The angular power spectrum of the recent microwave background data favor a purely baryonic universe over one dominated by CDM. Yet a conventional baryonic universe with faces the same problems mentioned in the introduction which led to the invention of CDM. For one, : dynamical measures give a total mass density an order of magnitude in excess of the nucleosynthesis constraint on the baryon density. The other is that the gravitational growth of structure is slow: . This makes it impossible to grow large scale structure from the smooth initial state indicated by the microwave background within the age of the universe.
These arguments are compelling, but are themselves based on the assumption that gravity behaves in a purely Newtonian fashion on all scales. A modification to the conventional force law might also suffice. One possibility which is empirically motivated is the modified Newtonian dynamics (MOND) hypothesized by MilgromM83 (1983). MOND supposes that for accelerations , the effective acceleration becomes , where gN is the usual Newtonian acceleration which applies when . There is no dark matter in this hypothesis, so the observed motions must relate directly to the distribution of baryonic mass through the modified force law.
MOND has had considerable success in predicting the dynamics of a remarkably wide variety of objects. These include spiral galaxies (Begeman, Broeils, & SandersBBS 1991; SandersS96 1996; Sanders & VerheijenSV 1998), low surface brightness galaxies (McGaugh & de BlokMBb 1998b; de Blok & McGaughBM 1998; McGaughBTF et al. 2000), dwarf Spheroidals (Milgrom7dw 1997; Mateomario 1998), giant Ellipticals (SandersS00 2000), groups (MilgromM98 1998) and clusters of galaxies (Sanders 1994cl1,1999cl2), and large scale filaments (MilgromM97 1997). The empirical evidence which supports MOND is rather stronger than is widely appreciated.
Moreover, MOND does a good job of explaining the two observations that motivated CDM. The dynamical mass is overestimated when purely Newtonian dynamics is employed in the MOND regime, so rather than one infers (Sanders 1998S98; McGaugh & de BlokMBb 1998b). The early universe is dense, so accelerations are high and MOND effects do not appear until after recombination. When they do, structure grows more rapidly than with conventional gravity (Sanders 1998S98), so the problem in going from a smooth microwave background to a rich amount of large scale structure is also alleviated. Since everything is normal in the high acceleration regime, all the usual early universe results are retained.
In order to get the position of the first peak right, we must invoke the cosmological constant in either the conventional or MOND case. In the former case, it was once hoped that there would be enough CDM that .In the latter case, may have its usual meaning, or it may simply be a place holder for whatever the geometry really is. One possible physical basis for MOND may be the origin of inertial mass in the interaction of particles with vacuum fields. A non zero cosmological constant modifies the vacuum and hence may modify inertia (MilgromM99 1999). In this context, it is interesting to note that for the parameters indicated by the data, and ,the transition from matter domination to -domination is roughly coincident with the transition to MOND domination.
The value of indicated by this scenario is in marginal conflict with estimates from high redshift supernovae (Riess et al. 1998hiz; Perlmutter et al. 1999SNCP). Modest systematic effects might be present in Type Ia supernovae data which could reconcile these results. It is difficult to tell at this early stage how significant the difference between and really is. Even if this difference is real, it may simply indicate the extent to which MOND affects the geometry. This is analogous to the variable- scenarios called Quintessence which have recently been considered (e.g., Caldwell, Dave, & Steinhardt, 1998CDS).