  We analyze the spectrum of cosmic microwave background (CMB) anisotropies in
the timescape cosmology: a potentially viable alternative to homogeneous
isotropic cosmologies without dark energy. We exploit the fact that the
timescape cosmology is extremely close to the standard cosmology at early
epochs to adapt existing numerical codes to produce CMB anisotropy spectra, and
to match these as closely as possible to the timescape expansion history. A
variety of matching methods are studied and compared. We perform Markov Chain
Monte Carlo analyses on the parameter space, and fit CMB multipoles $50 \le
\ell \le 2500$ to the Planck satellite data. Parameter fits include a dressed
Hubble constant, $H_0 = 61.0$ km/s/Mpc ($\pm$ 1.3% stat) ($\pm$ 8% sys), and a
present void volume fraction $f_{v0} = 0.627$ ($\pm$ 2.3% stat) ($\pm$ 13%
sys). We find best fit likelihoods which are comparable to that of the best fit
Lambda CDM cosmology in the same multipole range. In contrast to earlier
results, the parameter constraints afforded by this analysis no longer admit
the possibility of a solution to the primordial lithium abundance anomaly. This
issue is related to a strong constraint between the ratio of baryonic to
nonbaryonic dark matter and the ratio of heights of the second and third
acoustic peaks, which cannot be changed as long as the standard cosmology is
assumed up to the surface of last scattering. These conclusions may change if
backreaction terms are also included in the radiation-dominated primordial
plasma.
