Study of the Spectrum of Inflaton Perturbations

Abstract

We examine the spectrum of inflaton fluctuations resulting from any given long period of exponential inflation. Infrared and ultraviolet divergences in the inflaton dispersion summed over all modes do not appear in our approach. We show how the scale-invariance of the perturbation spectrum arises. We also examine the spectrum of scalar perturbations of the metric that are created by the inflaton fluctuations that have left the Hubble sphere during inflation and the spectrum of density perturbations that they produce at reentry after inflation has ended. When the inflaton dispersion spectrum is renormalized during the expansion, we show (for the case of the quadratic inflaton potential) that the density perturbation spectrum approaches a mass-independent limit as the inflaton mass approaches zero, and remains near that limiting value for masses less than about 1/4 of the inflationary Hubble constant. We show that this limiting behavior does not occur if one only makes the Minkowski space subtraction, without the further adiabatic subtractions that involve time derivatives of the expansion scale factor $a(t)$. We also find a parametrized expression for the energy density produced by the change in $a(t)$ as inflation ends. If the end of inflation were sufficiently abrupt, then the temperature corresponding to this energy density could be very significant. We also show that fluctuations of the inflaton field that are present before inflation starts are not dissipated during inflation, and could have a significant observational effect today. The mechanism for this is caused by the initial fluctuations through stimulated emission from the vacuum.

21 pages, 13 figures

References in corpus (12)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP data
• Superheavy dark matter
• Pointer states for primordial fluctuations in inflationary cosmology
• Adiabatic vacuum states on general spacetime manifolds: Definition, construction, and physical properties
• Short distance and initial state effects in inflation: stress tensor and decoherence
• Attractor states and infrared scaling in de Sitter space
• Revising the predictions of inflation for the cosmic microwave background anisotropies
• Inflationary Perturbations and Precision Cosmology
• The Power Spectrum in de Sitter Inflation, Revisited
• Hadamard States and Adiabatic Vacua

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