= Solution
With zero <scalar potential> and a homogeneous <scalar field>, the preceding <perfect fluid> identification gives
$$
\boxed{P=\rho=\frac12\dot\phi^2.}
$$
This <equation of state> is that of a <stiff fluid>. The field equation integrates to $a^3\dot\phi=K$, since $\partial_t(a^3\dot\phi)=0$. Hence $\rho=K^2/(2a^6)$, agreeing with the <cosmological continuity equation> for $w=1$. If this nonzero component dominates a flat universe, the <Friedmann equation> gives
$$
\left(\frac{\dot a}{a}\right)^2=\frac{4\pi G K^2}{3a^6},\qquad
\dot a=\sqrt{\frac{4\pi G}{3}}\,|K|a^{-2}
$$
on the expanding branch. Integrating once more, $a^3=3\sqrt{4\pi G/3}\,|K|(t-t_B)$. Choosing the <Big Bang> at $t_B=0$ yields
$$
\boxed{a(t)\propto t^{1/3}.}
$$
The <homogeneous free scalar as a stiff fluid> construction requires $K\ne0$; a constant zero-potential field has zero <energy density> and cannot dominate this expansion.
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