Our understanding of galaxy formation and evolution is in its infancy. So far, only the first steps were given in the direction of consolidating a theory in this field. The process is apparently so complex and non-linear that several specialists do not expect the emergence of a theory in the sense that a few driving parameters and factors might explain the main body of observations. Instead, the most popular trend now is to attain some description of galaxy evolution by simulating it in expensive computational runs. I believe that simulations are a valuable tool to extend a bridge between reality and the distorted (biased) information given by observations. However, the search of basic theories for explaining galaxy formation and evolution should not be replaced by the only effort of simulating in detail what in fact we want to get. The power of science lies in its predictive capability. Besides, if galaxy theory becomes predictive, then its potential to test fundamental and cosmological theories will be enormous.
Along this notes, potential difficulties or unsolved problems of the CDM scenario were discussed. Now I summarize and complement them:
What is non-baryonic DM? From the structure formation side, the preferred (and necessary!) type is CDM, though WDM with filtering masses below ~ 109 M is also acceptable. So far none of the well-motivated cold or warm non-baryonic particles have been detected in Earth experiments. The situation is even worth for proposals not based on elemental particles as DM from extra-dimensions.
What is Dark Energy? Dark Energy does not play apparently a significant role in the internal evolution of perturbations but it crucially defines the cosmic timescale and expansion rate, which are important for the growing factor of perturbations. The simplest interpretation of Dark Energy is the homogeneous and inert cosmological constant , with equation of state parameter w = -1 and = const. The combinations of different cosmological probes tend to favor the flat-geometry models with (M, ) (0.26, 0.74). However, the cosmological constant explanation of Dark Energy faces serious theoretical problems. Several alternatives to were proposed to ameliorate partially these problems (e.g. quintaessence, k-essence, Chaplygin gas, etc.). Also have been proposed unifying schemes of DM and Dark Energy through scalar fields (e.g, ).
Inflation provides a natural mechanism for the generation of primordial fluctuations. The nearly scale-invariance of the primordial power spectrum is well predicted by several inflation models, but its amplitude, rather than being predicted, is empirically inferred from observations of CMBR anisotropies. Another aspect of primordial fluctuations not well understood is related to their statistics, i.e., whether they are Gaussian-distributed or not. And this is crucial for cosmic structure formation.
Indirect pieces of evidence are consistent with the main predictions of inflation regarding primordial fluctuations. However, more direct tests of this theory are highly desirable. Hopefully, CMBR anisotropy observations will allow for some more direct tests (e.g., effects from primordial gravitational waves).
Issues at small scales. The excess of substructure (satellite galaxies) can be apparently solved by inhibition of galaxy formation in small halos due to UV-radiation produced by reionization and due to feedback, rather than to modifications to the scenario (e.g., the introduction of WDM). Observational inferences of the inner volume and phase-space densities of dwarf satellite galaxies are crucial to explore this question. The direct detection (with gravitational lensing) of the numerous subhalo (dark galaxy) population predicted by CDM for the Galaxy halo is a decisive test on the problem of substructure. The CDM prediction of cuspy halos is a more involved problem when confronting it with observational inferences. If the disagreement persists, then either the CDM scenario will need a modification (e.g., introduction of self-interaction or annihilation), or astrophysical processes involving gas baryon physics should be in action. However, there are still unsolved issues at the intermediate level: for example, the central halo density profile of galaxies is inferred from observations of inner rotation curves under several assumptions that could be incorrect. An interesting technique to overcome this problem is being currently developed: to simulate as realistically as possible a given galaxy, "observe" its rotation curve and then compare with that of the real galaxy (see Section 4.1).
The early formation of massive red elliptical galaxies can be accommodated in the hierarchical CDM scenario (Section 5.2) if spheroids are produced by the major merger of gaseous disks, and if the cold gas is transformed rapidly into stars during the merger in a dynamical time or so. Both conditions should be demonstrated, in particular the latter. A kind of positive feedback seems to be necessary for such an efficient star formation rate (ISM shocks produced by the jets generated in the vicinity of supermassive black holes?).
Once the elliptical has formed early, the next difficulty is how to avoid further (disk) growth around it. The problem can be partially solved by considering that ellipticals form typically in dense, clustered environments, and at some time they become substructures of larger virialized groups or clusters, truncating any possible accretion to the halo/galaxy. However, (i) galaxy halos, even in clusters, are filled with a reservoir of gas, and (ii) there are some ellipticals in the field. Therefore, negative feedback mechanisms are needed to stop gas cooling and accretion. AGN-triggered radio jets have been proposed as a possible mechanism, but further investigation is necessary.
The merging mechanism of bulge formation within the hierarchical model implies roughly bluer (later formed) disks as the bulge-to-disk ratio is larger, contrary to the observed trend. The secular scenario could solve this problem but it is not still clear whether bars disolve or not in favor of pseudobulges. It is not clear also if the secular scenario could predict the central supermassive black hole mass-velocity dispersion relation.
We lack a fundamental theory of star formation. So far, simple models, or even just phenomenological recipes, have been used in galaxy formation studies. The two proposed modes of star formation (the quiescent, inefficient, disk self-regulated regime, and the violent efficient star-bursting regime in mergers) are oversimplifications of a much more complex problem with more physical mechanisms (shocks, turbulence, etc.). Closely related to star formation is the problem of feedback. The feedback mechanisms are different in the ISM of disks, in the gaseous medium of merging galaxies with a powerful energy source (the AGN) other than stars, and in the diluted and hot intrahalo medium around galaxies.
We have seen in Section 2.2 that at the present epoch only 9% of baryons are within virialized structures. Where are the remaining 91% of the baryons? The fraction of particles in halos measured in CDM N-body cosmological simulations is ~ 50%. This sounds good but still we have to explain, within the CDM scenario, the ~ 40% of missing baryons. The question is were these baryons never trapped by collapsed halos or were they trapped but later expelled due to galaxy feedback. Large-scale N-body+hdydrodynamical simulations have shown that the gravitational collapse of filaments may heat the gas and keep a big fraction of baryons outside the collapsed halos . Nevertheless, feedback mechanisms, especially at high redshifts, are also predicted to be strong enough as to expel enriched gas back to the Intergalactic Medium. The problem is open.
The field has plenty of open and exciting problems. The CDM scenario has survived many observational tests but it still faces the difficulties typical of a theory constructed phenomenologically and heuristically. Even if in the future it is demonstrated that CDM does not exist (which is little probable), the CDM scenario would serve as an excellent "fitting" model to reality, which would strongly help researchers in developing new theories.
Acknowledgments.- I am in debt with Dr. I. Alcántara-Ayala and R. Núñez-López for their help in the preparation of the figures. I am also grateful to J. Benda for grammar corrections, and to the Editors for their infinite patience.