construct a holographic model of the Universe that preserves the scale invariance but not necessarily the full conformal invariance. Our sample computation using a weakly coupled dual field theory shows that the orthogonal type of non-Gaussianity is present over and above the equilateral type. The improvement ambiguity corresponds to the choice of the energy momentum tensor that will couple to our particle physics sector after inflation. Our results show that the holographic prediction of the cosmological parameters crucially depends on such a choice.
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References
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [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].
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].
D. Seery and J.E. Lidsey, Non-Gaussian Inflationary Perturbations from the dS/CFT Correspondence, JCAP 06 (2006) 001 [astro-ph/0604209] [INSPIRE].
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].
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].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
S.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].
P. McFadden and K. Skenderis, Holographic Non-Gaussianity, JCAP 05 (2011) 013 [arXiv:1011.0452] [INSPIRE].
I. Antoniadis, P.O. Mazur and E. Mottola, Conformal Invariance, Dark Energy and CMB Non-Gaussianity, JCAP 09 (2012) 024 [arXiv:1103.4164] [INSPIRE].
A. Bzowski, P. McFadden and K. Skenderis, Holographic predictions for cosmological 3-point functions, JHEP 03 (2012) 091 [arXiv:1112.1967] [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].
P. Creminelli, Conformal invariance of scalar perturbations in inflation, Phys. Rev. D 85 (2012) 041302 [arXiv:1108.0874] [INSPIRE].
R.M. Wald, Asymptotic behavior of homogeneous cosmological models in the presence of a positive cosmological constant, Phys. Rev. D 28 (1983) 2118 [INSPIRE].
V. Assassi, D. Baumann and D. Green, On Soft Limits of Inflationary Correlation Functions, JCAP 11 (2012) 047 [arXiv:1204.4207] [INSPIRE].
V. Assassi, D. Baumann and D. Green, Symmetries and Loops in Inflation, JHEP 02 (2013) 151 [arXiv:1210.7792] [INSPIRE].
A. Kehagias and A. Riotto, Operator Product Expansion of Inflationary Correlators and Conformal Symmetry of de Sitter, Nucl. Phys. B 864 (2012) 492 [arXiv:1205.1523] [INSPIRE].
A. Kehagias and A. Riotto, The Four-point Correlator in Multifield Inflation, the Operator Product Expansion and the Symmetries of de Sitter, Nucl. Phys. B 868 (2013) 577 [arXiv:1210.1918] [INSPIRE].
K. Hinterbichler and J. Khoury, The Pseudo-Conformal Universe: Scale Invariance from Spontaneous Breaking of Conformal Symmetry, JCAP 04 (2012) 023 [arXiv:1106.1428] [INSPIRE].
K. Hinterbichler, L. Hui and J. Khoury, Conformal Symmetries of Adiabatic Modes in Cosmology, JCAP 08 (2012) 017 [arXiv:1203.6351] [INSPIRE].
K. Hinterbichler, A. Joyce and J. Khoury, Non-linear Realizations of Conformal Symmetry and Effective Field Theory for the Pseudo-Conformal Universe, JCAP 06 (2012) 043 [arXiv:1202.6056] [INSPIRE].
I. Mata, S. Raju and S. Trivedi, CMB from CFT, JHEP 07 (2013) 015 [arXiv:1211.5482] [INSPIRE].
A. Ghosh, N. Kundu, S. Raju and S.P. Trivedi, Conformal Invariance and the Four Point Scalar Correlator in Slow-Roll Inflation, arXiv:1401.1426 [INSPIRE].
J. Garriga and Y. Urakawa, Inflation and deformation of conformal field theory, JCAP 07 (2013) 033 [arXiv:1303.5997] [INSPIRE].
J. Garriga and Y. Urakawa, Holographic inflation and the conservation of ζ, arXiv:1403.5497 [INSPIRE].
P. Creminelli, J. Norena and M. Simonovic, Conformal consistency relations for single-field inflation, JCAP 07 (2012) 052 [arXiv:1203.4595] [INSPIRE].
K. Schalm, G. Shiu and T. van der Aalst, Consistency condition for inflation from (broken) conformal symmetry, JCAP 03 (2013) 005 [arXiv:1211.2157] [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].
