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Astronomy & space · Advanced university

Redshift, expansion and cosmological distances · revision notes

Define z=(λobserved−λemitted)/λemitted. Redshift is dimensionless and can arise through different physical mechanisms.

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Key ideas and conditions

Redshift

Define z=(λobserved−λemitted)/λemitted. Redshift is dimensionless and can arise through different physical mechanisms.

Expansion

In a homogeneous expanding model, 1+z=a(now)/a(emission). Large cosmological redshifts are not generally converted to speed by the low-speed Doppler formula.

Local law

At small redshift and in an appropriate distance regime, v≈H0d provides a useful approximation. Stated H0 values in exercises are model inputs, not claims to resolve measurement tensions.

Distance choices

Luminosity distance, angular-diameter distance and comoving distance are different definitions. Specify which a calculation uses.

Explain without looking

  1. If scale factor at emission is 0.5 of its current value, find z.
  2. Distinguish a measured spectral shift from a model-derived expansion history.

Further reading and review references

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