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Precision calculation of inflation correlators at one loop

  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 11 February 2022
  • volume 2022, Article number: 85 (2022)
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Precision calculation of inflation correlators at one loop
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  • Lian-Tao Wang1,
  • Zhong-Zhi Xianyu2 &
  • Yi-Ming Zhong  ORCID: orcid.org/0000-0001-9922-61623 

  • 200 Accesses

  • 18 Citations

  • 8 Altmetric

  • 1 Mention

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A preprint version of the article is available at arXiv.

Abstract

We initiate a systematic study of precision calculation of the inflation correlators at the 1-loop level, starting in this paper with bosonic 1-loop bispectrum with chemical-potential enhancement. Such 1-loop processes could lead to important cosmological collider observables but are notoriously difficult to compute due to the lack of symmetries. We attack the problem from a direct numerical approach based on the real-time Schwinger-Keldysh formalism and show full numerical results for arbitrary kinematics containing both the oscillatory “signals” and the “backgrounds”. Our results show that, while the non-oscillatory part can be one to two orders of magnitude larger, the oscillatory signal can be separated out by applying appropriate high-pass filters. We have also compared the result with analytic estimates typically adopted in the literature. While the amplitude is comparable, there is a non-negligible deviation in the frequency of the oscillatory part away from the extreme squeezed limit.

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References

  1. P.D. Meerburg et al., Primordial non-Gaussianity, arXiv:1903.04409 [INSPIRE].

  2. 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].

  3. X. Chen and Y. Wang, Quasi-single field inflation and non-Gaussianities, JCAP 04 (2010) 027 [arXiv:0911.3380] [INSPIRE].

    Article  ADS  Google Scholar 

  4. X. Chen and Y. Wang, Quasi-single field inflation with large mass, JCAP 09 (2012) 021 [arXiv:1205.0160] [INSPIRE].

    Article  ADS  Google Scholar 

  5. S. Pi and M. Sasaki, Curvature perturbation spectrum in two-field inflation with a turning trajectory, JCAP 10 (2012) 051 [arXiv:1205.0161] [INSPIRE].

    Article  ADS  Google Scholar 

  6. J.-O. Gong, S. Pi and M. Sasaki, Equilateral non-Gaussianity from heavy fields, JCAP 11 (2013) 043 [arXiv:1306.3691] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  7. N. Arkani-Hamed and J. Maldacena, Cosmological collider physics, arXiv:1503.08043 [INSPIRE].

  8. X. Chen, Y. Wang and Z.-Z. Xianyu, Neutrino signatures in primordial non-Gaussianities, JHEP 09 (2018) 022 [arXiv:1805.02656] [INSPIRE].

    Article  ADS  Google Scholar 

  9. L.-T. Wang and Z.-Z. Xianyu, In search of large signals at the cosmological collider, JHEP 02 (2020) 044 [arXiv:1910.12876] [INSPIRE].

    Article  ADS  Google Scholar 

  10. L.-T. Wang and Z.-Z. Xianyu, Gauge boson signals at the cosmological collider, JHEP 11 (2020) 082 [arXiv:2004.02887] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  11. A. Bodas, S. Kumar and R. Sundrum, The scalar chemical potential in cosmological collider physics, JHEP 02 (2021) 079 [arXiv:2010.04727] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  12. X. Chen, Y. Wang and Z.-Z. Xianyu, Loop corrections to Standard Model fields in inflation, JHEP 08 (2016) 051 [arXiv:1604.07841] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. H. Lee, D. Baumann and G.L. Pimentel, Non-Gaussianity as a particle detector, JHEP 12 (2016) 040 [arXiv:1607.03735] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  14. X. Chen, Y. Wang and Z.-Z. Xianyu, Standard Model background of the cosmological collider, Phys. Rev. Lett. 118 (2017) 261302 [arXiv:1610.06597] [INSPIRE].

