Late time and early time approximation for EOS

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SUMMARY

The discussion focuses on the late time and early time approximations for effective potential as presented in the article "Effective Potential in the Early Universe" (arXiv:1112.1682). Key equations referenced include equation 16 for early universe approximations, equation 21 for derived results, and equations 4 and 5 for constraints. Participants seek clarification on the methodology behind these approximations, indicating a need for deeper understanding of the mathematical derivations involved.

PREREQUISITES
  • Familiarity with effective potential concepts in cosmology
  • Understanding of mathematical derivations in theoretical physics
  • Knowledge of early universe cosmology
  • Proficiency in analyzing equations and constraints in scientific literature
NEXT STEPS
  • Study the derivation of effective potential in cosmological models
  • Research the implications of equations 4 and 5 in the context of early universe physics
  • Examine the mathematical techniques used in equation 21 for approximation methods
  • Explore related literature on late time approximations in cosmology
USEFUL FOR

Researchers, theoretical physicists, and students in cosmology who are interested in understanding the mathematical foundations and implications of early and late time approximations in effective potential analysis.

djymndl07
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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.
 

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