He argues that early-forming stars could have cooked enough heavy elements rocky planets to form by 15 million years after the big bang. Ambient cosmic temperature would allow for liquid water on the surface of these planets. He claims that life could arise on such planets!
I'm skeptical of his model showing star formation this early, but let's grant that some few such early rocky worlds could have existed.
It turns out this "habitable epoch" is still far too short for the evolution of life to occur.
His Goldilocks epoch of 100 < (1 + z) < 110 corresponds to a time t after the big bang where:
That only leaves 2.317 million years for life to form in liquid water. Nowhere near enough time.
Even if we grant that single-celled life could miraculously evolve this quickly, and important precursor of life simply isn't present. Life needs an ordered source of energy to run its metabolic processes. The Sun or geothermal vents, for example.
This planet would not have a slow-burning sun by definition, because it lies in an active star-forming region. It would also lack geology because, again by definition, it's heated by the cosmic background.
Putting aside those problems, the paper draws an incorrect conclusion about the anthropic principle.
The possibility that the chemistry of life could have started in our universe only 15 Myr after the Big Bang argues against the anthropic explanation for the value of the cosmological constant.Assume we have some "fossil" of life from 15 million years after the Big Bang. How does this argue against the fine tuning of lambda being explained by selection bias (the anthropic explanation)?
It may have been far from zero for these fossil creatures, but it's still close to zero for us.
No new mechanism for our value of lambda is being offered by these or any short-lived fossils.