Our aim is to observationally investigate the cosmic Dark Ages in order to constrain star and structure formation models, as well as the chemical evolution in the early Universe. Spectral lines from atoms and molecules in primordial perturbations at high redshifts can give information about the conditions in the early universe before and during the formation of the first stars in addition to the epoch of reionisation. The lines may arise from moving primordial perturbations before the formation of the first stars (resonant scattering lines), or could be thermal absorption or emission lines at lower redshifts. The difficulties in these searches are that the source redshift and evolutionary state, as well as molecular species and transition are unknown, which implies that an observed line can fall within a wide range of frequencies. The lines are also expected to be very weak. Observations from space have the advantages of stability and the lack of atmospheric features which is important in such observations. We have therefore, as a first step in our searches, used the Odin satellite to perform two sets of spectral line surveys towards several positions. The first survey covered the band 547-578 GHz towards two positions, and the second one covered the bands 542.0-547.5 GHz and 486.5-492.0 GHz towards six positions selected to test different sizes of the primordial clouds. Two deep searches centred at 543.250 and 543.100 GHz with 1 GHz bandwidth were also performed towards one position. The two lowest rotational transitions of H2 will be redshifted to these frequencies from z~20-30, which is the predicted epoch of the first star formation. No lines are detected at an rms level of 14-90 and 5-35 mK for the two surveys, respectively, and 2-7 mK in the deep searches with a channel spacing of 1-16 MHz. The broad bandwidth covered allows a wide range of redshifts to be explored for a number of atomic and molecular species and transitions. From the theoretical side, our sensitivity analysis show that the largest possible amplitudes of the resonant lines are about 1 mK at frequencies <200 GHz, and a few micro K around 500-600 GHz, assuming optically thick lines and no beam-dilution. However, if existing, thermal absorption lines have the potential to be orders of magnitude stronger than the resonant lines. We make a simple estimation of the sizes and masses of the primordial perturbations at their turn-around epochs, which previously has been identified as the most favourable epoch for a detection. This work may be considered as an important pilot study for our forthcoming observations with the Herschel Space Observatory.
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