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

TL;DR

This work examines how a step-like variation of the primordial GW speed $c_T$ during inflation, allowed in certain modified gravity and string-inspired models, imprints an oscillatory modulation on the tensor power spectrum $P_T$. By solving the tensor mode equation with a sudden $c_T$ transition and matching across the transition, the authors derive a modulated spectrum $P_T = P_T^{inf} f(k,k0,x)/(c_T1^3 Q_T)$, where $x=c_T2/c_T1$ and $k0$ encodes the transition scale. When projected onto the CMB, the oscillations in $P_T$ induce distinctive features in the B-mode spectrum, notably oscillations around the recombination peak and altered reionization bumps, while TT/EE are largely unaffected. The study argues that high-precision B-mode measurements can tightly constrain $c_T$ dynamics and thus test the underlying modified gravity or string-theory scenarios, provided foregrounds are well controlled.

Abstract

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 step-like 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 CMB polarization observations will be able to put tight constraint on the variation of $c_T$, and so the corresponding theories.

Figures (4)

• 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 (\ref{['PTT']})(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 (\ref{['PTT']}) with different $x$(solid lines) and the power-law GWs spectrum with different $\tau_{ri}$(dashed lines).
• Figure 4: The variation of $\varphi$ 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 $b_1=50$, $b_2=-50$.