Question 19N.3.HL.TZ0.16

spectra of galaxies are redshifted «compared to spectra on Earth» ✔

redshift/longer wavelength implies galaxies recede/ move away from us
OR
redshift is interpreted as cosmological expansion of space ✔

«hence universe expands»

NOTE: Universe expansion is given, so no mark for repeating this.
Do not accept answers based on CMB radiation.

ALTERNATIVE 1

$z=\frac{392-122}{122}=2.21$ ✔

$\frac{R}{R_0}=«2.21+1=» 3.21$ ✔

ALTERNATIVE 2

$\frac{R}{R_0}=\frac{{\displaystyle 392}}{122}$ ✔

= 3.21 ✔

density of flat/Euclidean universe
OR
density for which universe has zero curvature
OR
density resulting in universe expansion rate tending to zero ✔

$H=«\frac{70\times {10}^3}{\left({10}^6\times 3.26\times 9.46\times {10}^{15}\right)}=»2.27\times {10}^{-18}\hspace{0.17em}«{\mathrm{s}}^{-1}»$✔

$\rho =0.32\times \frac{3\times {\left(2.27\times {10}^{-18}\right)}^2}{8\mathrm{\pi }\times 6.67\times {10}^{-11}}$✔

$3.0\times {10}^{-27}\hspace{0.17em}«\mathrm{kg} {\mathrm{m}}^{-3}»$✔

NOTE: MP1 for conversion of H to base units.
Allow ECF from MP1, but NOT if H is left as 70.

rotation speed of galaxies is larger than expected away from the centre ✔

there must be more mass «at the edges» than is visually observable «indicating the presence of dark matter» ✔