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Redshift

Redshift is the stretching of light waves due to the expansion of the universe, observed as a shift towards longer wavelengths (redder colors).

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The statement of the theorem

Define the emitted wavelength

\lambda_{em}

at time

t_{em}

and the observed wavelength

\lambda_{obs}

at time

t_{obs}

. Redshift (

z

) is defined by the ratio of these wavelengths: \n\n

1 + z = \frac{\lambda_{obs}}{\lambda_{em}}

\n\nIn the context of cosmic expansion, the ratio of wavelengths is directly proportional to the ratio of the scale factors at the respective times:\n\n

1 + z = \frac{a(t_{obs})}{a(t_{em})}