Abstract
We calculate 1-loop corrections to the Schwinger-Keldysh propagators of Standard-Model-like fields of spin-0, 1/2, and 1, with all renormalizable interactions during inflation. We pay special attention to the late-time divergences of loop corrections, and show that the divergences can be resummed into finite results in the late-time limit using dynamical renormalization group method. This is our first step toward studying both the Standard Model and new physics in the primordial universe.
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References
A.H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D 23 (1981) 347 [INSPIRE].
A.D. Linde, A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems, Phys. Lett. B 108 (1982) 389 [INSPIRE].
A. Albrecht and P.J. Steinhardt, Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking, Phys. Rev. Lett. 48 (1982) 1220 [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity, Astron. Astrophys. 571 (2014) A24 [arXiv:1303.5084] [INSPIRE].
CMBPol Study Team collaboration, D. Baumann et al., CMBPol Mission Concept Study: Probing Inflation with CMB Polarization, AIP Conf. Proc. 1141 (2009) 10 [arXiv:0811.3919] [INSPIRE].
T. Matsumura et al., Mission design of LiteBIRD, J. Low Temp. Phys. 176 (2014) 733 [arXiv:1311.2847] [INSPIRE].
O. Doré et al., Cosmology with the SPHEREX All-Sky Spectral Survey, arXiv:1412.4872 [INSPIRE].
J.B. Muñoz, Y. Ali-Haïmoud and M. Kamionkowski, Primordial non-Gaussianity from the bispectrum of 21-cm fluctuations in the dark ages, Phys. Rev. D 92 (2015) 083508 [arXiv:1506.04152] [INSPIRE].
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].
X. Chen and Y. Wang, Quasi-Single Field Inflation and Non-Gaussianities, JCAP 04 (2010) 027 [arXiv:0911.3380] [INSPIRE].
N. Arkani-Hamed and J. Maldacena, Cosmological Collider Physics, arXiv:1503.08043 [INSPIRE].
D. Baumann and D. Green, Signatures of Supersymmetry from the Early Universe, Phys. Rev. D 85 (2012) 103520 [arXiv:1109.0292] [INSPIRE].
V. Assassi, D. Baumann and D. Green, On Soft Limits of Inflationary Correlation Functions, JCAP 11 (2012) 047 [arXiv:1204.4207] [INSPIRE].
T. Noumi, M. Yamaguchi and D. Yokoyama, Effective field theory approach to quasi-single field inflation and effects of heavy fields, JHEP 06 (2013) 051 [arXiv:1211.1624] [INSPIRE].
X. Chen, Primordial Non-Gaussianities from Inflation Models, Adv. Astron. 2010 (2010) 638979 [arXiv:1002.1416] [INSPIRE].
Y. Wang, Inflation, Cosmic Perturbations and Non-Gaussianities, Commun. Theor. Phys. 62 (2014) 109 [arXiv:1303.1523] [INSPIRE].
D. Baumann and L. McAllister, Inflation and String Theory, arXiv:1404.2601.
F.L. Bezrukov and M. Shaposhnikov, The Standard Model Higgs boson as the inflaton, Phys. Lett. B 659 (2008) 703 [arXiv:0710.3755] [INSPIRE].
F. Bezrukov, The Higgs field as an inflaton, Class. Quant. Grav. 30 (2013) 214001 [arXiv:1307.0708] [INSPIRE].
X. Chen, Y. Wang and Z. Xianyu, in preparation.
A.D. Linde, Scalar Field Fluctuations in Expanding Universe and the New Inflationary Universe Scenario, Phys. Lett. B 116 (1982) 335 [INSPIRE].
A.A. Starobinsky, Dynamics of Phase Transition in the New Inflationary Universe Scenario and Generation of Perturbations, Phys. Lett. B 117 (1982) 175 [INSPIRE].
A.A. Starobinsky and J. Yokoyama, Equilibrium state of a selfinteracting scalar field in the de Sitter background, Phys. Rev. D 50 (1994) 6357 [astro-ph/9407016] [INSPIRE].
F. Finelli, G. Marozzi, A.A. Starobinsky, G.P. Vacca and G. Venturi, Generation of fluctuations during inflation: Comparison of stochastic and field-theoretic approaches, Phys. Rev. D 79 (2009) 044007 [arXiv:0808.1786] [INSPIRE].
F. Finelli, G. Marozzi, A.A. Starobinsky, G.P. Vacca and G. Venturi, Stochastic growth of quantum fluctuations during slow-roll inflation, Phys. Rev. D 82 (2010) 064020 [arXiv:1003.1327] [INSPIRE].
