Solution (source code)

= Solution

A larger <cosmological constant> changes both the expansion history and the growth history: it alters cosmological distances, the <baryon acoustic oscillation> scale as observed in angle and redshift, and the time at which growth begins to freeze. The new interaction in part (d) leaves the background <Friedmann equation> unchanged but changes clustering abruptly from $t_f$ onward.

Redshift-resolved measurements of the <linear growth factor>, weak <gravitational lensing>, galaxy clustering, and <cosmological distance measures> can therefore compare geometry with growth. Equal present amplitudes do not imply equal $D(z)$, and only the higher-dark-energy model changes the distance-redshift relation. This breaks the degeneracy.