Foreground Model and Antenna Calibration Errors in the Measurement of
  the Sky-Averaged \lambda 21 cm Signal at z~20
  The most promising near-term observable of the cosmic dark age prior to
widespread reionization (z~15-200) is the sky-averaged \lambda 21 cm background
arising from hydrogen in the intergalactic medium. Though an individual antenna
could in principle detect the line signature, data analysis must separate
foregrounds that are orders of magnitude brighter than the \lambda 21 cm
background (but that are anticipated to vary monotonically and gradually with
frequency). Using more physically motivated models for foregrounds than in
previous studies, we show that the intrinsic "spectral smoothness" of the
foregrounds is likely not a concern, and that data analysis for an ideal
antenna should be able to detect the \lambda 21 cm signal after deprojecting a
~5th order polynomial in log(\nu). However, we find that the foreground signal
is corrupted by the frequency-dependent response of a real antenna. The
frequency dependence complicates modeling of foregrounds commonly based on the
assumption of spectral smoothness. Much of our study focuses on the
Large-aperture Experiment to detect the Dark Age (LEDA), which combines both
radiometric and interferometric measurements. We show that statistical
uncertainty remaining after fitting antenna gain patterns to interferometric
measurements does not compromise extraction of the \lambda 21 cm signal for a
range of cosmological models after fitting a 7th order polynomial to
radiometric data. Our results generalize to most efforts to measure the
sky-averaged spectrum.
