Late time and early time approximation for EOS

[djymndl07]

TL;DR

What are the the conditions for early universe when scale factor a is small so that we can approximate a complicated potential?

In the article https://arxiv.org/abs/1112.1682 effective potential in equation 16 is approximated for early universe and obtained equation 21 and for later time in equation 26. Some constraints are given in equation 4 and 5. Can anyone explain how this approximations are made? I was trying to calculate but could not find the desired expression.