Here is a quote from Loeb's abstract of his paper:
In the redshift range 100<(1+z)<110, the cosmic microwave background (CMB) had a temperature of 273-300K (0-30 degrees Celsius), 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 LCDM 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 15 million years old.
While Loeb's paper is not quite 100% pure bunk, malarkey, and hogwash, I will explain here why it is very close to groundless sensationalistic hype which no one should take very seriously.
No, not really
First let me explain the reasoning used in the paper. Everyone knows that life requires some degree of warmth, at least something warmer than the cold temperature of interstellar space. We normally think of life as something that can only evolve on a planet near a star, in the habitable zone near a sun. But in the early universe it seems that the cosmic background radiation (the afterglow from the Big Bang) created quite a bit of heat. Loeb imagines a brief period of cosmic history beginning 15 million years after the Big Bang, a time when all of space might have been pervaded with an energy sufficient to create the warm temperature needed for life to evolve. In such a cosmic environment, life might be able to appear on a planet or moon that didn't have a nearby sun. The warm temperature of space during this short period might have provided the necessary warmth.
How long a time period is Loeb talking about? He mentions “a few Myr,” using an abbreviation for megayears, or a million years. We can get a more specific number from Loeb's statement about a redshift range between 100 and 110. Using the calculator here, we find that a redshift of 110 equals a cosmic age of 0.0145 Gyr (Gigayears), and redshift of 100 equals a cosmic age of 0.0168 Gyr (Gigayears). The difference between the two is .0023 Gigayears, which is a time period of about two million years. This matches Loeb's statement of “a few Myr” (megayears), but clarifies that he is talking about a potential habitable period of only two million years, between the time that the universe was about 15 million years old and the time when it was 17 million years old.
There are four grave problems with the idea of visible life of any type appearing during such a period. One huge problem is that all the radiation from the much denser early universe would have probably prevented any life from appearing. A second problem is that every model of the early solar system imagines it as a kind of shooting gallery under constant bombardment from asteroids and other projectiles. This heavy bombardment would have worked against the appearance of life in the very early universe, when the probability of projectile bombardment would have been even greater.
A third problem concerns the availability of heavy elements in the early universe. A few thousand years after the Big Bang, the universe consisted of basically just hydrogen, helium, and lithium. Other elements needed for life (such as carbon, oxygen, and nitrogen) were produced by stars, both as the result of regular stellar evolution and supernova explosions. But scientists believe it took a long, long time to get elements such as carbon, oxygen, and nitrogen to be produced in appreciable amounts. Astronomers think that it took many generations of stars before the heavy elements were produced in large abundances. The oldest known planets revolve around the star HIP 11952, and they have been dated as coming from about a billion years after the Big Bang. No one has detected any planets that formed earlier than a billion years after the Big Bang. So imagining, as Loeb does, that planets might have formed only about 15 million years after the Big Bang is highly implausible.
But the most decisive reason why visible life could not have formed during the time frame imagined by Loeb is that visible life would not have had time to evolve during this time frame of only two million years. Scientists have no evidence of visible life in the first billion years of Earth's history. The oldest traces of life are microscopic traces from 3.5 billion years ago, as discussed here, which is about a billion years after the formation of our planet. Scientists think that cellular organisms only appeared on Earth about 2.5 billion years after our planet formed. So the two million year time frame described by Loeb is way too short for the evolution of any life, and way, way too short for the evolution of visible life.
For Loeb to call a two million year time frame (in conditions of very scarce heavy elements, high radiation, and very heavy bombardment) a “habitable epoch” is like saying that a one-day tent rental in the middle of a much-used Air Force bombing practice site is “establishing a stable home environment.”