in his paper "the habitable epoch in the early universe" A. Loeb makes the observation that the CMB in the early universe would have kept everything at temperatures allowing water to be liquid, and that during that time the Universe was a giant habitable zone. can you estimate how long (in years) this period lasted?

The author states that the habitable epoch he considers is between z=110 and z=100. At this time the Universe can be considered to be matter dominated (true at the few % level anyway) and the time between these two redshifts can be calculated to be ~2.3 Myr.

ReplyDeleteCQW agrees with the post and concludes that this is possibly much too short in comparison to an evolutionary time scale on which life would develop:

ReplyDeleteYou can estimate the time scale $\Delta t$ by linking it to the temperature drop $\Delta T$ with the scale factor $a$ as an intermediate variable:

\begin{equation}

\Delta T = \frac{\partial T}{\partial a}\frac{\partial a}{\partial t}\Delta t

\end{equation}

where you can use the temperature scaling for radiation, $T=T_0/a$ and the Hubble function $\dot{a} = aH(a)$ in matter domination. combining these results give

\begin{equation}

\Delta t = \frac{a}{H(a)}\frac{\Delta T}{T_0} \simeq \frac{10^{-3}}{H_0}

\end{equation}

i.e. for $\Delta T/T_0=100$ roughly $10^7$ years.

perhaps there's a second coincidence problem in having to explain why the evolutionary time scale is so similar to $1/H_0$ :)

ReplyDeleteWell, without having read the paper, the point is really funny. In a way it is also perfectly ridiculous to call this state "habitable".

ReplyDeleteAt z=100 there would perhaps be enough oxygen in the universe for a few drops of liquid water per cubic megaparsec, let alone the quantities of sulfur, calcium, iron, ... to make life.

Even worse: Life needs free energy - lots of! - in other words, it needs strong thermal inbalance. Free energy would probably be as rare as oxygen and iron at the time. To be sure: I mean free energy in the thermodynamic sense, not stolen electricity or gratis petrol.

Science can be so much fun! Many thanks to Spirou for having shared this bit.

Uli Bastian