The pre-inflationary vacuum in the cosmic microwave background

Abstract

We consider the effects on the primordial power spectrum of a period of radiation-dominated expansion prior to the inflationary era. If inflation lasts a total of only 60 e-folds or so, the boundary condition for quantum modes cannot be taken in the short-wavelength limit as in the standard perturbation calculation. Instead, the boundary condition is set by the vacuum state of the prior radiation-dominated epoch, which only corresponds to the inflationary vacuum state in the ultraviolet limit. This altered vacuum state results in a modulation of the inflationary power spectrum. We calculate the modification to a best-fit model from the WMAP3 data set, and find that power is suppressed at large scales. The modified power spectrum is favored only very weakly by the data.

arXiv comment4 pages, 2 figures, references added. Version submitted to PRL. (v3: 9 pages, 4 figures, detailed justification of Eq. 11 of v2. Version accepted for publication by PRD.)

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