Journal of High Energy Physics

, 2013:171 | Cite as

Anomalous dimensions and non-gaussianity

  • Daniel Green
  • Matthew Lewandowski
  • Leonardo Senatore
  • Eva Silverstein
  • Matias Zaldarriaga
Open Access


We analyze the signatures of inflationary models that are coupled to interacting field theories, a basic class of multifield models also motivated by their role in providing dynamically small scales. Near the squeezed limit of the bispectrum, we find a simple scaling behavior determined by operator dimensions, which are constrained by the appropriate unitarity bounds. Specifically, we analyze two simple and calculable classes of examples: conformal field theories (CFTs), and large-N CFTs deformed by relevant time-dependent double-trace operators. Together these two classes of examples exhibit a wide range of scalings and shapes of the bispectrum, including nearly equilateral, orthogonal and local non-Gaussianity in different regimes. Along the way, we compare and contrast the shape and amplitude with previous results on weakly coupled fields coupled to inflation. This signature provides a precision test for strongly coupled sectors coupled to inflation via irrelevant operators suppressed by a high mass scale up to ~ 103 times the inflationary Hubble scale.


Cosmology of Theories beyond the SM Conformal and W Symmetry 


  1. [1]
    L. Senatore and M. Zaldarriaga, The Effective Field Theory of Multifield Inflation, JHEP 04 (2012) 024 [arXiv:1009.2093] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    D. Lopez Nacir, R.A. Porto, L. Senatore and M. Zaldarriaga, Dissipative effects in the Effective Field Theory of Inflation, JHEP 01 (2012) 075 [arXiv:1109.4192] [INSPIRE].CrossRefGoogle Scholar
  3. [3]
    J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    D. Salopek and J. Bond, Nonlinear evolution of long wavelength metric fluctuations in inflationary models, Phys. Rev. D 42 (1990) 3936 [INSPIRE].MathSciNetADSGoogle Scholar
  5. [5]
    A.D. Linde and V.F. Mukhanov, Nongaussian isocurvature perturbations from inflation, Phys. Rev. D 56 (1997) 535 [astro-ph/9610219] [INSPIRE].ADSGoogle Scholar
  6. [6]
    G. Dvali, A. Gruzinov and M. Zaldarriaga, Cosmological perturbations from inhomogeneous reheating, freezeout and mass domination, Phys. Rev. D 69 (2004) 083505 [astro-ph/0305548] [INSPIRE].ADSGoogle Scholar
  7. [7]
    L. Kofman, Probing string theory with modulated cosmological fluctuations, astro-ph/0303614 [INSPIRE].
  8. [8]
    M. Zaldarriaga, Non-Gaussianities in models with a varying inflaton decay rate, Phys. Rev. D 69 (2004) 043508 [astro-ph/0306006] [INSPIRE].ADSGoogle Scholar
  9. [9]
    X. Chen and Y. Wang, Quasi-Single Field Inflation and Non-Gaussianities, JCAP 04 (2010) 027 [arXiv:0911.3380] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    X. Chen and Y. Wang, Large non-Gaussianities with Intermediate Shapes from Quasi-Single Field Inflation, Phys. Rev. D 81 (2010) 063511 [arXiv:0909.0496] [INSPIRE].ADSGoogle Scholar
  11. [11]
    E. Sefusatti, J.R. Fergusson, X. Chen and E. Shellard, Effects and Detectability of Quasi-Single Field Inflation in the Large-Scale Structure and Cosmic Microwave Background, JCAP 08 (2012) 033 [arXiv:1204.6318] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    D. Baumann and D. Green, Signatures of Supersymmetry from the Early Universe, Phys. Rev. D 85 (2012) 103520 [arXiv:1109.0292] [INSPIRE].ADSGoogle Scholar
  13. [13]
    X. Dong, B. Horn, E. Silverstein and G. Torroba, Unitarity bounds and RG flows in time dependent quantum field theory, Phys. Rev. D 86 (2012) 025013 [arXiv:1203.1680] [INSPIRE].ADSGoogle Scholar
  14. [14]
    D. Baumann and L. McAllister, Advances in Inflation in String Theory, Ann. Rev. Nucl. Part. Sci. 59 (2009) 67 [arXiv:0901.0265] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    L. McAllister and E. Silverstein, String Cosmology: A Review, Gen. Rel. Grav. 40 (2008) 565 [arXiv:0710.2951] [INSPIRE].MathSciNetADSCrossRefzbMATHGoogle Scholar
  16. [16]
    L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].MathSciNetADSCrossRefzbMATHGoogle Scholar
  17. [17]
    S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].MathSciNetADSGoogle Scholar
  18. [18]
