It follows from the above discussion that the nature of the extremely red galaxies should be intensively investigated in order to understand their role in galaxy evolution. The reddest galaxies (candidate to be the most dusty) have a poorly determined sky surface density of 0.010- 0.015 arcmin-2 at (Hu & Ridgway 1994), and they are very faint in the optical.
Because of their extremely steep and red spectra, these galaxies can be found with (1) moderately deep J-band imaging, (2) with very deep optical imaging in BVRI, and bf (3) covering a relatively large area of the sky.
The availability of a J filter for the LBT Wide Field Imager provides a unique possibility to perform a very deep and wide-field survey for extremely red galaxies. Adopting a conservative sky surface density of 0.01 arcmin-2 (Hu & Ridgway 1994), we will need to image about 3 square degrees in order to select a statistically significant and complete sample of about 100 objects with . Such a sky area can be covered with the LBT Wide Field Imager (FOV arcmin = 600 arcmin2) observing totally 18 fields at moderately deep magnitude limit in J and at very deep limits in BVRI. The sample will be selected in J, but the key point in such a survey will be to reach extremely deep magnitudes in BVRI in order to be able to : (1) reliably find and classify the extremely red galaxies, (2) characterize their SEDs, i.e. detecting them in at least one of the BVRI bands. For example, if the limiting (completeness) magnitude in J will be 23.0, we will need to detect objects with magnitudes , and even fainter in BVR. These limits will be reachable with integration times in Iof the order of >10000 seconds. The great advantage of the LBT will be the possibility to image simultaneously the same field with the blue and the red channels.
The use of at least 3 filters (e.g. RIJ) will be also very useful in order to produce colour-colour plots (R-K) vs. (R-I) where it is easier to investigate, to isolate and to characterize the various populations of objects present in the field (stars, brown dwarfs, galaxies at low- and high- redshifts).
The proposed survey will immediately constrain the surface density of these galaxies, and it will provide samples for additional photometric follow-up (in order to estimate the photometric redshifts) and for spectroscopic optical and/or near-IR spectroscopy with 8-10m class telescopes (when the object will be not too faint).
In addition, the JCMT+SCUBA and IRAM 30m telescopes will be used to do photometry at 450,850,1250m in order to measure the dust content and the far-IR luminosity of these systems. We then can address the following issues related to these galaxies: (1) what is their space density ? (2) what fraction of distant galaxies is hidden by dust ? (3) how much do they contribute to the total star formation rate per comoving volume in the Universe, and does it really peak at ? (4) what fraction of stars are being formed in major starburst as opposed to the more quiescent star-forming rates as inferred for spirals ? (5) is it a likely scenario that a large fraction of massive elliptical went through a dusty phase in which most of their stars were formed ? (6) Are the extremely red galaxies a major contributor to the cosmic far-IR-mm background ? (7) As a byproduct, we will investigate also the galaxies which will turn out to have no dust thermal emission and whose colours are therefore intrinsically red because of an evolved (>1 Gyr) stellar population, thus being cosmologically important because they would represent the oldest envelope of the distant galaxy population, and whose ages would in principle constrain the earliest epoch of galaxy formation, H0 and q0.
Finally, we would like to stress a point which is valid for our two programmes, and also probably for several others: the LBT-WF imager will be a necessary complement of the other LBT instruments (spectrographs and high resolution imagers), since it takes a very efficient and wide field imager like the LBT-WF to find interesting targets at a sufficient rate to feed the other LBT instruments.