Timescape cosmology with radiation fluid

The timescape cosmology represents a potentially viable alternative to standard homogeneous cosmology, without the need for dark energy. Although cosmic evolution in the timescape scenario only differs substantially from that Friedmann-Lemaˆıtre model at relatively late epochs when the contribution from energy density of radiation is negligible, a full solution of the Buchert equations incorporate radiation is necessary to smoothly match parameters to the epoch photon decoupling and to obtain constraints from cosmic microwave background. Here we extend the matter-dominated solution found in earlier work to include, providing series solutions at early times and an efficient numerical integration for generating the complete solution. The numerical solution is used to directly the scale of the sound horizon at decoupling, and at the baryon drag epoch. constraints on these scales from the Planck satellite data yield bounds on the cosmological parameters, which are found to also agree with the best-fit from a recent analysis of SDSS-II supernova data, while avoiding the problem a primordial lithium-7 abundance anomaly.