We report new calculations of the cooling rate of primordial gas by the HD molecule, taking into account its ro-vibrational structure. The HD cooling function is calculated including radiative and collisional transitions for J\le8 rotational levels, and for the vibrational levels v=0,1,2 and 3. The ro-vibrational level population is calculated from the balance equation assuming steady state. The cooling function is evaluated in the ranges of the kinetic temperatures, T_k, from 1e2 to 2e4 K and the number densities, n_H, from 1 to 1e8 cm**-3. We find that the inclusion of collisional ro-vibrational transitions increases significantly the HD cooling efficiency, in particular for high densities and temperatures. For n_H>~1e5 and T_k~1e4 K the cooling function becomes more than an order of magnitude higher than previously reported. We give also the HD cooling rate in the presence of the cosmic microwave radiation field for radiation temperatures of 30, 85 and 275 K (redshifts of 9, 29 and 99). The tabulated cooling functions are available at http://www.cifus.uson.mx/Personal\_Pages/anton/DATA/HD\_cooling/HD\_cool.html. We discuss the relevance to explore the effects of including our results into models and simulations of galaxy formation, especially in the regime when gas cools down from temperatures above ~3000 K.Comment: 5 pages, 3 figures. Accepted for publication in MNRAS. Minor changes after referee's report; one figure has been adde

Within the framework of Einstein-Cartan-Shrödinger formalism with asymmetric connections, the Planck constant is calculated from the first principles (from geometry of our Universe), as the adiabatic invariant of electromagnetic field on the Riemann-Cartan manifold. The Planck constant, calculated with actually measured cosmological parameters, coincide with that one, measured in laboratory with precision up to the second digit. The non-local generalization of quantum theory is suggested. The fundamental sense of the Quantum Theory is discussed, and physical sense of the cosmological constant is revealed. Within the mentioned framework, the quantum theory is naturally unified with gravity.

Context. Some models of Big Bang nucleosynthesis suggest that very high baryon density regions were formed in the early Universe, and generated the production of heavy elements other than lithium such as fluorine F. Aims. We present a comprehensive chemistry of fluorine in the post-recombination epoch. Methods. Calculation of F, F− and HF abundances, as a function of redshift z, are carried out. Results. The main result is that the chemical conditions in the early Universe can lead to the formation of HF. The final abundance of the diatomic molecule HF is predicted to be close to 3.75 × 10 −17 when the initial abundance of neutral fluorine F is 10 −15 . Conclusions. These results indicate that molecules of fluorine HF were already present during the dark age. This could have implications on the evolution of proto-objects and on the anisotropies of cosmic microwave background radiation. Hydride of fluorine HF may affect enhancement of the emission line intensity from the proto-objects and could produce spectral-spatial fluctuations.

Possible detection of signatures of structure formation at the end of the 'dark age' epoch (z ∼ 40 − 20) is examined. We discuss the spectral-spatial fluctuations in the CMBR temperature produced by elastic resonant scattering of CMBR photons on HD molecules located in protostructures moving with peculiar velocity. Detailed chemical kinematic evolution of HD molecules in the expanding homogeneous medium is calculated. Then, the HD abundances are linked to protostructures at their maximum expansion, whose properties are estimated by using the top-hat spherical approach and the ΛCDM cosmology. We find that the optical depths in the HD three lowest pure rotational lines for high-peak protohaloes at their maximum expansion are much higher than those in LiH molecule. The corresponding spectralspatial fluctuation amplitudes however are probably too weak as to be detected by current and forthcoming millimeter-telescope facilities. We extend our estimates of spectral-spatial fluctuations to gas clouds inside collapsed CDM haloes by using results from a crude model of HD production in these clouds. The fluctuations for the highest-peak CDM haloes at redshifts ∼ 20 − 30 could be detected in the future. Observations will be important to test model predictions of early structure formation in the universe.

We study a cosmological model in 1+D+d dimensions where D dimensions are associated with the usual Friedman-Robertson-Walker type metric with radio a(t) and d dimensions corresponds to an additional homogeneous space with radio b(t). We make a general analysis of the field equations and then we obtain solutions involving the two cosmological radii, a(t) and b(t). The particular case D=3, d=1 is studied in some detail.