Detecting primordial gravitational waves with circular polarization of the redshifted 21 cm line: II. Forecasts

In the first paper of this series, we showed that the CMB quadrupole at high redshifts results in a small circular polarization of the emitted 21 cm radiation. In this paper we forecast the sensitivity of future radio experiments to measure the CMB quadrupole during the era of first cosmic light ($z\sim 20$). The tomographic measurement of 21 cm circular polarization allows us to construct a 3D remote quadrupole field. Measuring the $B$-mode component of this remote quadrupole field can be used to put bounds on the tensor-to-scalar ratio $r$. We make Fisher forecasts for a future Fast Fourier Transform Telescope (FFTT), consisting of an array of dipole antennas in a compact grid configuration, as a function of array size and observation time. We find that a FFTT with a side length of 100 km can achieve $\sigma(r)\sim 4\times 10^{-3}$ after ten years of observation and with a sky coverage $f_{\mathrm{sky}}\sim 0.7$. The forecasts are dependent on the evolution of the Lyman-$\alpha$ flux in the pre-reionization era, that remains observationally unconstrained. Finally, we calculate the typical order of magnitudes for circular polarization foregrounds and comment on their mitigation strategies. We conclude that detection of primordial gravitational waves with 21 cm observations is in principle possible, so long as the primordial magnetic field amplitude is small, but would require a very futuristic experiment with corresponding advances in calibration and foreground suppression techniques.Comment: 19 pages, matches PRD accepted versio

Spin-Charge Decoupling and Orthofermi Quantum Statistics

Currently Gutzwiller projection technique and nested Bethe ansatz are two main methods used to handle electronic systems in the $U$ infinity limit. We demonstrate that these two approaches describe two distinct physical systems. In the nested Bethe ansatz solutions, there is a decoupling between the spin and charge degrees of freedom. Such a decoupling is absent in the Gutzwiller projection technique. Whereas in the Gutzwiller approach, the usual antisymmetry of space and spin coordinates is maintained, we show that the Bethe ansatz wave function is compatible with a new form of quantum statistics, viz., orthofermi statistics. In this statistics, the wave function is antisymmetric in spatial coordinates alone. This feature ultimately leads to spin-charge decoupling.Comment: 12 pages, LaTex Journal_ref: A slightly abridged version of this paper has appeared as a brief report in Phys. Rev. B, Vol. 63, 132405 (2001