Angular Diameter Distances (Z~1 Peak)

In expanding FRW cosmologies the angular diameter distance D_A(z) is predicted to increase with redshift, reach a maximum near z˜1–1.6, and then decrease so that objects at higher redshift again appear larger in angle, a non-intuitive “turnover” that depends sensitively on the assumed expansion history and dark-energy content (McCrea 1935; Melia 2018). In ΛCDM this maximum and its redshift are used as a geometric consistency check, but detailed analyses using standard rods such as radio cores or compact galaxies show that the inferred D_A(z) and location of the peak can shift once source evolution and selection effects are included, leading to tension between different datasets and highlighting how strongly ΛCDM must control intrinsic size evolution to keep the observed turnover compatible with its dark-energy parameters (Blanchard 2006; Melia 2018).

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