We propose to carry out a comprehensive study of the rest-frame optical properties of 1000 galaxies at, including: morphology, structure, kinematics, dust content, star formation rate (SFR), metallicity, luminosity and mass functions, clustering, and large scale-structure. The fundamental questions that we are attempting to answer include:

• What is the nature of the galaxy population at z>2? What are their local counterparts?
  
  At z~2 the 1-2.5 microns range translates into rest-frame ~3500-8000Å, the region of the spectrum that has been most widely studied in nearby galaxies. COSMOS will address these questions by comparing directly the properties of the high redshift galaxies with those of the nearby population in the same parameter space, including half-light radii (Re), surface brightnesses (SBe), emission line ratios (e.g., [OII]3727/[OIII]5007, [OIII]5007/Hb, [NII]6584/Ha), SFRs (from both Ha and [OII]3727 emission), metallicities (from various line strength indices), dust content (using Balmer decrements), and internal kinematics (from Ha velocity widths). This procedure avoids the uncertainties in the calibrations and biases that affect similar studies of high-redshift galaxies in the rest-frame UV. A similar approach has been succesfully used to identify unambiguously the local counterparts of compact emission-line galaxies at z~1. For instance, Figures 1 and 2 show the diagrams for a sample of galaxies at z=1 (Phillips et al. 1997; Guzmán et al. 1997). These two diagrams provide a complete description of the global galaxy structural properties. The high blue luminosities and surface brightnesses of this z=1 galaxy sample, together with their small sizes and velocity widths, are consistent with their being low-mass (log M<10), extreme star-forming systems similar to nearby HII galaxies. This is also corroborated in Figures 3 and 4, showing that HII galaxies and 1 galaxies have the same emission-line ratios and specific SFR's. Another important diagnostic diagram is the luminosity-linewidth relation (Tully-Fisher for spirals, Faber-Jackson or the 'fundamental plane' for ellipticals and for HII galaxies). Figure 5 shows the relation for the same galaxy sample at , confirming the similarity between high redshift galaxies and nearby HII galaxies (Guzmán et al. 1997). Note that a key new aspect common to these studies at high redshift, including COSMOS, is to measure galaxy internal motions, which are not affected by the luminosity evolution of the stellar population.
  

  Figure 1: SBe vs. M_B. Meaning of symbols: crosses: nearby HII galaxies; dotted lines indicate the locus occupied by various other types of local galaxies; the arrow (F) represents the direction of fading.

  
  Figure 2: Re vs. sigma-velocity width. Symbols as before; dashed lines represent constant mass-lines in; the arrows represent the effects of dissipation (D), mergers (M), stripping (S) and winds (W) on Re and sigma. We adopt H=50 km/s/Mpc and q=0.05.
  
  

• How have galaxies at evolved? Are they the progenitors of today's quiescent stellar systems?
  
  Galaxies at z>2 are being observed when the universe was 20% of its current age. Many of them will be truly 'primeval' galaxies, i.e., galaxies that are most likely undergoing their first episode of star formation. Once their counterparts both at lower redshifts and at the present epoch have been identified, COSMOS will be able to assess the evolution of galaxies from the early universe till the present like a step-by-step movie of galaxy evolution. This sequence will define 'evolutionary tracks' on the various diagnostic diagrams discussed above, which can then be compared to model predictions of galaxy formation and evolution including physical processes such as: fading of the stellar population, SN-driven galactic winds, mergers, tidal stripping or galaxy harassment (see Figures 3a and 3b). This procedure has been used to identify for the first time a class of extreme star-forming galaxies at as progenitors of today's population of dwarf elliptical galaxies (Koo et al. 1995; Guzmán et al. 1996).
  
  

  Figure 3: M_B vs. [OIII]/Hb. Local galaxies (Gallego et al. 1997): DANS=Dwarf Amorphous Nuclear Starbursts; SBN=Starburst Nuclei; Sy2:=Seyfert 2 galaxies; HII=HII galaxies. Dashed lines represent the approximate location of spiral galaxies.
  

  
  Figure 4: Mass vs. SFR/M. Symbols as before (from Guzmán, Gallego et al. 1997) .
  
  
• What is the real evolution of the star formation history of the universe with look-back time?
  
  It is now widely assumed that the Star Formation Rate (SFR) density of the Universe had a peak at z~1 and from then, it descended to the local value (Madau et al. 1996; Figure 5). However, the interpretation of this figure should be approached with caution, given the likely differences in the calibrations for the various SFR tracers used, incompleteness of the data sets, and uncertainties in the corrections for dust. Indeed, new estimates of the global SFR rate density at high redshifts differ in more than a factor among various researches. Most of the caveats surrounding these estimates can be avoided by measuring the SFR using Ha emission, the best SFR tracer. This is the method adopted by Gallego et al. (1995) to estimate the local value of the global SFR density, and will also be used by the COHSI project (Aragón-Salamanca et al.\ 1998) to derive the value at 1<z<2. COSMOS will be the first major survey to measure Ha emission at 2<z<3 and, combined with similar surveys at lower redshift, will define a homogenous, unambiguous picture of the star formation history of the universe from till the present. In addition, since [OII]3727 is also a fair measure of the star formation rate, COSMOS will be able to provide a well-calibrated measurement of the global star formation rate to via observations of the [OII]3727 emission down to 2.5 microns.
  
  

  Figure 5: Evolution of the global SFR density of the universe with redshift (Glazebrook et al 1998).
  
  

• What is the earliest epoch of galaxy formation?
  
  The quest to observe the birth and formation of normal galaxies like our own has proved to be a very elusive one... till now. The advent of the 10m-class telescopes combined with powerful new instrumentation has yielded in only two years over 600 high redshift candidates of which are spectroscopically confirmed galaxies at 2<z<4 (Steidel et al. 1996; Lowenthal et al. 1997; Steidel et al. 1998). The record holder for the galaxy with the highest redshift known goes to a very recent discovery of an object at z=5.34 by Spinrad et al. (1998). This is obviously the beginning of a new era of discovery of primeval galaxies in the early universe. The new near-infrared spectrographs planned for the 10m-class telescopes will allow systematic searches for primeval galaxies at z<3.5, by looking for [OII]3727 from emission-line galaxies, and Ca H+K and 4000Å break from absorption-line objects over the range 0.9 to 1.8 microns. COSMOS will be able to extend this search to -and to much higher redshifts via observations of Ly-a by extending the wavelength coverage to 2.5 microns.
  
  
• When did galaxies group into large-scale structures and how have these structures evolved?
  
  Recent years have seen spectacular progress in the study of the large scale structure of the universe, which is now well constrained at the highest redshifts from microwave background measurements, and at low redshifts from redshift surveys and peculiar motions measurements. The key piece of information missing is the measurement of large scale structure at 1<z<6. These measurements are vital to resolve the degeneracy among current cosmological models and to directly constrain the mean density, age and biasing of the universe. Recent, very preliminary studies of clustering at z~1 suggest that there does seem to be a significant amount of large scale structure at high redshifts, and that it may vary strongly with the galaxy type, indicating that biasing may be important (e.g., Neuschafer & Windhorst 1995; Cole et al. 1994; Wolfe 1993). These studies are based on direct observations of galaxies through [OII]3727 emission, or, indirectly, through QSO absorption-line measurements. The new major redshift surveys will be able to map the large-scale structure up to z~3.5 via observations of the [OII]3727 emission-line down to 1.8 microns. COSMOS will be the only such survey able to extend these studies to z~6.