L. Berezhiani and J. Khoury, Slavnov-Taylor Identities for Primordial Perturbations, JCAP 02 (2014) 003 [arXiv:1309.4461] [INSPIRE].
Y. Nakayama, A lecture note on scale invariance vs conformal invariance, arXiv:1302.0884 [INSPIRE].
V. Riva and J.L. Cardy, Scale and conformal invariance in field theory: a physical counterexample, Phys. Lett. B 622 (2005) 339 [hep-th/0504197] [INSPIRE].
J.P. van der Schaar, Inflationary perturbations from deformed CFT, JHEP 01 (2004) 070 [hep-th/0307271] [INSPIRE].
A. Bzowski, P. McFadden and K. Skenderis, Holography for inflation using conformal perturbation theory, JHEP 04 (2013) 047 [arXiv:1211.4550] [INSPIRE].
E. Kiritsis, Asymptotic freedom, asymptotic flatness and cosmology, JCAP 11 (2013) 011 [arXiv:1307.5873] [INSPIRE].
U. Kol, On the dual flow of slow-roll Inflation, JHEP 01 (2014) 017 [arXiv:1309.7344] [INSPIRE].
J. Bourdier and E. Kiritsis, Holographic RG flows and nearly-marginal operators, Class. Quant. Grav. 31 (2014) 035011 [arXiv:1310.0858] [INSPIRE].
Y. Nakayama, Holographic Renormalization of Foliation Preserving Gravity and Trace Anomaly, Gen. Rel. Grav. 44 (2012) 2873 [arXiv:1203.1068] [INSPIRE].
Y. Nakayama, Consistency of local renormalization group in d = 3, Nucl. Phys. B 879 (2014) 37 [arXiv:1307.8048] [INSPIRE].
M. Yamaguchi, Supergravity based inflation models: a review, Class. Quant. Grav. 28 (2011) 103001 [arXiv:1101.2488] [INSPIRE].
A. Strominger, Inflation and the dS/CFT correspondence, JHEP 11 (2001) 049 [hep-th/0110087] [INSPIRE].
H.J. Boonstra, K. Skenderis and P.K. Townsend, The domain wall/QFT correspondence, JHEP 01 (1999) 003 [hep-th/9807137] [INSPIRE].
BICEP2 collaboration, P.A.R. Ade et al., BICEP2 I: Detection Of B-mode Polarization at Degree Angular Scales, arXiv:1403.3985 [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity, arXiv:1303.5084 [INSPIRE].
S.-S. Lee, Quantum Renormalization Group and Holography, JHEP 01 (2014) 076 [arXiv:1305.3908] [INSPIRE].
Y. Nakayama, a − c test of holography vs quantum renormalization group, arXiv:1401.5257 [INSPIRE].
H. Osborn, Weyl consistency conditions and a local renormalization group equation for general renormalizable field theories, Nucl. Phys. B 363 (1991) 486 [INSPIRE].
G. Leibbrandt, Introduction to the Technique of Dimensional Regularization, Rev. Mod. Phys. 47 (1975) 849 [INSPIRE].
WMAP collaboration, E. Komatsu et al., Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation, Astrophys. J. Suppl. 192 (2011) 18 [arXiv:1001.4538] [INSPIRE].
WMAP collaboration, C.L. Bennett et al., Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results, Astrophys. J. Suppl. 208 (2013) 20 [arXiv:1212.5225] [INSPIRE].
A. Gangui, F. Lucchin, S. Matarrese and S. Mollerach, The three point correlation function of the cosmic microwave background in inflationary models, Astrophys. J. 430 (1994) 447 [astro-ph/9312033] [INSPIRE].
E. Komatsu and D.N. Spergel, Acoustic signatures in the primary microwave background bispectrum, Phys. Rev. D 63 (2001) 063002 [astro-ph/0005036] [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].
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].
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Kawai, S., Nakayama, Y. Improvement of energy-momentum tensor and non-Gaussianities in holographic cosmology. J. High Energ. Phys. 2014, 52 (2014). https://doi.org/10.1007/JHEP06(2014)052
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DOI: https://doi.org/10.1007/JHEP06(2014)052