    S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, De Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].MathSciNetADSGoogle Scholar
  19. [19]
    S. Dimopoulos, S. Kachru, N. Kaloper, A.E. Lawrence and E. Silverstein, Generating small numbers by tunneling in multithroat compactifications, Int. J. Mod. Phys. A 19 (2004) 2657 [hep-th/0106128] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    S. Dimopoulos, S. Kachru, N. Kaloper, A.E. Lawrence and E. Silverstein, Small numbers from tunneling between brane throats, Phys. Rev. D 64 (2001) 121702 [hep-th/0104239] [INSPIRE].MathSciNetADSGoogle Scholar
  21. [21]
    D. Baumann and D. Green, Desensitizing Inflation from the Planck Scale, JHEP 09 (2010) 057 [arXiv:1004.3801] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    D. Baumann and D. Green, Inflating with Baryons, JHEP 04 (2011) 071 [arXiv:1009.3032] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    A. Maleknejad and M. Sheikh-Jabbari, Gauge-flation: Inflation From Non-Abelian Gauge Fields, Phys. Lett. B 723 (2013) 224 [arXiv:1102.1513] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  24. [24]
    S. Dubovsky, A. Lawrence and M.M. Roberts, Axion monodromy in a model of holographic gluodynamics, JHEP 02 (2012) 053 [arXiv:1105.3740] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    P. Adshead and M. Wyman, Chromo-Natural Inflation: Natural inflation on a steep potential with classical non-Abelian gauge fields, Phys. Rev. Lett. 108 (2012) 261302 [arXiv:1202.2366] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    E. Silverstein and D. Tong, Scalar speed limits and cosmology: Acceleration from D-cceleration, Phys. Rev. D 70 (2004) 103505 [hep-th/0310221] [INSPIRE].MathSciNetADSGoogle Scholar
  27. [27]
    M. Alishahiha, E. Silverstein and D. Tong, DBI in the sky, Phys. Rev. D 70 (2004) 123505 [hep-th/0404084] [INSPIRE].ADSGoogle Scholar
  28. [28]
    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].ADSCrossRefGoogle Scholar
  29. [29]
    C. Cheung, P. Creminelli, A.L. Fitzpatrick, J. Kaplan and L. Senatore, The Effective Field Theory of Inflation, JHEP 03 (2008) 014 [arXiv:0709.0293] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  30. [30]
    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].ADSCrossRefGoogle Scholar
  31. [31]
    A.J. Tolley and M. Wyman, The Gelaton Scenario: Equilateral non-Gaussianity from multi-field dynamics, Phys. Rev. D 81 (2010) 043502 [arXiv:0910.1853] [INSPIRE].ADSGoogle Scholar
  32. [32]
    S. Cremonini, Z. Lalak and K. Turzynski, Strongly Coupled Perturbations in Two-Field Inflationary Models, JCAP 03 (2011) 016 [arXiv:1010.3021] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    A. Achucarro, J.-O. Gong, S. Hardeman, G.A. Palma and S.P. Patil, Features of heavy physics in the CMB power spectrum, JCAP 01 (2011) 030 [arXiv:1010.3693] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    D. Baumann and D. Green, Equilateral Non-Gaussianity and New Physics on the Horizon, JCAP 09 (2011) 014 [arXiv:1102.5343] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    S. Weinberg, Quantum contributions to cosmological correlations, Phys. Rev. D 72 (2005) 043514 [hep-th/0506236] [INSPIRE].MathSciNetADSGoogle Scholar
  36. [36]
    S.R. Behbahani and D. Green, Collective Symmetry Breaking and Resonant Non-Gaussianity, JCAP 11 (2012) 056 [arXiv:1207.2779] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    L. Senatore and M. Zaldarriaga, On Loops in Inflation, JHEP 12 (2010) 008 [arXiv:0912.2734] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    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].ADSCrossRefGoogle Scholar
  39. [39]
    N. Dalal, O. Dore, D. Huterer and A. Shirokov, The imprints of primordial non-Gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects, Phys. Rev. D 77 (2008) 123514 [arXiv:0710.4560] [INSPIRE].ADSGoogle Scholar
  40. [40]
