Graduate Late time and early time approximation for EOS

djymndl07
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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.
 

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