A Late time and early time approximation for EOS

AI Thread Summary
The discussion revolves around approximations made for effective potential in the early universe and later times as presented in the referenced article. Specifically, equation 21 addresses early universe conditions, while equation 26 focuses on later time scenarios. The constraints outlined in equations 4 and 5 are also significant to the analysis. Participants seek clarification on the methodology behind these approximations, indicating a need for deeper understanding of the calculations involved. Overall, the thread highlights challenges in deriving the desired expressions from the provided equations.
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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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