= Solution
A <cosmological constant> has fixed density and <equation of state> $w=p/(\rho c^2)=-1$. A separately conserved dynamical component obeys
$$
\rho_{\rm de}(z)=\rho_{{\rm de},0}\exp\!\left[3\int_0^z\frac{1+w(z')}{1+z'}\,dz'\right].
$$
If $w$ departs from $-1$, its history changes the <Hubble parameter>, <luminosity distances> and angular-diameter distances. Type Ia supernovae probe a relative distance-redshift relation, <baryon acoustic oscillations> provide standard-ruler distances and expansion information, and the <cosmic microwave background> fixes early-time scales and geometric combinations. Combining these breaks some degeneracies with <matter density>, <curvature> and <calibration>. Distance observables integrate the expansion history, so they smooth rapid variations in $w$ and cannot determine an arbitrary function exactly.
Structure-growth measurements add a dynamical test. Galaxy clustering, <redshift-space distortions> and <weak gravitational lensing> constrain the growth of matter perturbations and metric potentials. The late <Integrated Sachs-Wolfe effect> probes potential evolution through CMB-matter correlations. A scalar-field dark-energy model can have perturbations and an effective <sound speed> different from other models with a similar background expansion. Comparisons of geometry and growth can therefore distinguish some models and test gravity assumptions.
\b[A statistically significant, robust departure from $w=-1$ or from constant dark-energy density would disfavor a pure <cosmological constant> within the stated framework.] Consistency with $w=-1$ over a finite redshift range does not prove exact constancy: a slowly rolling field can mimic it. Supernova <calibration>/evolution, <galaxy bias>, <photometric redshift> errors, <intrinsic galaxy alignments> and foregrounds must be controlled; modified gravity can also change growth. Parameterizations such as $w(a)=w_0+w_a(1-a)$ are useful finite-dimensional tests rather than a complete classification of all dark-energy histories.
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