The first is what is the basic theory of particles? People have the theory of everything, grand unified theories, string theory, supergravity, quantum gravity and so on. All these different aspects of physics of very small scales can be understood a little better by looking at them in the cosmic framework. One make progress by examining the physics of the very early stages after the big bang.
The second question is, how did the universe acquire a bias in favour of matter? We know that matter and antimatter exist on equal footing at least in theoretical physics. But the real world that our astronomers can observe, seems to be made up of matter. So what happened to antimatter? How did antimatter disappear from the scene? This is a basic question big bang cosmologists have to answer with the help of physicists.
Whenever grand
unified theories are considered one talks of energies of the
order of 
and that is very high energy physics. Now as the
universe expands the energy would drop below this threshold and a stage will come when all the three interactions no longer operate in a unified mode and so the nature of physics changes. When this
happens we have a phase transition i.e. the state of matter changes significantly. A familiar example of phase transition is from steam to water. When you are cooling the steam something happens around the boiling
point of water and it starts condensing into water drops. So the state
of matter changes. What did happen to the universe as
it passed through that stage when the grand unified theory ceased to operate?
One of the consequences was that the universe
for a little while got into a mode of very rapid expansion called inflation. This inflation is supposed to have lasted a very very short time and then again
the universe reverted to normal expansion. This is considered a very
important phase in the history of the big bang universe.
Another question is: how did particles like neutrons, protons, electrons, muons, leptons form? This is again a fundamental question and we cannot answer it entirely within the scope of particle physics; nor can we answer it entirely within the scope of cosmology. The two disciplines have to combine in order to get the answer.
Another mysterious problem which cosmologists have to face is the nature of dark matter. When you look at galaxies individually or at clusters of galaxies you find a very high level of dynamical activity. High level of dynamical activity means that there is a lot of gravitating matter around. But observations suggest that the amount of matter seen is only 1/10 or a few percent of what you expect there should be in order to generate this much dynamics. So the conclusion is that there is a lot of dark matter around that we cannot see. Cosmologists would like to know what that dark matter is made of. This is an area where ideas from particle physics can help.
Another aspect in which the nature of dark matter would help us is in understanding the origin and evolution of large scale structures. How did the galaxies and their clusters form? Cosmologists think that from elementary small seeds entire galaxies grew. But how did this happen? How did this evolution take place? This is what cosmologists are trying to understand today.
When you look at this whole bunch of problems you begin to ask the question how much of it is speculation and how much is factually based? There are two limitations to this exercise which I earlier referred to, but I want to bring them together. First the epochs of the early universe are beyond astronomical observations. You are not able to see the very early stages of the universe for the reason I mentioned. Secondly, the physics of the epoch is untested in the laboratory because laboratory accelerators cannot produce that kind of high energy particles. Therefore there is a problem. This second issue also gets more difficult because these events are unrepeatable. One of the hallmarks of science is that whatever experiment you do today you should be able to repeat tomorrow and produce the same result. Now there is only one universe and it has gone through that stage and brought us here. You cannot say let me try another universe and see whether it works there; because this is once and only once kind of event. So events like inflation are unrepeatable. Finally we have to understand that both cosmologists and particle physicists are speculating as the former cannot observe and the latter cannot experiment. The only thing we can expect is that their speculations about what happened match each other in such a way as to produce relics which we can observe today. If you have relics, like an archaeologist you are using them to check back on what happened long time back in the past. You are trying to guess what those events were from the relics you have got today. What kind of relics can we look at which will tell us about this very exciting early universe?
There are certain relics which I very briefly want to enumerate. One is the ratio of number of photons (particles of light) and number of baryons like protons and neutrons. This ratio is found to be of the order of something like a few billions. What we have to understand is why did the universe have this particular ratio? Another relic is the particle called neutrino. How many different kinds of neutrinos are there? Is there any basic reason for understanding that?
A tangible and important relic is the cosmic microwave background. We can look at this background more and more precisely with the help of better and better telescopes. This work is going on. Can the small scale anisotropies of this background tell us anything about its early history? Other relics are clusters and superclusters of galaxies. When did clustering begin? That may tell us something about the very early universe and the kind of dark matter we find ultimately, as and when we do, will tell us about the physics which operated at those early epochs.
The origin of magnetic field is not understood. There is magnetic field on a cosmic scale, but where it first came from we don't know.
Then there is a mysterious result now being claimed as real which Einstein had first proposed and later withdrawn. It is the cosmological constant. It tells you that the universe is influenced not only by a force of gravity but also by a force of repulsion. It is very weak at small distances but large at large distances. If you have a theory of everything you have to produce from it relics more than what we have found so far. The question is can you match observations of these relics to your speculations? If one is a cynic in this whole affair one can say that at worst the exercise may deteriorate to arguments like `my speculations are better than yours'. Two scientists may have different scenarios for the early universe and they would start fighting whose scenario for the early universe is correct. The only way to judge is to look at the relics and see whose theory matches the relics best. At best if everybody agrees that this is the scenario you can conclude that it is a self consistent scenario that explains the present. But this need not be a unique scenario. There could be other ways of getting at the same observations. So one should leave the door open for alternatives. One can say that although the scope of astronomical observations is steadily deepening and widening considerable uncertainty still remains regarding the self-consistency of the competing models let alone the emergence of a unique one.