Conclusions

Modern cosmological models require copious amounts of nonbaryonic cold dark matter for well established reasons. Yet the existence of CDM has yet to be confirmed. The alternative to dark matter postulated by MilgromM83 (1983), MOND, has long had considerable success in describing the rotation curves of spiral galaxies (Begeman et al. 1991BBS; SandersS96 1996; Sanders & VerheijenSV 1998), a fact which has no explanation in the standard framework. Moreover, MOND successfully predicted, a priori, the behavior of low surface brightness galaxies (McGaugh & de Blok 1998bMBb; de Blok & McGaugh 1998BM), a test which CDM models fail (McGaugh & de Blok 1998aMBa; Moore et al.MQGL 1999). Yet MOND has no clear cosmology.

In this paper, I have attempted to make some predictions for the temperature anisotropies in the microwave background which might potentially discriminate between CDM and MOND dominated cosmologies. In this context, the essential difference between the two is the baryon fraction ($f_b \approx 0.1$ for CDM and f_b =1 for MOND). I have used this fact to examine the differences expected for microwave background observations in as conservative and model independent a way as possible.

Upcoming experiments to measure the anisotropies of the microwave background to high precision should be able to distinguish between CDM and MOND. For the simple assumptions investigated here, the observational signatures are surprisingly subtle, requiring high accuracy (i.e., peak position or amplitude to $\sim 5\%$ at $\ell \gt 500$.) Perhaps the most promising test is the ratio of peak-to-trough amplitudes of the first two peaks, with $(C_{\ell,1}/C_{\ell,2})_{rel} < 4$ in plausible CDM models and $(C_{\ell,1}/C_{\ell,2})_{rel} \gt 5$ in MOND.

These predictions are offered in the hope of clearly distinguishing between CDM and MOND in the near future.

 

Figure 1: The power spectrum of temperature anisotropies in the microwave background with (a) and without (b) CDM. Three choices for the baryon density are illustrated in each case. The highest (lowest) baryon content corresponds to the highest (lowest) curve. CDM models with $\Omega_{\rm CDM} = 0.2$, 0.3, and 0.4 all gave indistinguishable results provided the baryon fraction was the same and H₀ was scaled to maintain the same baryon-to-photon ratio. CDM models have several distinct peaks before $\ell = 1000$ while in the pure baryon cases representing MOND the even numbered peaks have disappeared. Also shown are current measurements with errors $\Delta T < 40 \mu$K from the compilation of Tegmark (http://www.sns.ias.edu/~max/main.html#CMB) as of March 1999.