= Effective equation of state of an oscillating scalar field
Suppose a homogeneous scalar field oscillates much faster than the <Hubble parameter> in a monomial potential $V(\phi)=\lambda|\phi|^n$. The <virial theorem> averaged over one oscillation gives $\langle\dot\phi^2\rangle=n\langle V\rangle$, and hence
$$
\langle w\rangle=\frac{\langle P\rangle}{\langle\rho\rangle}=\frac{n-2}{n+2},
\qquad
\rho\propto a^{-6n/(n+2)}.
$$
A quadratic minimum therefore behaves like <pressureless matter>, whereas a quartic minimum behaves like <radiation in cosmology>.
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