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Register a new userUnified approach to secondary effects on the CMB B-mode polarization
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We develop a systematic and unified approach to estimate all possible secondary (i.e. non-primordial) nonlinear effects to the cosmic microwave background (CMB) polarization, named curve-of-sight integration approach. In this approach, the Boltzmann equation for polarized photons is rewritten in a line-of-sight integral along an exact geodesic in the perturbed universe, rather than a geodesic in the background universe used in the linear-order CMB calculation. This approach resolves the difficulty to solve the Boltzmann hierarchy with the nonlinear gravitational effects in the photon free-streaming regime and thus unifies the standard remapping approach for CMB lensing into the direct approach solving the Boltzmann equation for the nonlinear collisional effects. In this paper, we derive formulae that: (i) include all the nonlinear effects; (ii) can treat extended sources such as the contributions after the reionization. It offers a solid framework to discuss possible systematics in the standard estimation of CMB lensing by the remapping approach. As an explicit demonstration, we estimate the secondary B-mode power spectrum induced by all foreground gravitational effects: lensing, redshift, time-delay, emission-angle, and polarization-rotation effects. We define these effects properly so that they do not have any overlap, also without overlooking any effect. Then, we show that these effects only give corrections of the order of 0.001-0.01% to the standard lensing-induced B-mode power spectrum in the concordance $Lambda$ cold dark matter model. Our result confirms the reliability of using the remapping approach in upcoming CMB experiments aiming to detect the primordial gravitational waves with the tensor-to-scalar ratio of $r sim 10^{-3}$.
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We explore the impact of modified gravity on B-modes, identifying two main separate effects: lensing and propagation of tensor modes. The location of the inflationary peak of the BB spectrum depends on the speed of gravitational waves; the amplitude of the lensing contribution depends on the anisotropic stress. We single out these effects using the quasi-static regime and considering models for which the background and the growth of matter perturbations are standard. Using available data we obtain that the gravitational wave speed is compatible with the speed of light and constrained to within about 10%.
STPpol, POLARBEAR and BICEP2 have recently measured the cosmic microwave background (CMB) B-mode polarization in various sky regions of several tens of square degrees and obtained BB power spectra in the multipole range 20-3000, detecting the components due to gravitational lensing and to inflationary gravitational waves. We analyze jointly the results of these three experiments and propose modifications of their analysis of the spectra to include in the model, in addition to the gravitational lensing and the inflationary gravitational waves components, also the effects induced by the cosmic polarization rotation (CPR), if it exists within current upper limits. Although in principle our analysis would lead also to new constraints on CPR, in practice these can only be given on its fluctuations <{delta}{alpha}^2>, since constraints on its mean angle are inhibited by the de-rotation which is applied by current CMB polarization experiments, in order to cope with the insufficient calibration of the polarization angle. The combined data fits from all three experiments (with 29% CPR-SPTpol correlation, depending on theoretical model) gives constraint <{delta}{alpha}^2>^1/2 < 27.3 mrad (1.56{deg}) with r = 0.194 pm 0.033. These results show that the present data are consistent with no CPR detection and the constraint on CPR fluctuation is about 1.5{deg}. This method of constraining the cosmic polarization rotation is new, is complementary to previous tests, which use the radio and optical/UV polarization of radio galaxies and the CMB E-mode polarization, and adds a new constraint for the sky areas observed by SPTpol, POLARBEAR and BICEP2.
Gravitational waves from inflation induce polarization patterns in the cosmic microwave background (CMB). It is known that there are only two types of non-Gaussianities of the gravitaional waves in the most general scalar field theories having second-order field equations. One originates from the inherent non-Gaussianity in general relativity, and the other from a derivative coupling between the Einstein tensor and a kinetic term of the scalar field. We calculate polarization bispectra induced by these non-Gaussianities by transforming them into separable forms by virtue of the Laplace transformation. It is shown that future experiments can detect only the new one if the latter coupling parameter takes an extremely large value, which, however, does not cotradict the current observational data.
We investigate the effect of the stochastic gravitational wave (GW) background produced by kinks on infinite cosmic strings, whose spectrum was derived in our previous work, on the B-mode power spectrum of the cosmic microwave background (CMB) anisotropy. We find that the B-mode polarization due to kinks is comparable to that induced by the motion of the string network and hence the contribution of GWs from kinks is important for estimating the B-mode power spectrum originating from cosmic strings. If the tension of cosmic strings mu is large enough i.e., Gmu >~ 10^{-8}, B-mode polarization induced by cosmic strings can be detected by future CMB experiments.
B-modes in CMB polarization from patchy reionization arise from two effects: generation of polarization from scattering of quadrupole moments by reionization bubbles, and fluctuations in the screening of E-modes from recombination. The scattering contribution has been studied previously, but the screening contribution has not yet been calculated. We show that on scales smaller than the acoustic scale (l>300), the B-mode power from screening is larger than the B-mode power from scattering. The ratio approaches a constant ~2.5 below the damping scale (l>2000). On degree scales relevant for gravitational waves (l<100), screening B-modes have a white noise tail and are subdominant to the scattering effect. These results are robust to uncertainties in the modeling of patchy reionization.
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