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Physics LibreTexts

S15 Pressure and Energy Density Evolution SOLUTIONS

  • Page ID
    7882
  • Exercise 15.1.1

    Answer

    The equation is 

    \[a\frac{d\rho}{da} = -3(P/c^2+\rho) \nonumber\]

    Plugging in \(\rho \propto a^n\) we get \(n\rho = -3(P/c^2 + \rho)\). Solving for \(P\) for \(n=-3, -4, 0\) we find \(P=0\), \(P=\rho c^2/3\), and \(P = -\rho c^2\) respectively.