My arXiv lecture recommendation of today is this short article: http://arxiv.org/abs/1312.0613, by Avi Loeb, on the possibility of life at z=100! At that epoch, the CMB had room temperature, allowing for liquid water on rocky planets. The probability of the existence of such planets at those early times is however very slim, one would need the first stars to have formed and enriched the primordial gas with heavy elements. The necessary collapsed dark-matter halos of suitable mass could only have formed with a non-zero primordial non-Gaussianity. For Gaussian fields these halos are in the tail at 8.5 sigma, and thus extremely unlikely to form. I don’t know how to translate this into a value for f_NL, but Loeb claims that this level is not ruled out by current observations.
This alone is an interesting read, but the main conclusion goes further and aims at the anthropic principle, that is often used to explain the small value of Lambda (or the vacuum density) today. If life had already been possible at z=100 (corresponding to 15 Million years after the Big Bang), the ratio of matter density to Lambda, scaling with (1+z)^3, would be 10^6 larger than today. To quote the last phrase of the paper:
“Even when placed on a logarithmic scale, the corresponding discrepancy in the vacuum energy density is substantial, spanning ∼ 5% of the ∼ 120 orders of magnitude available up to the Planck density.”
So our epoch might not be that special after all…