Problem Set 03 Solutions: BAO and the sound horizon

ASTR 476: Observational Cosmology ยท 2026-09-25

Instructor key. Numeric values are generated by build_astr476_package.py from the computation module and the included source subset.

Solution 1

z=0.38: D_V(model)=1477.922 Mpc.

Solution 2

z=0.51: D_V(model)=1886.964 Mpc.

Solution 3

z=0.61: D_V(model)=2171.002 Mpc.

Solution 4

At z=0.38, residual=(1477.922-1477.0)/16.0=0.058; conditional on r_d=r_d,fid and not a full likelihood.

Solution 5

D_V^scaled=D_V r_d,fid/r_d. If r_d is 0.98 r_d,fid, the scale is D_V/0.98, 1.0204 D_V, about 2.04% larger.

Solution 6

Isotropic compression improves signal-to-noise for an averaged scale but discards separate radial/transverse geometric information.