TY - JOUR

T1 - On the problem of predicting inflationary perturbations

AU - Wang, Limin

AU - Mukhanov, V. F.

AU - Steinhardt, Paul J.

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 1997/11/20

Y1 - 1997/11/20

N2 - We examine the theoretical foundations of standard methods for computing density perturbations in inflationary models. We find that: (1) the time-delay formalism (introduced by Guth and Pi [Phys. Rev. Lett. 49 (1982) 1110]) is only valid when inflation is well-described by the de Sitter solution and the equation-of-state is nearly unchanging; and, (2) the horizon-crossing/Bessel approximation extends to non-exponential inflation, but only if the equation-of-state is changing slowly. Integration of the gauge-invariant perturbation equations mode-by-mode is the only method reliable for general models. For models with rapidly varying equation-of-state, the correction leads to significantly different predictions for the microwave background anisotropy. An important corollary is that methods proposed for "reconstruction" of the inflaton potential from anisotropy data are unreliable for general models.

AB - We examine the theoretical foundations of standard methods for computing density perturbations in inflationary models. We find that: (1) the time-delay formalism (introduced by Guth and Pi [Phys. Rev. Lett. 49 (1982) 1110]) is only valid when inflation is well-described by the de Sitter solution and the equation-of-state is nearly unchanging; and, (2) the horizon-crossing/Bessel approximation extends to non-exponential inflation, but only if the equation-of-state is changing slowly. Integration of the gauge-invariant perturbation equations mode-by-mode is the only method reliable for general models. For models with rapidly varying equation-of-state, the correction leads to significantly different predictions for the microwave background anisotropy. An important corollary is that methods proposed for "reconstruction" of the inflaton potential from anisotropy data are unreliable for general models.

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U2 - 10.1016/S0370-2693(97)01166-0

DO - 10.1016/S0370-2693(97)01166-0

M3 - Article

AN - SCOPUS:0347873705

VL - 414

SP - 18

EP - 27

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 1-2

ER -