Pre-inflationary vacuum in the cosmic microwave background

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 WMAP3 temperature and polarization data.

Figure 1

Best-fit WMAP3 spectrum calculated using standard inflationary initial conditions along with the same inflation model but with a radiation-dominated pre-inflationary phase.

Figure 2

$C_{\ell }^{TT}$-spectra for the best-fit WMAP3 model (solid black) together with models for which inflation is preceded by radiation-dominated expansion. Models are plotted for varying durations of inflation. Note the suppression of power at large scales.

Figure 3

$C_{\ell }^{EE}$-spectra of the models presented in Fig. 2. The pre-inflation phase has a reduced effect on the $EE$ spectra.

Figure 4

$C_{\ell }^{TE}$-spectra of the models presented in Fig. 2. The suppression is more pronounced in these spectra than in the $TT$- and $EE$-spectra, making this effect potentially observable with future data.