We cannot demonstrate that there is not some other physics, applied to some other cosmology, that equally well agrees with the cosmological tests. The same applies to the whole enterprise of physical science, of course. Parts of physics are so densely checked as to be quite convincing approximations to the way the world really is. The web of tests is much less dense in cosmology, but, we have tried to demonstrate, by no means negligible, and growing tighter.
A decade ago there was not much discussion of how to test general relativity theory on the scales of cosmology. That was in part because the theory seems so logically compelling, and certainly in part also because there was not much evidence to work with. The empirical situation is much better now. We mentioned two tests, of the relativistic active gravitational mass density and of the gravitational inverse square law. The consistency of constraints on M0 from dynamics and the redshift-magnitude relation adds a test of the effect of space curvature on the expansion rate. These tests are developing; they will be greatly improved by work in progress. There certainly may be surprises in the gravity physics of cosmology at redshifts z 1010, but it already is clear that if so the surprises are subtly hidden.
A decade ago it was not at all clear which direction the theory of large-scale structure formation would take. Now the simple CDM model has proved to be successful enough that there is good reason to expect the standard model ten years from now will resemble CDM. We have listed challenges to this structure formation model. Some may well be only apparent, a result of the complications of interpreting the theory and observations. Others may prove to be real and drive adjustments of the model. Fixes certainly will include one element from the ideas of structure formation that were under debate a decade ago: explosions that rearrange matter in ways that are difficult to compute. Fixes may also include primeval isocurvature departures from homogeneity, as in spacetime curvature fluctuations frozen in during inflation, and maybe in new cosmic fields. It would not be surprising if cosmic field defects, that have such a good pedigree from particle physics, also find a role in structure formation. And a central point to bear in mind is that fixes, which do not seem unlikely, could affect the cosmological tests.
A decade ago we had significant results from the cosmological tests. For example, estimates of the product H0 t0 suggested we might need positive , though the precision was not quite adequate for a convincing case. That still is so; the community will be watching for further advances. We had pretty good constraints on B0 from the theory of the origin of the light elements. The abundance measurements are improving; an important recent development is the detection of deuterium in gas clouds at redshifts z ~ 3. Ten years ago we had useful estimates of masses from peculiar motions on relatively small scales, but more mixed messages from larger scales. The story seems more coherent now, but there still is room for improved consistency. We had a case for nonbaryonic dark matter, from the constraint on B0 and from the CDM model for structure formation. The case is tighter now, most notably due to the successful fit of the CDM model prediction to the measurements of the power spectrum of the anisotropy of the 3 K cosmic microwave background radiation. In 1990 there were believable observations of galaxies identified as radio sources at z ~ 3. Now the distributions of galaxies and the intergalactic medium at z ~ 3 are mapped out in impressive detail, and we are seeing the development of a semi-empirical picture of galaxy formation and evolution. Perhaps that will lead us back to the old dream of using galaxies as markers for the cosmological tests.
Until recently it made sense to consider the constraints on one or two of the parameters of the cosmology while holding all the rest at "reasonable" values. That helps us understand what the measurements are probing; it is the path we have followed in Sec. IV.B. But the modern and very sensible trend is to consider joint fits of large numbers of parameters to the full suite of observations. 107 This includes a measure of the biasing or antibiasing of the distribution of galaxies relative to mass, rather than our qualitative argument that one usefully approximates the other. In a fully satisfactory cosmological test the parameter set will also include parametrized departures from standard physics extrapolated to the scales of cosmology.
Community responses to advances in empirical evidence are not always close to linear. The popularity of the Einstein-de Sitter model continued longer into the 1990s than seems logical to us, and the switch to the now standard CDM cosmological model -- with flat space sections, nonbaryonic cold dark matter, and dark energy -- arguably is more abrupt than warranted by the advances in the evidence. Our review leads us to conclude that there is now a good scientific case that the matter density parameter is M0 ~ 0.25, and a pretty good case that about three quarters of that is not baryonic. The cases for dark energy and for the CDM model are significant, too, though beclouded by observational issues of whether we have an adequate picture of structure formation. But we expect the rapid advances in the observations of structure formation will soon dissipate these clouds, and, considering the record, likely reveal new clouds on the standard model for cosmology a decade from now.
A decade ago the high energy physics community had a well-defined challenge: show why the dark energy density vanishes. Now there seems to be a new challenge and clue: show why the dark energy density is exceedingly small but not zero. The present state of ideas can be compared to the state of research on structure formation a decade ago: in both situations there are many lines of thought but not a clear picture of which is the best direction to take. The big difference is that a decade ago we could be reasonably sure that observations in progress would guide us to a better understanding of how structure formed. Untangling the physics of dark matter and dark energy and their role in gravity physics is a much more subtle challenge, but, we may hope, will also be guided by advances in the exploration of the phenomenology. Perhaps in another ten years that will include detection of evolution of the dark energy, and maybe detection of the gravitational response of the dark energy distribution to the large-scale mass distribution. There may be three unrelated phenomena to deal with: dark energy, dark matter, and a vanishing sum of zero-point energies and whatever goes with them. Or the phenomena may be related. Because our only evidence of dark matter and dark energy is from their gravity it is a natural and efficient first step to suppose their properties are as simple as allowed by the phenomenology. But it makes sense to watch for hints of more complex physics within the dark sector.
The past eight decades have seen steady advances in the technology of application of the cosmological tests, from telescopes to computers; advances in the theoretical concepts underlying the tests; and progress through the learning curves on how to apply the concepts and technology. We see the results: the basis for cosmology is much firmer than a decade ago. And the basis surely will be a lot more solid a decade from now.
Einstein's cosmological constant, and the modern variant, dark energy, have figured in a broad range of topics in physics and astronomy that have been under discussion, in at least some circles, much of the time for the past eight decades. Many of these issues undoubtedly have been discovered more than once. But in our experience such ideas tend to persist for a long time at low visibility and sometimes low fidelity. Thus the community has been very well prepared for the present evidence for detection of dark energy. And for the same reason we believe that dark energy, whether constant, or rolling toward zero, or maybe even increasing, still will be an active topic of research, in at least some circles, a decade from now, whatever the outcome of the present work on the cosmological tests. Though this much is clear, we see no basis for a prediction of whether the standard cosmology a decade from now will be a straightforward elaboration of CDM, or whether there will be more substantial changes of direction.
We are indebted to Pia Mukherjee, Michael Peskin, and Larry Weaver for detailed comments on drafts of this review. We thank Uwe Thumm for help in translating and discussing papers written in German. We have also benefited from discussions with Neta Bahcall, Robert Caldwell, Gang Chen, Andrea Cimatti, Mark Dickinson, Michael Dine, Masataka Fukugita, Salman Habib, David Hogg, Avi Loeb, Stacy McGaugh, Paul Schechter, Chris Smeenk, Gary Steigman, Ed Turner, Michael Turner, Jean-Philippe Uzan, David Weinberg, and Simon White. BR acknowledges support from NSF CAREER grant AST-9875031, and PJEP acknowledges support in part by the NSF.
107 Examples are Cole et al. (1997), Jenkins et al. (1998), Lineweaver (2001), and Percival et al. (2002). Back.