  15. X. Chen, Y. Wang and Z.-Z. Xianyu, Standard Model mass spectrum in inflationary universe, JHEP 04 (2017) 058 [arXiv:1612.08122] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. H. An, M. McAneny, A.K. Ridgway and M.B. Wise, Quasi single field inflation in the non-perturbative regime, JHEP 06 (2018) 105 [arXiv:1706.09971] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  17. S. Kumar and R. Sundrum, Heavy-lifting of gauge theories by cosmic inflation, JHEP 05 (2018) 011 [arXiv:1711.03988] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. X. Chen, Y. Wang and Z.-Z. Xianyu, Schwinger-Keldysh diagrammatics for primordial perturbations, JCAP 12 (2017) 006 [arXiv:1703.10166] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Y.-P. Wu, Higgs as heavy-lifted physics during inflation, JHEP 04 (2019) 125 [arXiv:1812.10654] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  20. L. Li, T. Nakama, C.M. Sou, Y. Wang and S. Zhou, Gravitational production of superheavy dark matter and associated cosmological signatures, JHEP 07 (2019) 067 [arXiv:1903.08842] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  21. S. Lu, Y. Wang and Z.-Z. Xianyu, A cosmological Higgs collider, JHEP 02 (2020) 011 [arXiv:1907.07390] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  22. T. Liu, X. Tong, Y. Wang and Z.-Z. Xianyu, Probing P and CP-violations on the cosmological collider, JHEP 04 (2020) 189 [arXiv:1909.01819] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  23. A. Hook, J. Huang and D. Racco, Searches for other vacua. Part II. A new Higgstory at the cosmological collider, JHEP 01 (2020) 105 [arXiv:1907.10624] [INSPIRE].

  24. A. Hook, J. Huang and D. Racco, Minimal signatures of the Standard Model in non-Gaussianities, Phys. Rev. D 101 (2020) 023519 [arXiv:1908.00019] [INSPIRE].

  25. S. Kumar and R. Sundrum, Cosmological collider physics and the curvaton, JHEP 04 (2020) 077 [arXiv:1908.11378] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  26. S. Alexander, S.J. Gates, L. Jenks, K. Koutrolikos and E. McDonough, Higher spin supersymmetry at the cosmological collider: sculpting SUSY rilles in the CMB, JHEP 10 (2019) 156 [arXiv:1907.05829] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  27. D.-G. Wang, On the inflationary massive field with a curved field manifold, JCAP 01 (2020) 046 [arXiv:1911.04459] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  28. Y. Wang and Y. Zhu, Cosmological collider signatures of massive vectors from non-Gaussian gravitational waves, JCAP 04 (2020) 049 [arXiv:2001.03879] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  29. L. Li, S. Lu, Y. Wang and S. Zhou, Cosmological signatures of superheavy dark matter, JHEP 07 (2020) 231 [arXiv:2002.01131] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  30. J. Fan and Z.-Z. Xianyu, A cosmic microscope for the preheating era, JHEP 01 (2021) 021 [arXiv:2005.12278] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  31. S. Aoki and M. Yamaguchi, Disentangling mass spectra of multiple fields in cosmological collider, JHEP 04 (2021) 127 [arXiv:2012.13667] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  32. N. Maru and A. Okawa, Non-Gaussianity from X , Y gauge bosons in cosmological collider physics, arXiv:2101.10634 [INSPIRE].

  33. P.D. Meerburg, M. Münchmeyer, J.B. Muñoz and X. Chen, Prospects for cosmological collider physics, JCAP 03 (2017) 050 [arXiv:1610.06559] [INSPIRE].

    Article  ADS  Google Scholar 

  34. A. Moradinezhad Dizgah, H. Lee, J.B. Muñoz and C. Dvorkin, Galaxy bispectrum from massive spinning particles, JCAP 05 (2018) 013 [arXiv:1801.07265] [INSPIRE].

  35. K. Kogai, K. Akitsu, F. Schmidt and Y. Urakawa, Galaxy imaging surveys as spin-sensitive detector for cosmological colliders, JCAP 03 (2021) 060 [arXiv:2009.05517] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. N. Barnaby and M. Peloso, Large non-Gaussianity in axion inflation, Phys. Rev. Lett. 106 (2011) 181301 [arXiv:1011.1500] [INSPIRE].

  37. N. Barnaby, R. Namba and M. Peloso, Phenomenology of a pseudo-scalar inflaton: naturally large non-Gaussianity, JCAP 04 (2011) 009 [arXiv:1102.4333] [INSPIRE].

    Article  ADS  Google Scholar 

  38. P. Adshead, E. Martinec and M. Wyman, Gauge fields and inflation: chiral gravitational waves, fluctuations, and the Lyth bound, Phys. Rev. D 88 (2013) 021302 [arXiv:1301.2598] [INSPIRE].

  39. P. Adshead and E.I. Sfakianakis, Fermion production during and after axion inflation, JCAP 11 (2015) 021 [arXiv:1508.00891] [INSPIRE].

    Article  ADS  Google Scholar 

  40. M. Peloso, L. Sorbo and C. Unal, Rolling axions during inflation: perturbativity and signatures, JCAP 09 (2016) 001 [arXiv:1606.00459] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  41. S. Weinberg, Quantum contributions to cosmological correlations, Phys. Rev. D 72 (2005) 043514 [hep-th/0506236] [INSPIRE].

