5.3.2. Can CDM be Saved?

The basic result that is communicated in Figure 5-1 is that the CDM model can not simultaneously fit the large scale and small scale power. In this sense, we have a true cosmological crisis in that we have no viable structure formation model that readily accounts for all the scales on which structure is observed. However, the CDM model remains quite attractive as a seed model because it qualitatively has the correct spectral shape and it is a natural consequence of the inflationary paradigm. Since the shape of the CDM spectrum is essentially correct, the problem when comparing with the data is its amplitude at some spatial scale. Perhaps CDM can be can be augmented with elements of other theories to correct this.

Turner (1995ab) has advanced five clever twists or augmentations that keeps CDM somewhat viable. Here we briefly outline the elements of these 5 variations of standard CDM and confront them and others with the available observational constraints. In general, these variations are designed to "fix" CDM so that it produces the correct shape and normalization of the power spectrum at both large and small scales. From both observational and physical points of view, some of these modifications should best be viewed as "desperate" or at least rather complex.

Low Hubble Constant + Standard CDM: From chapter 1 we have that the critical density of the Universe goes as H₀². Lowering H₀ then significantly lowers the matter density which in turn means it takes longer for the Universe to reach the point where the energy density in the radiation field is equal to that in the matter field. This gives the Universe more time to wash out small scale fluctuations and thus reduces the clustering on small scales. Furthermore, lowering H₀ makes the Universe older and hence there is more time available for gravitational instability to build the largest structures which are observed. However, for this variant to work, H₀ has to be around 30 and there is no observational evidence for a value this low.

Mixed Dark Matter: This is a case of fine tuning where the idea is to mix in just enough HDM to allow for the observed power on large scales, while retaining enough CDM to allow for early structure formation on small scales. The required amounts range from 10-30% of HDM which puts rather stringent limits on the combined mass of the various neutrino species.

Extra radiation + CDM: Again the goal here is to delay the epoch of matter-radiation energy density equality. The Low H₀ model lets this happen by lowering the matter-density. Equivalently we can simply raise the radiation density. Since the observed entropy of the Universe provides a strong constraint on the radiation in the form of CMB photons, we must look towards extra sources. One which has been proposed is an unstable relativistic particle (in particular the tau neutrino) whose main decay channel is radiation. But again, some fine tuning is necessary as if this particle decays during the epoch of primordial nucleosynthesis, that would upset one of the more accurate predictions of Big Bang Cosmology. Hence, we need just the right mass range for this particle to allow for a relatively late decay.

Extra Sources of Anisotropy: In its simplest form, inflation strongly predicts a scale-invariant spectrum of Gaussian density perturbations. In the scale-invariant limit, the spectral index (see equation 32 ) is n 1 - in excellent agreement with the COBE observations. If however, the spectrum is not quite scale invariant and has a spectral index slightly less than 1, then there will be less power on small scales. This deviation from the n 1 case is called Tilted CDM. A similar "fix" can occur if we allow gravitational radiation to be a significant source of the anisotropy observed in the CMB. In this case, the overall amplitude of the density perturbations must also be lower.

Non-zero : The standard inflationary theory strongly predicts that the Universe has zero spatial curvature at the present day. For most models in the past, this is accomplished by letting = 1. However, a broader class of inflationary models reaches zero curvature via a combination of and . If most of the contribution to zero curvature comes from the term, then the lower leads to lower matter density, as in the case of low H₀. dominated zero-curvature also leads to a larger expansion age at fixed H₀ which helps to relieve some of the apparent conflict discussed in Chapter 3 between the H₀^-1 and the ages of globular clusters. This larger age also allows for more time for gravitational instability and aggregation to build larger scale structure. Hence, non-zero would appear to solve several problems simultaneously.