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I am new here, an avid Physics reader, but have lots of questions and doubts on which I'd like to get the help of a pro physicist. Here goes some about the theory of Inflation:

a) after the first expansion (which lasted like 10^-38 secs), how big did the Universe get?

b) why such a irregular rate of expansion, one that takes almost 0 time and another that takes 13B years?

c) If the universe is flat, how come space time is warped around masses like the Sun?

d) If the duration of inflation was so infinitesimal, could it have been enough to allow that tiny region of space-time to come to an equilibrium at all as far as temperature and distribution was concerned? The speed of light is fast but given small enough time, it's not fast enough to cross the distance in that tiny area.

e) Also, was Eisntein's GR valid at all under those extreme circumstances?

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    $\begingroup$ You should be aware that the whole concept of inflation is questionable. Some physicists reject the idea. $\endgroup$ – garyp Apr 26 '16 at 2:47
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Firstly, you must know that there are many models for inflation which give different results to your a) and b) questions, and we still don't know which is the right one. I'll try to answer regarding the most accepted and simple models.

a) During the period of inflation the distance between two separated points in the Universe increased at least $e^{60}\approx 10^{26}$ times. The exact minimum depends on the specific model, and there is not an upper limit as far as I know (it could have expanded $e^{100}$ or $e^{1000}$ times).

b) The mechanism that drives the expansion is the "inflaton field". During the inflation epoch this field was at a higher (not minimum) energy state, acting as a repulsive force and expanding the Universe. Later, the field decayed to its lowest energy state, releasing its potential energy as matter and radiation. When the space is filled with a constant positive energy density it expands exponentially, that is the reason why inflation took place when the field was at a higher energy and stopped when it reached a minimum.

c) All the mass/energy content of the Universe warps the space around it, but these deformations are local perturbations on an average flat space. When we say that the Universe is flat we talk about cosmic scale. Nevertheless, space surrounding a star or a black hole is not exactly flat.

d) No, it wasn't enough to allow the space-time to come to an equilibrium. However, the expansion was so enormous that inhomogeneities were diluted, resulting the incredibly homogeneous Universe that we can see today.

e) We are not sure, but most models use Occam's razor and assume so.

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