    T. Baldauf, U. Seljak, L. Senatore and M. Zaldarriaga, Galaxy Bias and non-Linear Structure Formation in General Relativity, JCAP 10 (2011) 031 [arXiv:1106.5507] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    A. Slosar, C. Hirata, U. Seljak, S. Ho and N. Padmanabhan, Constraints on local primordial non-Gaussianity from large scale structure, JCAP 08 (2008) 031 [arXiv:0805.3580] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    T. Baldauf, U. Seljak and L. Senatore, Primordial non-Gaussianity in the Bispectrum of the Halo Density Field, JCAP 04 (2011) 006 [arXiv:1011.1513] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    J. Norena, L. Verde, G. Barenboim and C. Bosch, Prospects for constraining the shape of non-Gaussianity with the scale-dependent bias, JCAP 08 (2012) 019 [arXiv:1204.6324] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    E. Sefusatti, J.R. Fergusson, X. Chen and E. Shellard, Effects and Detectability of Quasi-Single Field Inflation in the Large-Scale Structure and Cosmic Microwave Background, JCAP 08 (2012) 033 [arXiv:1204.6318] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    U. Seljak, Extracting primordial non-Gaussianity without cosmic variance, Phys. Rev. Lett. 102 (2009) 021302 [arXiv:0807.1770] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    D. Babich, P. Creminelli and M. Zaldarriaga, The Shape of non-Gaussianities, JCAP 08 (2004) 009 [astro-ph/0405356] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    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].ADSCrossRefGoogle Scholar
  48. [48]
    WMAP collaboration, C. 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].ADSCrossRefGoogle Scholar
  49. [49]
    F. Caracciolo and V.S. Rychkov, Rigorous Limits on the Interaction Strength in Quantum Field Theory, Phys. Rev. D 81 (2010) 085037 [arXiv:0912.2726] [INSPIRE].ADSGoogle Scholar
  50. [50]
    D. Poland, D. Simmons-Duffin and A. Vichi, Carving Out the Space of 4D CFTs, JHEP 05 (2012) 110 [arXiv:1109.5176] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    T. Suyama and M. Yamaguchi, Non-Gaussianity in the modulated reheating scenario, Phys. Rev. D 77 (2008) 023505 [arXiv:0709.2545] [INSPIRE].ADSGoogle Scholar
  52. [52]
    N.S. Sugiyama, E. Komatsu and T. Futamase, Non-Gaussianity Consistency Relation for Multi-field Inflation, Phys. Rev. Lett. 106 (2011) 251301 [arXiv:1101.3636] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    A. Lewis, The real shape of non-Gaussianities, JCAP 10 (2011) 026 [arXiv:1107.5431] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    K.M. Smith, M. LoVerde and M. Zaldarriaga, A universal bound on N-point correlations from inflation, Phys. Rev. Lett. 107 (2011) 191301 [arXiv:1108.1805] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    V. Assassi, D. Baumann and D. Green, On Soft Limits of Inflationary Correlation Functions, JCAP 11 (2012) 047 [arXiv:1204.4207] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    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].MathSciNetADSCrossRefGoogle Scholar
  57. [57]
    K.M. Smith and M. LoVerde, Local stochastic non-Gaussianity and N-body simulations, JCAP 11 (2011) 009 [arXiv:1010.0055] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    D. Baumann, S. Ferraro, D. Green and K.M. Smith, Stochastic Bias from Non-Gaussian Initial Conditions, JCAP 05 (2013) 001 [arXiv:1209.2173] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    B. Grinstein, K.A. Intriligator and I.Z. Rothstein, Comments on Unparticles, Phys. Lett. B 662 (2008) 367 [arXiv:0801.1140] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  60. [60]
    S. Endlich, A. Nicolis and J. Wang, Solid Inflation, arXiv:1210.0569 [INSPIRE].
  61. [61]
    L. Senatore and M. Zaldarriaga, A Naturally Large Four-Point Function in Single Field Inflation, JCAP 01 (2011) 003 [arXiv:1004.1201] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    I. Antoniadis, P.O. Mazur and E. Mottola, Conformal Invariance, Dark Energy and CMB Non-Gaussianity, JCAP 09 (2012) 024 [arXiv:1103.4164] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA 2013

Authors and Affiliations

  • Daniel Green
    • 1
    • 3
  • Matthew Lewandowski
    • 1
  • Leonardo Senatore
    • 1
    • 2
    • 3
    • 4
  • Eva Silverstein
    • 1
    • 2
    • 3
  • Matias Zaldarriaga
    • 5
  1. 1.Stanford Institute for Theoretical PhysicsStanford UniversityStanfordU.S.A.
  2. 2.SLAC National Accelerator LaboratoryMenlo ParkU.S.A.
  3. 3.Kavli Institute for Particle Astrophysics and CosmologyStanfordU.S.A.
  4. 4.CERN, Theory DivisionGeneva 23Switzerland
  5. 5.School of Natural SciencesInstitute for Advanced StudyPrincetonU.S.A.

Personalised recommendations