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We study constraints on allowed reionization histories by comparing predictions of a physical semi-numerical model with secondary temperature and polarization anisotropies of the cosmic microwave background (CMB). Our model has four free parameters characterizing the evolution of ionizing efficiency $zeta$ and the minimum mass $M_{mathrm{min}}$ of haloes that can produce ionizing radiation. Comparing the model predictions with the presently available data of the optical depth $tau$ and kinematic Sunyaev-Zeldovich signal, we find that we can already rule out a significant region of the parameter space. We limit the duration of reionization $Delta z=1.30^{+0.19}_{-0.60}$ ($Delta z < 2.9$ at $99%$ C.L.), one of the tightest constraints on the parameter. The constraints mildly favour $M_{mathrm{min}} gtrsim 10^9 mathrm{M}_{odot}$ (at $68%$ C.L.) at $z sim 8$, thus indicating the presence of reionization feedback. Our analysis provides an upper bound on the secondary $B$-mode amplitude $D_{l=200}^{BB}<18$ nK$^2$ at $99%$ C.L. We also study how the constraints can be further tightened with upcoming space and ground-based CMB missions. Our study, which relies solely on CMB data, has implications not only for upcoming CMB surveys for detecting primordial gravitational waves but also redshifted 21 cm studies.
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We present constraints on the patchy reionization by measuring the trispectrum of the Planck 2015 cosmic microwave background (CMB) temperature anisotropies. The patchy reionization leads to anisotropies in the CMB optical depth, and the statistics of the observed CMB anisotropies is altered. We estimate the trispectrum of the CMB temperature anisotropies to constrain spatial variation of the optical depth. We show that the measured trispectrum is consistent with that from the standard lensed CMB simulation at $2sigma$. While no evidence of the patchy reionization is found in the Planck 2015 temperature trispectrum, the CMB constraint on the patchy reionization is significantly improved from previous works. Assuming the analytic bubble-halo model of Wang and Hu (2006), the constraint obtained in this work rules out the typical bubble size at the ionization fraction of $sim0.5$ as $Rgtrsim 10$ Mpc. Further, our constraint implies that large-scale $B$-modes from the patchy reionization are not a significant contamination in detecting the primordial gravitational waves of $rgtrsim0.001$ if the $B$ mode induced by the patchy reionization is described by Dvorkin et al. (2009). The CMB trispectrum data starts to provide meaningful constraints on the patchy reionization.
Current cosmic microwave background (CMB) bounds on the sum of the neutrino masses assume a sudden reionization scenario described by a single parameter that determines the onset of reionization. We investigate the bounds on the neutrino mass in a more general reionization scenario based on a principal component approach. We found the constraint on the sum of the neutrino masses from CMB data can be relaxed by a $sim$40% in a generalized reionization scenario. Moreover, the amplitude of the r.m.s. mass fluctuations $sigma_8$ is also considerably lower providing a better consistency with a low amplitude of the Sunyaev-Zeldovich signal.
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We show that a non-minimal coupling of electromagnetism with background torsion can produce birefringence of the electromagnetic waves. This birefringence gives rise to a B-mode polarization of the CMB. From the bounds on B-mode from WMAP and BOOMERanG data, one can put limits on the background torsion at $xi_{1}T_{1}=(-3.35 pm 2.65) times 10^{-22} GeV^{-1}$.
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