I often hear about cosmic inflation occurring rapidly after the Big Bang, but have never came across any explanation for it. What supposedly caused this inflationary period in the early universe? Also, my assumption is that the laws of physics, i.e. light speed and relativity, did not exist during inflation, but were after effects. Is that a correct assumption? Thanks!
With normal matter, the strength of gravity depends on the stress-energy tensor, which, in an isotropic homogeneous universe, has trace of $\rho + 3p$. The positive pressure from relativistic particles (photons and neutrinos) enhances the gravity in slowing down expansion. In inflation theory, it is assumed that there was a negative pressure scalar field in the universe that began in a "false vacuum state". That is, the field's energy density dropped very slowly as the universe inflated, and therefore the total energy of this field grew as the volume of the universe grew. The field's pressure was negative, overwhelming the compressional forces of gravity from normal matter, so that gravity was strongly repulsive. The negative pressure rapidly expanded this section of the universe by many factors.
Throughout this epic of inflation, standard physics is expected to hold with just the addition of this new scalar field. It is introduced because it helps to explain why the entire visible universe today is so homogeneous. Previously, subregions of the visible universe that are far from each other would have not been in contact in any way until well after the epoch of recombination observed by microwave background experiments. It also explains why the curvature of the universe is very nearly flat. It converted a small section of the universe to extremely large radii and thus small curvature.
We do not know the specifics about the inflationary scalar field. In quantum field theory, there are multiple quantum fields (such as Higgs field) which at a local minimum in energy are in a vacuum state (i.e., have no particles). Inflaton particles are excitations in this field, where it deviates from the vacuum state. These decayed into the hot, dense particles of the Big Bang.