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It is difficult to `conclude' about what is an ongoing and ever growing part of physics. What I hope is apparent from these lectures is that the interaction between theory and observation is very strong. The data being acquired today is constraining the theories we have developed.

Of course that could be because our theories are somewhat naive, but all that is required is to be willing to update our ideas as new data makes its impact. The key question today seems to be whether the Cold Dark Matter theory will survive after playing such a prominent role over the past years. I think that people are too eager to pronounce it dead. There are very many places where the theory is rather weak (biasing must be the main weakness), and there are equally many places where things can be changed without dramatically altering the whole concept (I think of introducing non-Gaussian perturbations, for example). What bothers me most is that we have no strong, alternative to take the place of CDM. Even if we were to go back to Peebles' open baryon-dominated universe with initial isocurvature perturbations having an n = - 1 power spectrum, we would still have to fix it in order to get around the microwave background anisotropy constraints.

I think the future here lies in getting bigger and better N-body models with an attempt to inject more `realism' into the galaxy formation process. It might be that CDM is fine if we do that, except that we are normalizing everything to the large scales.

From the point of view of the surveys - we obviously need more of them. It is impossible to assess the Broadhurst et al. pencil beam surveys without a better basis for doing statistics. My present inclination is to take that data at face value and see whether the N-body experiments can produce such an effect. I would like the comparison to be done statistically, not an eyeball test claiming that two pictures look pretty much the same.

Do Great Attractors exist and if so do they pose a problem for the standard CDM picture? That is another poorly phrased question, for there is certainly something out there perturbing the Hubble flow. If we accept the data at face value, we will have to make the amplitude (if not the spectrum) of the primordial fluctuations fit the large scales. That is where the models are best understood and where the data is probably clearest. As pointed out by numerous authors, that leaves us with a problem on the small scales, but I am prepared to say that we do not really understand what is going on there. We certainly do not understand what is involved in the formation of clusters (it has been suggested that dynamical friction and mergers will play a role there), and we understand even less of what is happening on galaxy scales. The present models are too simple.

So cosmology is not, in my opinion, in a state of crisis - at least not yet! It is in a state of rapid development and that is what makes it exciting from both the observational and theoretical point of view.


I owe considerable thanks to the audience who listened so carefully and criticized so enthusiastically. The school and these lectures would not have existed without them, they made the weeks of learning a lot of fun. I also wish to thank the Institute of Astrophysics of the Canarias for their efforts in organizing this school and their hospitality, and in particular Raphael Rebolo and Manolo Collados for their hard work. I would like to come again!

These lecture notes written up while I enjoyed the hospitality of the Astronomy Center of the University of Sussex, partially supported by the SERC. I have benefitted enormously from discussing the Universe with many friends in diverse places. I would particularly like to thank Lone Appel (Copenhagen), Rien van de Weygaert (Leiden) and Vicent Martínez (Valencia) for being perpetually willing to argue and suggest new ideas.

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