= Exponential-potential power-law inflation
{title2=$V=V_0e^{-c\phi/m_P},\quad a\propto t^{16\pi/c^2}$}
Use <natural units>, the unreduced <Planck mass> $m_P=G^{-1/2}$, $V_0>0$ and $c\ne0$. In a flat universe dominated by a canonical <inflaton>, $\phi=(2m_P/c)\log(\beta t)$ and $a\propto t^p$ solve the <inflaton equation of motion> and <Friedmann equation> exactly when $p=16\pi/c^2$ and $\beta^2=V_0c^2/[2m_P^2(3p-1)]$. The positive-potential scaling solution requires $p>1/3$, while <cosmic inflation> requires $p>1$. Its constant <equation-of-state parameter> is $w=-1+2/(3p)$. In terms of the <reduced Planck mass> $M=m_P/\sqrt{8\pi}$, the exponential slope is $\lambda=c/\sqrt{8\pi}$ and the same exponent is $p=2/\lambda^2$.
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