We saw in the lecture 13 how we could get some observational constraints on the hot early Universe. Recombination of protons and electrons lets the cosmic microwave background radiation freely escape. This requires temperatures of ~3000K, maybe 300,00 years after the big bang. Even better constraints come from primordial nucleosynthesis because that needs higher temperatures - bigger than 109 K, corresponding to times less than 3 minutes after the big bang! Can we look earlier than this ?
At earlier times the Universe would have been hotter still. The protons would smash together, but the Universe was so hot that the blackbody photons would break the nuclei apart as soon as they were formed. At even earlier times, when the Universe was less than a millisecond old and its temperature was 1012K then the Universe would be so hot that the blackbody photons crashing into each other would make particles and their antiparticles (remember E=mc2 - matter and energy are the same thing!). Protons must then slightly have outnumbered antiprotons (by only 1 in a billion!) in order to have the Universe made of protons as we see it today. Why ? Plainly there are some observable constraints here!
Back even further and the Universe getts hotter and hotter. At 10-10 of a second after the big bang then the temperature was more than 1015 K. At this point the electromagnetic force and weak nuclear force (the one that the neutrino interacts by) become one and the same thing - called the electroweak force (like water and ice are the same thing - but look very different!). We have experimental evidence backing up these theories from particle accelerators - the theories prediced some new particles (W and Z bosons), and these have been seen!
Back even further, and we are into temperatures/energies which are higher than we can currently attain in particle accelerators. Theories have been developed which unify the electroweak and strong nuclear force into a single force at very high energies - maybe something like 10-35 seconds after the big bang (these are called grand unified theories or GUT's). Its in these theories that we have to look for the slight imbalance between matter and antimatter that could result in the fact that we and the rest of the Universe is made of matter. And there are GUT theories can do this, which is interesting and makes them potentially believable even if we can't yet test them directly in particle accelerators. And they might also make some odd, heavy particles which make up the dark matter.
And most physisics believe that if you go to high enough energies then all the forces (ie GUT+gravity) unify into a single force. But that is on timescales of 10-43 seconds (called the Planck time) after the big bang. We don't yet have even a theory of how to unify gravity with the other forces, so we can't get anywhere closer to the origin of the big bang than this (though its pretty close!). Here is a nice overview
So, the fact that we are made of matter gets us into the GUT era which isn't well understood. Since we are, can we work the expansion of the Universe forward from say 10-10 seconds after the big bang to the present day and get a Universe like the one we see ? Actually, no! there are some nasty problems in there. The cosmic microwave background is incredibly uniform over all of the sky - it has the same temperature everywhere to about 1 part in 105. Yet diametrically opposite bits of the sky are not close enough together to ever have exchanged photons so its very surprising that they are at such similar temperatures. This is called the horizon problem. And even worse, why do we see Omega of order unity ? Both the density and critical density of the universe change rapidly with time as the universe expands, but they change in different ways. For Omega to be so close to unity now means that it must have been very very close to unity very soon after the big bang. This is the flatness problem.
Once way to solve all these simultaneously is to postulate a period in the very early universe when the expansion was dramatically larger than it is now - a period of inflation. And it'd better be in an era which we don't understand (because there isn't any reason to get it in anything we do understand!). One idea is that at the end of the GUT era, when the strong force parted company from the electroweak then that released a tremendous amount of energy, powering inflation. Anyway, if we do this way way back, then we start off with a universe which is much much smaller, so things on opposite sides of our current sky DO get time to exchange photons and get into equilibrium. The expansion dramatically flattens out the curvature of the Universe and the size of the fluctuations! Nice! And from this we CAN get to the sort of Universe we see today. See the overview of the beginning of the Universe. And there are some more good pages doing a similar review on the web site for the cambridge cosmology group, and the Microwave anisotropy probe
But this is a backwards test - we have the observational problems and so we postulate something to fix them. To test a model rather than just say that its consistent with what we see then we want it to predict something! And these inflationary models make a fairly strong prediction that space is flat, ie Omega=1. But the amount of matter (including dark matter) really doesn't look like this - it looks much more like Omega~0.3. But recent observations using supernovae to get distances to remote galaxies show an accelerating expansion - see here for a nice introduction (you need to have java enabled) - you can start at The High-Z SN Search page as you already know a lot of the background information! If this truely what the data are telling us then it is completely at odds with our ideas about how the expansion must be slowing down because of gravity! This acceleration (termed the cosmological constant) is currently interpreted as space itself having some energy density, which is causing it to accelerate away from itself. But however it gets interpreted it should be including in our calculations of Omega. And it looks like it would give a effecive contribution of Omega~0.7 so the total Omega ~ 1. But having this odd acceleration breaks the nice picture whereby whether or not the Universe will expand forever is the same as asking about the curvature of the Universe. These accelerating models are spatially flat, but dramatically expand forever! For those of you who are brave have a quick glance at this page on the cosmological constant - ignore the maths, just have a quick read of the text and pictures!
So, here we are, at the very end of our current knowledge. For the truely brave (or foolhardy!) here is a link to frequently asked questions in cosmology.