  42. N. Arkani-Hamed, D. Baumann, H. Lee and G.L. Pimentel, The cosmological bootstrap: inflationary correlators from symmetries and singularities, JHEP 04 (2020) 105 [arXiv:1811.00024] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee and G.L. Pimentel, The cosmological bootstrap: weight-shifting operators and scalar seeds, JHEP 12 (2020) 204 [arXiv:1910.14051] [INSPIRE].

  44. D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee and G.L. Pimentel, The cosmological bootstrap: spinning correlators from symmetries and factorization, SciPost Phys. 11 (2021) 071 [arXiv:2005.04234] [INSPIRE].

  45. C. Sleight, A Mellin space approach to cosmological correlators, JHEP 01 (2020) 090 [arXiv:1906.12302] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  46. C. Sleight and M. Taronna, Bootstrapping inflationary correlators in Mellin space, JHEP 02 (2020) 098 [arXiv:1907.01143] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. E. Pajer, D. Stefanyszyn and J. Supeł, The boostless bootstrap: amplitudes without Lorentz boosts, JHEP 12 (2020) 198 [arXiv:2007.00027] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. H. Goodhew, S. Jazayeri and E. Pajer, The cosmological optical theorem, JCAP 04 (2021) 021 [arXiv:2009.02898] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  49. C. Sleight and M. Taronna, From AdS to dS exchanges: spectral representation, Mellin amplitudes and crossing, arXiv:2007.09993 [INSPIRE].

  50. S. Jazayeri, E. Pajer and D. Stefanyszyn, From locality and unitarity to cosmological correlators, JHEP 10 (2021) 065 [arXiv:2103.08649] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  51. S. Melville and E. Pajer, Cosmological cutting rules, JHEP 05 (2021) 249 [arXiv:2103.09832] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  52. L. Di Pietro, V. Gorbenko and S. Komatsu, Analyticity and unitarity for cosmological correlators, arXiv:2108.01695 [INSPIRE].

  53. C. Sleight and M. Taronna, From dS to AdS and back, JHEP 12 (2021) 074 [arXiv:2109.02725] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  54. Q. Lu, M. Reece and Z.-Z. Xianyu, Missing scalars at the cosmological collider, JHEP 12 (2021) 098 [arXiv:2108.11385] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  55. X. Chen, Primordial non-Gaussianities from inflation models, Adv. Astron. 2010 (2010) 638979 [arXiv:1002.1416] [INSPIRE].

  56. Y. Wang, Inflation, cosmic perturbations and non-Gaussianities, Commun. Theor. Phys. 62 (2014) 109 [arXiv:1303.1523] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  57. D. Marolf and I.A. Morrison, The IR stability of de Sitter: loop corrections to scalar propagators, Phys. Rev. D 82 (2010) 105032 [arXiv:1006.0035] [INSPIRE].

  58. W.Z. Chua, Q. Ding, Y. Wang and S. Zhou, Imprints of Schwinger effect on primordial spectra, JHEP 04 (2019) 066 [arXiv:1810.09815] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  59. F. Johansson et al., mpmath: a python library for arbitrary-precision floating-point arithmetic, version 0.18, http://mpmath.org/, December 2013.

  60. ComplexPlot — Wolfram Language & System Documentation Center, https://reference.wolfram.com/language/ref/ComplexPlot.html.

  61. HighpassFilter — Wolfram Language & System Documentation Center, https://reference.wolfram.com/language/ref/HighpassFilter.html.

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Author information

Authors and Affiliations

  1. Department of Physics, University of Chicago, Chicago, IL, 60637, USA

    Lian-Tao Wang

  2. Department of Physics, Tsinghua University, Beijing, 100084, China

    Zhong-Zhi Xianyu

  3. Kavli Institute for Cosmological Physics, University of Chicago, 5640 S Ellis Ave, Chicago, IL, 60637, USA

    Yi-Ming Zhong

Authors
  1. Lian-Tao Wang
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  2. Zhong-Zhi Xianyu
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  3. Yi-Ming Zhong
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Correspondence to Yi-Ming Zhong.

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ArXiv ePrint: 2109.14635

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Cite this article

Wang, LT., Xianyu, ZZ. & Zhong, YM. Precision calculation of inflation correlators at one loop. J. High Energ. Phys. 2022, 85 (2022). https://doi.org/10.1007/JHEP02(2022)085

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  • Received: 14 October 2021

  • Revised: 16 December 2021

  • Accepted: 30 January 2022

  • Published: 11 February 2022

  • DOI: https://doi.org/10.1007/JHEP02(2022)085

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Keywords

  • Cosmology of Theories beyond the SM
  • Beyond Standard Model
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