First of all, we still do not know if the 4 fundamentals forces can be unified. The best we have came up to are grand unification theories (GUT), which join three of the fundamental forces except gravity. The fact that gravitational waves have been detected, may point towards GUT since they address energies of the GUT scale.
Nonetheless, assuming that String theory, which is a good candidate to unify gravity with the other forces, is correct, there is a theory based on them which is favored with the BICEP2-Data. This is a theory developed by Robert Brandenberger, called String Gas Cosmology (see http://arxiv.org/abs/1105.3247). This theory suggest that the universe started with a gas of strings whose thermodynamic properties avoid the temperature singularity of the big bang. This theory also predicts why we see 3 dimensions of space and one of time. If two strings meet, their edges can form a single, twisted loop. That would release three dimensions of space and one of time, which can then swell to the scales we see in the universe today.
Furthermore, the BICEP2 data suggest a blue tilt in the gravitational waves predicted by string gas cosmology and hard to explain by standard inflationary cosmology, which predicts a red tilt. So if the BICEP2 data is confirmed and this blue tilt is favored, then it would be a evidence for string theory and oponents cannot say that string theory does not match with data.
So if your question is if the BICEP2 data can help prove string theory, you are answer is yes
Best Answer
The terms quark epoch and lepton epoch do not mean that is when those particles were created. As far as we know the Standard model particles were created at the end of the inflationary epoch and both quarks and leptons would have been created at this time (though it must be emphasised that all the theories for what happened this early in the history of the universe are speculative). Instead the terms refer to the times when the behaviour of the matter in the universe was dominated by the quarks and leptons respectively.
The quark epoch refers to the time when the quarks were not bound into hadrons but instead existed as a quark gluon plasma. The leptons would have been present at this time, but it was the QGP that dominated the properties of the matter in the universe. We have managed to create a quark gluon plasma in the ALICE detector at the LHC, but even so I think it's fair to say it's early days and the QGP isn't fully understood so we need to be a little cautious about what exactly went on at this point in the evolution of the universe.
The lepton epoch is the time when the quarks had all combined into hadrons to produce the particles we see today, but the temperature was still high enough to create electron-positron pairs. These pairs were produced in such large numbers that the combined mass of the electrons and positrons was larger than the hadrons and therefore the leptons briefly dominated the universe.
The lepton epoch followed the quark epoch because it needs much more energy to separate quarks into a quark-gluon plasma than it does to create electron-positron pairs, so it happened earlier in the evolution of the universe when the temperature was higher.