C.P. Burgess, R. Holman and G. Tasinato, Open EFTs, IR effects & late-time resummations: systematic corrections in stochastic inflation, JHEP 01 (2016) 153 [arXiv:1512.00169] [INSPIRE].
C.P. Burgess, L. Leblond, R. Holman and S. Shandera, Super-Hubble de Sitter Fluctuations and the Dynamical RG, JCAP 03 (2010) 033 [arXiv:0912.1608] [INSPIRE].
C.P. Burgess, R. Holman, L. Leblond and S. Shandera, Breakdown of Semiclassical Methods in de Sitter Space, JCAP 10 (2010) 017 [arXiv:1005.3551] [INSPIRE].
V.K. Onemli and R.P. Woodard, Superacceleration from massless, minimally coupled ϕ 4, Class. Quant. Grav. 19 (2002) 4607 [gr-qc/0204065] [INSPIRE].
T. Brunier, V.K. Onemli and R.P. Woodard, Two loop scalar self-mass during inflation, Class. Quant. Grav. 22 (2005) 59 [gr-qc/0408080] [INSPIRE].
E.O. Kahya, V.K. Onemli and R.P. Woodard, The ζ-ζ Correlator Is Time Dependent, Phys. Lett. B 694 (2011) 101 [arXiv:1006.3999] [INSPIRE].
V.K. Onemli, Quantum corrected mode function and power spectrum for a scalar field during inflation, Phys. Rev. D 89 (2014) 083537 [arXiv:1312.6409] [INSPIRE].
A. Rajaraman, On the proper treatment of massless fields in Euclidean de Sitter space, Phys. Rev. D 82 (2010) 123522 [arXiv:1008.1271] [INSPIRE].
M. Beneke and P. Moch, On “dynamical mass” generation in Euclidean de Sitter space, Phys. Rev. D 87 (2013) 064018 [arXiv:1212.3058] [INSPIRE].
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].
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].
A. Higuchi, D. Marolf and I.A. Morrison, On the Equivalence between Euclidean and In-In Formalisms in de Sitter QFT, Phys. Rev. D 83 (2011) 084029 [arXiv:1012.3415] [INSPIRE].
E.T. Akhmedov, IR divergences and kinetic equation in de Sitter space. Poincaré patch: Principal series, JHEP 01 (2012) 066 [arXiv:1110.2257] [INSPIRE].
D. Krotov and A.M. Polyakov, Infrared Sensitivity of Unstable Vacua, Nucl. Phys. B 849 (2011) 410 [arXiv:1012.2107] [INSPIRE].
A.M. Polyakov, Infrared instability of the de Sitter space, arXiv:1209.4135 [INSPIRE].
J.I. Kapusta and C. Gale, Finite-Temperature Field Theory, Principles and Applications, second editon, Cambridge University Press (2006).
J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [INSPIRE].
R.D. Jordan, Effective Field Equations for Expectation Values, Phys. Rev. D 33 (1986) 444 [INSPIRE].
M. van der Meulen and J. Smit, Classical approximation to quantum cosmological correlations, JCAP 11 (2007) 023 [arXiv:0707.0842] [INSPIRE].
B. Garbrecht and T. Prokopec, Fermion mass generation in de Sitter space, Phys. Rev. D 73 (2006) 064036 [gr-qc/0602011] [INSPIRE].
B. Greene, M. Parikh and J.P. van der Schaar, Universal correction to the inflationary vacuum, JHEP 04 (2006) 057 [hep-th/0512243] [INSPIRE].
A.-C. Davis, K. Dimopoulos, T. Prokopec and O. Tornkvist, Primordial spectrum of gauge fields from inflation, Phys. Lett. B 501 (2001) 165 [astro-ph/0007214] [INSPIRE].
T. Prokopec, O. Tornkvist and R.P. Woodard, One loop vacuum polarization in a locally de Sitter background, Annals Phys. 303 (2003) 251 [gr-qc/0205130] [INSPIRE].
T. Prokopec, O. Tornkvist and R.P. Woodard, Photon mass from inflation, Phys. Rev. Lett. 89 (2002) 101301 [astro-ph/0205331] [INSPIRE].
T. Prokopec and E. Puchwein, Photon mass generation during inflation: de Sitter invariant case, JCAP 04 (2004) 007 [astro-ph/0312274] [INSPIRE].
T. Prokopec and R.P. Woodard, Dynamics of superhorizon photons during inflation with vacuum polarization, Annals Phys. 312 (2004) 1 [gr-qc/0310056] [INSPIRE].
N.C. Tsamis and R.P. Woodard, The Quantum gravitational back reaction on inflation, Annals Phys. 253 (1997) 1 [hep-ph/9602316] [INSPIRE].
