Preinflationary genesis with CMB B-mode polarization

Recent B-mode polarization observation seems to imply the tensor tilt $n_T\gtrsim 1$ at large angular scale if the primordial signal is dominated. We show that for a primordial universe, which is in a slowly expanding genesis phase before the slow-roll inflation, the primordial tensor spectrum will get a large-scale cutoff, i.e., $n_T\gtrsim 1$ at large scales while $n_T\simeq 0$ at small scale. We find that this inflationary scenario not only may be consistent with the observation, but also predicts a large-scale anomaly in BB power spectrum, i.e., due to the large suppression of tensor perturbation amplitude we will hardly see the reionization bump at low-$l$, which may be falsified by the Planck polarization data.

Figure 1

The sketch of the evolution of primordial perturbations in our scenario. The perturbation mode at large scale is from the preinflationary genesis phase, while others are from the inflationary phase.

Figure 2

The sketch of the evolution of $H$. During the preinflationary phase, it initially is negligible, but rapidly increases with the time. After $H=H_{\text{inf}}$, it becomes nearly unchanged, the slow-roll inflation will begin. The inset is the power spectrum (12) of the primordial tensor perturbation in our scenario with respect to $k/{\mathcal{H}}_{*}$, which has a large-scale cutoff, i.e., $n_T\gtrsim 1$ for $k<{\mathcal{H}}_{*}$ and $n_T\simeq 0$ for $k>{\mathcal{H}}_{*}$. The figure of the evolution of $H$ with the time should be almost coincident with that of the tensor spectrum with respect to $k$, because the amplitude of tensor mode with wavelength $1/k$ is $\sim H$ at the time $k=aH$.

Figure 3

Theoretical CMB BB power spectra for the conventional slow-roll inflationary scenario (black solid line), in which the tensor spectrum is power law, and ${\mathrm{\Omega }}_b{h}^2=0.02184$, ${\mathrm{\Omega }}_c{h}^2=0.118$, $\tau =0.08$, $100{\mathrm{\Theta }}_s=1.04$, $n_{\mathcal{R}}=0.96$, $A_s=2.14\times {10}^{-9}$, and our scenario (red dashed line), in which $n_T$ is replaced with Eq. (12).

Figure 4

Theoretical CMB BB power spectra for the conventional slow-roll inflationary scenario (black solid line), in which the tensor spectrum is power-law, and ${\mathrm{\Omega }}_b{h}^2=0.02184$, ${\mathrm{\Omega }}_c{h}^2=0.118$, $\tau =0.08$, $100{\mathrm{\Theta }}_s=1.04$, $n_{\mathcal{R}}=0.96$ $A_s=2.14\times {10}^{-9}$, and our parametrized model, in which $n_T$ is replaced with the parametrization (1). We consider two cases: $n_{\text{cutoff}}=1$ (blue dashed line) and $n_{\text{cutoff}}=2$ (red dashed line).