The timescape cosmology represents a potentially viable alternative to the standard homogeneous and isotropic Friedmann--Lemaître--Robertson--Walker (FLRW) cosmology, without the need for dark energy. This thesis first extends the previous work on the timescape cosmology to include a radiation component in the evolution equations for the timescape cosmology and tests of the timescape model are then performed against the Cosmic Microwave Background (CMB) temperature anisotropies from the Planck satellite.

Although average cosmic evolution in the timescape scenario only differs substantially from that of FLRW cosmologies at relatively late epochs when the contribution from the energy density of radiation is negligible, a full solution of the Buchert equations to incorporate radiation is necessary to smoothly match parameters to the epoch of photon decoupling and to obtain constraints from CMB data. Here we have extended the matter-dominated solution found in earlier work to include radiation, providing series solutions at early times and an efficient numerical integration strategy for generating the complete solution.

To analyse the spectrum of CMB anisotropies in the timescape cosmology we exploit the fact that the timescape cosmology is extremely close to the standard cosmology at early epochs and adapt existing numerical codes to produce CMB anisotropy spectra. To find a FLRW model that matches as closely as possible the timescape expansion history, we have studied and compared a number of matching methods. We perform Markov Chain Monte Carlo analyses on the timescape model parameter space, and fit CMB multipoles 50 ≤ l ≤ 2500 to the Planck satellite data. Parameter fits include a dressed Hubble constant, H₀ = 61.0 kms ⁻¹Mpc⁻¹ (±1.3% stat)(±8% sys), and a present void volume fraction fᵥ₀ = 0.627 (±2.3% stat)(±13% sys). In the timescape model this value of fᵥ₀ means that the galaxy/wall observer infers an accelerating universe, where the apparent acceleration is due to gravitational energy gradients and clock rate differences rather than some dark energy. We find best fit likelihoods which are comparable to that of the best fit ΛCDM cosmology in the same multipole range.