CMB polarization from secondary vector and tensor modes

Abstract

We consider a novel contribution to the polarization of the Cosmic Microwave Background induced by vector and tensor modes generated by the non-linear evolution of primordial scalar perturbations. Our calculation is based on relativistic second-order perturbation theory and allows to estimate the effects of these secondary modes on the polarization angular power-spectra. We show that a non-vanishing B-mode polarization unavoidably arises from pure scalar initial perturbations, thus limiting our ability to detect the signature of primordial gravitational waves generated during inflation. This secondary effect dominates over that of primordial tensors for an inflationary tensor-to-scalar ratio $r<10^{-6}$. The magnitude of the effect is smaller than the contamination produced by the conversion of polarization of type E into type B, by weak gravitational lensing. However the lensing signal can be cleaned, making the secondary modes discussed here the actual background limiting the detection of small amplitude primordial gravitational waves.

Figures (3)

• Figure 1: The functions $W_V$ (dashed line) and $W_\chi$ (solid line) for $n_s=1$.
• Figure 2: Angular power-spectrum of B (left panel) and E (right panel) polarization by secondary vector (solid lines) and tensor modes (dashed lines), in a $\Lambda$CDM model without reionization (thin lines) and with an optical depth to reionization $\tau_{\rm ri}=0.17$ (thick lines).
• Figure 3: Angular power-spectrum of secondary total (vector plus tensor) B-polarization (thick solid line) compared with that induced by primordial gravitational waves (dashed line) with a tensor to scalar ratio $r=10^{-6}$, in a flat $\Lambda$CDM model ($\Omega_m=0.3$) with $\tau_{\rm ri}=0.17$. The thin solid line is the signal due to gravitational lensing cleaned by a factor 40.