Discovery of a Perseus-like cloud in the early Universe: HI-to-H2
  transition, carbon monoxide and small dust grains at zabs=2.53 towards the
  quasar J0000+0048
  We present the discovery of a molecular cloud at zabs=2.5255 along the line
of sight to the quasar J0000+0048. We perform a detailed analysis of the
absorption lines from ionic, neutral atomic and molecular species in different
excitation levels, as well as the broad-band dust extinction. We find that the
absorber classifies as a Damped Lyman-alpha system (DLA) with
logN(HI)(cm^-2)=20.8+/-0.1. The DLA has super-Solar metallicity with a
depletion pattern typical of cold gas and an overall molecular fraction ~50%.
This is the highest f-value observed to date in a high-z intervening system.
Most of the molecular hydrogen arises from a clearly identified narrow (b~0.7
km/s), cold component in which CO molecules are also found, with logN(CO)~15.
We study the chemical and physical conditions in the cold gas. We find that the
line of sight probes the gas deep after the HI-to-H2 transition in a ~4-5
pc-size cloud with volumic density nH~80 cm^-3 and temperature of only 50 K.
Our model suggests that the presence of small dust grains (down to about 0.001
{\mu}m) and high cosmic ray ionisation rate (zeta_H a few times 10^-15 s^-1)
are needed to explain the observed atomic and molecular abundances. The
presence of small grains is also in agreement with the observed steep
extinction curve that also features a 2175 A bump. The properties of this cloud
are very similar to what is seen in diffuse molecular regions of the nearby
Perseus complex. The high excitation temperature of CO rotational levels
towards J0000+0048 betrays however the higher temperature of the cosmic
microwave background. Using the derived physical conditions, we correct for a
small contribution (0.3 K) of collisional excitation and obtain TCMB(z =
2.53)~9.6 K, in perfect agreement with the predicted adiabatic cooling of the
Universe. [abridged]
