Abstract
We study one-loop corrections to the two-point correlation function of tensor perturbations in primordial cosmology induced by massless spectator matter fields. Using the Schwinger-Keldysh formalism in cosmological perturbation theory, we employ dimensional regularization and cutoff regularization to study the finite quantum corrections at one-loop arising from isocurvature fields of the massless scalar, fermion and abelian gauge field which are freely propagating on the FRW spacetime. For all cases, we find a logarithmic running of the form \( \frac{C}{q^3}\frac{H^4}{M_p^4} \) log \( \left(\frac{H}{\mu}\right) \) where C is a negative constant related to the beta function, H is the Hubble parameter at horizon exit and μ is the renormalization scale.
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References
S. Weinberg, Quantum contributions to cosmological correlations, Phys. Rev. D 72 (2005) 043514 [hep-th/0506236] [INSPIRE].
L. Senatore and M. Zaldarriaga, On Loops in Inflation, JHEP 12 (2010) 008 [arXiv:0912.2734] [INSPIRE].
K. Chaicherdsakul, Quantum Cosmological Correlations in an Inflating Universe: Can fermion and gauge fields loops give a scale free spectrum?, Phys. Rev. D 75 (2007) 063522 [hep-th/0611352] [INSPIRE].
H.S. Tan, Noncommutative spacetime geometry and one-loop effects in primordial cosmology, Phys. Rev. D 98 (2018) 063518 [arXiv:1807.04323] [INSPIRE].
T. Tanaka and Y. Urakawa, Loops in inflationary correlation functions, Class. Quant. Grav. 30 (2013) 233001 [arXiv:1306.4461] [INSPIRE].
K. Feng, Y.-F. Cai and Y.-S. Piao, IR Divergence in Inflationary Tensor Perturbations from Fermion Loops, Phys. Rev. D 86 (2012) 103515 [arXiv:1207.4405] [INSPIRE].
P. Adshead, R. Easther and E.A. Lim, The ‘in-in’ Formalism and Cosmological Perturbations, Phys. Rev. D 80 (2009) 083521 [arXiv:0904.4207] [INSPIRE].
P. Adshead, R. Easther and E.A. Lim, Cosmology With Many Light Scalar Fields: Stochastic Inflation and Loop Corrections, Phys. Rev. D 79 (2009) 063504 [arXiv:0809.4008] [INSPIRE].
T. Markkanen, Renormalization of the inflationary perturbations revisited, JCAP 05 (2018) 001 [arXiv:1712.02372] [INSPIRE].
T. Markkanen and A. Tranberg, A Simple Method for One-Loop Renormalization in Curved Space-Time, JCAP 08 (2013) 045 [arXiv:1303.0180] [INSPIRE].
D. Baumann and L. McAllister, Inflation and String Theory, in Cambridge Monographs on Mathematical Physics , Cambridge University Press, Cambridge U.K. (2015) [arXiv:1404.2601] [INSPIRE].
D. Baumann, Primordial Cosmology, PoS TASI2017 (2018) 009 [arXiv:1807.03098] [INSPIRE].
S. Weinberg, Cosmology, Oxford University Press, Oxford U.K. (2008).
S. Weinberg, The quantum theory of fields. Volume 3: Supersymmetry, Cambridge University Press, Cambridge U.K. (2013) [INSPIRE].
D. Marolf and I.A. Morrison, The IR stability of de Sitter QFT: results at all orders, Phys. Rev. D 84 (2011) 044040 [arXiv:1010.5327] [INSPIRE].
X. Chen, Y. Wang and Z.-Z. Xianyu, Loop Corrections to Standard Model Fields in Inflation, JHEP 08 (2016) 051 [arXiv:1604.07841] [INSPIRE].
N. Arkani-Hamed and J. Maldacena, Cosmological Collider Physics, arXiv:1503.08043 [INSPIRE].
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].
H.S. Tan, One-loop corrections to the scalar and tensor spectrum from gravitinos, work in progress.
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Tan, H.S. One-loop corrections to the primordial tensor spectrum from massless isocurvature fields. J. High Energ. Phys. 2020, 186 (2020). https://doi.org/10.1007/JHEP10(2020)186
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DOI: https://doi.org/10.1007/JHEP10(2020)186