Oscillating modulation to B-mode polarization from varying propagating speed of primordial gravitational waves

In low-energy effective string theory and modified gravity theories, the propagating speed $c_T$ of primordial gravitational waves may deviate from unity. We find that the steplike variation of $c_T$ during slow-roll inflation may result in an oscillating modulation to the B-mode polarization spectrum, which can hardly be imitated by adjusting other cosmological parameters, and the intensity of the modulation is determined by the dynamics of $c_T$. Thus provided that the foreground contribution is under control, high-precision cosmic microwave background (CMB) polarization observations will be able to put tight constraint on the variation of $c_T$, and so the corresponding theories.

Figure 1

The function $f(k,k_0,x)$, where $x=c_{T2}/c_{T1}$. We have set $x=0.9$ on the left panel and $x=1.1$ on the right panel, respectively.

Figure 2

Theoretical CMB BB and TT-mode power spectra for our oscillating GWs spectrum (15) (brown line in the left panel and red solid line in the right panel) and the power-law GWs spectrum for reference (blue dashed line in the left panel and green dashed line in the right panel). The insets of the right panels are the TT-mode spectra for our oscillating GWs spectrum (the yellow solid lines) and the power-law GWs spectrum (the blue dashed lines) for reference. We set $r=0.05$ and $k_0=1/30000{\mathrm{Mpc}}^{-1}$.

Figure 3

BB-mode spectra at low multipoles for our oscillating GWs spectrum (15) with different $x$ (solid lines) and the power-law GWs spectrum with different ${\tau }_{\text{ri}}$ (dashed lines).

Figure 4

The variation of $\phi$ and $c_T^2$ with respect to cosmological time $t$ in the case of $x=c_{T2}/c_{T1}=10$, i.e., $A=-0.9$, where $t=0$ corresponds to ${\tau }_0$. We have set $b_1=50$, $b_2=-50$.