N.C. Tsamis and R.P. Woodard, One loop graviton selfenergy in a locally de Sitter background, Phys. Rev. D 54 (1996) 2621 [hep-ph/9602317] [INSPIRE].
E. Dimastrogiovanni and N. Bartolo, One-loop graviton corrections to the curvature perturbation from inflation, JCAP 11 (2008) 016 [arXiv:0807.2790] [INSPIRE].
N. Bartolo, E. Dimastrogiovanni and A. Vallinotto, One-loop corrections to the power spectrum in general single-field inflation, JCAP 11 (2010) 003 [arXiv:1006.0196] [INSPIRE].
S.B. Giddings and M.S. Sloth, Semiclassical relations and IR effects in de Sitter and slow-roll space-times, JCAP 01 (2011) 023 [arXiv:1005.1056] [INSPIRE].
W. Xue, X. Gao and R. Brandenberger, IR Divergences in Inflation and Entropy Perturbations, JCAP 06 (2012) 035 [arXiv:1201.0768] [INSPIRE].
W.H. Kinney, Horizon crossing and inflation with large η, Phys. Rev. D 72 (2005) 023515 [gr-qc/0503017] [INSPIRE].
M.H. Namjoo, H. Firouzjahi and M. Sasaki, Violation of non-Gaussianity consistency relation in a single field inflationary model, Europhys. Lett. 101 (2013) 39001 [arXiv:1210.3692] [INSPIRE].
X. Chen, H. Firouzjahi, M.H. Namjoo and M. Sasaki, A Single Field Inflation Model with Large Local Non-Gaussianity, Europhys. Lett. 102 (2013) 59001 [arXiv:1301.5699] [INSPIRE].
Q.-G. Huang and Y. Wang, Large Local Non-Gaussianity from General Single-field Inflation, JCAP 06 (2013) 035 [arXiv:1303.4526] [INSPIRE].
X. Chen, H. Firouzjahi, M.H. Namjoo and M. Sasaki, Fluid Inflation, JCAP 09 (2013) 012 [arXiv:1306.2901] [INSPIRE].
X. Chen, H. Firouzjahi, E. Komatsu, M.H. Namjoo and M. Sasaki, In-in and δN calculations of the bispectrum from non-attractor single-field inflation, JCAP 12 (2013) 039 [arXiv:1308.5341] [INSPIRE].
D.H. Lyth, K.A. Malik and M. Sasaki, A General proof of the conservation of the curvature perturbation, JCAP 05 (2005) 004 [astro-ph/0411220] [INSPIRE].
V. Assassi, D. Baumann and D. Green, Symmetries and Loops in Inflation, JHEP 02 (2013) 151 [arXiv:1210.7792] [INSPIRE].
L. Senatore and M. Zaldarriaga, On Loops in Inflation, JHEP 12 (2010) 008 [arXiv:0912.2734] [INSPIRE].
L. Senatore and M. Zaldarriaga, On Loops in Inflation II: IR Effects in Single Clock Inflation, JHEP 01 (2013) 109 [arXiv:1203.6354] [INSPIRE].
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].
L. Senatore and M. Zaldarriaga, The constancy of ζ in single-clock Inflation at all loops, JHEP 09 (2013) 148 [arXiv:1210.6048] [INSPIRE].
S. Weinberg, Quantum contributions to cosmological correlations, Phys. Rev. D 72 (2005) 043514 [hep-th/0506236] [INSPIRE].
S. Weinberg, Quantum contributions to cosmological correlations. II. Can these corrections become large?, Phys. Rev. D 74 (2006) 023508 [hep-th/0605244] [INSPIRE].
A.A. Starobinsky and J. Yokoyama, Equilibrium state of a selfinteracting scalar field in the de Sitter background, Phys. Rev. D 50 (1994) 6357 [astro-ph/9407016] [INSPIRE].
N. Bartolo, S. Matarrese, M. Pietroni, A. Riotto and D. Seery, On the Physical Significance of Infra-red Corrections to Inflationary Observables, JCAP 01 (2008) 015 [arXiv:0711.4263] [INSPIRE].
N.C. Tsamis, A. Tzetzias and R.P. Woodard, Stochastic Samples versus Vacuum Expectation Values in Cosmology, JCAP 09 (2010) 016 [arXiv:1006.5681] [INSPIRE].
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Chen, X., Wang, Y. & Xianyu, ZZ. Loop Corrections to Standard Model fields in inflation. J. High Energ. Phys. 2016, 51 (2016). https://doi.org/10.1007/JHEP08(2016)051
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DOI: https://doi.org/10.1007/JHEP08(2016)051