How long before the end of inflation were observable perturbations produced?

Abstract

We reconsider the issue of the number of e-foldings before the end of inflation at which observable perturbations were generated. We determine a plausible upper limit on that number for the standard cosmology which is around 60, with the expectation that the actual value will be up to 10 below this. We also note a special property of the $\lambda {\varphi }^4$ model which reduces the uncertainties in that case and favours a higher value, giving a fairly definite prediction of 64 e-foldings for that model. We note an extreme (and highly implausible) situation where the number of e-foldings can be even higher, possibly up to 100, and discuss the shortcomings of quantifying inflation by e-foldings rather than by the change in $aH$. Finally, we discuss the impact of non-standard evolution between the end of inflation and the present, showing that again the expected number of e-foldings can be modified, and in some cases significantly increased.

arXiv comment7 pages RevTeX4 file with one figure incorporated. Minor updates to match version accepted by Physical Review D

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• Primordial Perturbations Including Second-Order Derivatives of the Inflationary Potential
• Thermal History of the Universe After Inflation
• The Primordial Magnetic Field (PMF) Generated in Large Field Inflation (LFI), Natural Inflation (NI) and $R^2$-Inflation by $f^{2}FF$ Model
• Complex Inflaton Potentials with Nonminimal Coupling: Robust Inflation and Geometric Reheating
• Relic gravitons at intermediate frequencies and the expansion history of the Universe
• Dark Matter Freeze-in from a $Z^{\prime }$ Reheaton
• Retrofitting Models of Inflation
• Non-Gaussianity in D3-brane inflation
• Installing of cosmological constant
• The effective Higgs potential and vacuum decay in Starobinsky inflation
• Non-Gaussianity after many-field reheating
• Bridging inflation and reheating: chiral gravitational waves from aHz to GHz
• Mixed constraints to inflationary models