The habitable epoch of the early Universe

In the redshift range 100<~(1+z)<~137, the cosmic microwave background (CMB) had a temperature of 273-373 K (0-100°C), allowing early rocky planets (if any existed) to have liquid water chemistry on their surface and be habitable, irrespective of their distance from a star. In the standard ΛCDM cosmology, the first star-forming halos within our Hubble volume started collapsing at these redshifts, allowing the chemistry of life to possibly begin when the Universe was merely 10-17 million years old. The possibility of life starting when the average matter density was a million times bigger than it is today is not in agreement with the anthropic explanation for the low value of the cosmological constant.