Abstract
In this short note we organize a perturbation theory for the Bunch-Davies wavefunction in flat, accelerating cosmologies. The calculational technique avoids the in-in formalism and instead uses an analytic continuation from Euclidean signature. We will consider both massless and conformally coupled self-interacting scalars. These calculations explicitly illustrate two facts. The first is that IR divergences get sharper as the acceleration slows. The second is that UV-divergent contact terms in the Euclidean computation can contribute to the absolute value of the wavefunction in Lorentzian signature. Here UV divergent refers to terms involving inverse powers of the radial cutoff in the Euclidean computation. In Lorentzian signature such terms encode physical time dependence of the wavefunction.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [INSPIRE].
L.V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [INSPIRE].
K.T. Mahanthappa, Multiple production of photons in quantum electrodynamics, Phys. Rev. 126 (1962) 329 [INSPIRE].
P.M. Bakshi and K.T. Mahanthappa, Expectation value formalism in quantum field theory. 1., J. Math. Phys. 4 (1963) 1 [INSPIRE].
P.M. Bakshi and K.T. Mahanthappa, Expectation value formalism in quantum field theory. 2., J. Math. Phys. 4 (1963) 12 [INSPIRE].
E. Calzetta and B.L. Hu, Closed Time Path Functional Formalism in Curved Space-Time: Application to Cosmological Back Reaction Problems, Phys. Rev. D 35 (1987) 495 [INSPIRE].
M. Morikawa, Cosmological inflation as a quantum phase transition, Prog. Theor. Phys. 93 (1995) 685 [INSPIRE].
N.C. Tsamis and R.P. Woodard, Strong infrared effects in quantum gravity, Annals Phys. 238 (1995) 1.
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, Matter contributions to the expansion rate of the universe, Phys. Lett. B 426 (1998) 21 [hep-ph/9710466] [INSPIRE].
V.K. Onemli and R.P. Woodard, Quantum effects can render w < −1 on cosmological scales, Phys. Rev. D 70 (2004) 107301 [gr-qc/0406098] [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. 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].
T. Prokopec and R.P. Woodard, Production of massless fermions during inflation, JHEP 10 (2003) 059 [astro-ph/0309593] [INSPIRE].
H. Collins and R. Holman, Renormalization of initial conditions and the trans-Planckian problem of inflation, Phys. Rev. D 71 (2005) 085009 [hep-th/0501158] [INSPIRE].
D. Boyanovsky, H.J. de Vega and N.G. Sanchez, Quantum corrections to slow roll inflation and new scaling of superhorizon fluctuations, Nucl. Phys. B 747 (2006) 25 [astro-ph/0503669] [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].
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].
S. Weinberg, Quantum contributions to cosmological correlations, Phys. Rev. D 72 (2005) 043514 [hep-th/0506236] [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].
D. Seery, Infrared effects in inflationary correlation functions, Class. Quant. Grav. 27 (2010) 124005 [arXiv:1005.1649] [INSPIRE].
D. Anninos, T. Anous, D.Z. Freedman and G. Konstantinidis, Late-time Structure of the Bunch-Davies de Sitter Wavefunction, JCAP 11 (2015) 048 [arXiv:1406.5490] [INSPIRE].
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
E. Shaghoulian, FRW cosmologies and hyperscaling-violating geometries: higher curvature corrections, ultrametricity, Q-space/QFT duality and a little string theory, JHEP 03 (2014) 011 [arXiv:1308.1095] [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].
P. McFadden and K. Skenderis, Observational signatures of holographic models of inflation, in On recent developments in theoretical and experimental general relativity, astrophysics and relativistic field theories, proceedings of the 12th Marcel Grossmann Meeting on General Relativity, Paris, France, 12-18 July 2009, pp. 2315-2323 (2010). [arXiv:1010.0244] [INSPIRE].
P. McFadden and K. Skenderis, Holographic Non-Gaussianity, JCAP 05 (2011) 013 [arXiv:1011.0452] [INSPIRE].
C. Charmousis, B. Gouteraux, B.S. Kim, E. Kiritsis and R. Meyer, Effective Holographic Theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [INSPIRE].
L. Huijse, S. Sachdev and B. Swingle, Hidden Fermi surfaces in compressible states of gauge-gravity duality, Phys. Rev. B 85 (2012) 035121 [arXiv:1112.0573] [INSPIRE].
S. Hellerman and I. Swanson, Cosmological solutions of supercritical string theory, Phys. Rev. D 77 (2008) 126011 [hep-th/0611317] [INSPIRE].
M. Dodelson, X. Dong, E. Silverstein and G. Torroba, New solutions with accelerated expansion in string theory, JHEP 12 (2014) 050 [arXiv:1310.5297] [INSPIRE].
F. Lucchin and S. Matarrese, Power Law Inflation, Phys. Rev. D 32 (1985) 1316 [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XXII. Constraints on inflation, Astron. Astrophys. 571 (2014) A22 [arXiv:1303.5082] [INSPIRE].
H. Ringstrom, Power law inflation, Commun. Math. Phys. 290 (2009) 155.
A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE].
E. Witten, Quantum gravity in de Sitter space, in Strings 2001: International Conference, Mumbai, India, 5-10 January 2001 [hep-th/0106109] [INSPIRE].
D. Anninos, F. Denef and D. Harlow, Wave function of Vasiliev’s universe: A few slices thereof, Phys. Rev. D 88 (2013) 084049 [arXiv:1207.5517] [INSPIRE].
D. Anninos, F. Denef, G. Konstantinidis and E. Shaghoulian, Higher Spin de Sitter Holography from Functional Determinants, JHEP 02 (2014) 007 [arXiv:1305.6321] [INSPIRE].
G. Conti and T. Hertog, Two wave functions and dS/CFT on S1 × S2, JHEP 06 (2015) 101 [arXiv:1412.3728] [INSPIRE].
J.B. Hartle, S.W. Hawking and T. Hertog, No-Boundary Measure of the Universe, Phys. Rev. Lett. 100 (2008) 201301 [arXiv:0711.4630] [INSPIRE].
D. Anninos, de Sitter Musings, Int. J. Mod. Phys. A 27 (2012) 1230013 [arXiv:1205.3855] [INSPIRE].
S. Banerjee, A. Belin, S. Hellerman et al., Topology of Future Infinity in dS/CFT, JHEP 11 (2013) 026 [arXiv:1306.6629] [INSPIRE].
D. Anninos, T. Hartman and A. Strominger, Higher Spin Realization of the dS/CFT Correspondence, arXiv:1108.5735 [INSPIRE].
D. Anninos, R. Mahajan, D . Radičević and E. Shaghoulian, Chern-Simons-Ghost Theories and de Sitter Space, JHEP 01 (2015) 074 [arXiv:1405.1424] [INSPIRE].
C.-M. Chang, A. Pathak and A. Strominger, Non-Minimal Higher-Spin DS4/CFT3, arXiv:1309.7413 [INSPIRE].
D. Anninos and F. Denef, Cosmic Clustering, JHEP 06 (2016) 181 [arXiv:1111.6061] [INSPIRE].
D.A. Roberts and D. Stanford, On memory in exponentially expanding spaces, JHEP 06 (2013) 042 [arXiv:1210.5238] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1608.06163
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Konstantinidis, G., Mahajan, R. & Shaghoulian, E. Late-time structure of the Bunch-Davies FRW wavefunction. J. High Energ. Phys. 2016, 103 (2016). https://doi.org/10.1007/JHEP10(2016)103
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2016)103