The relation between redshift and the CMB temperature , T _ { CMB } ( z ) = T _ { 0 } ( 1 + z ) is a key prediction of standard cosmology , but is violated in many non-standard models .
Constraining possible deviations to this law is an effective way to test the \Lambda CDM paradigm and search for hints of new physics .
We present state-of-the-art constraints , using both direct and indirect measurements .
In particular , we point out that in models where photons can be created or destroyed , not only does the temperature-redshift relation change , but so does the distance duality relation , and these departures from the standard behaviour are related , providing us with an opportunity to improve constraints .
We show that current datasets limit possible deviations of the form T _ { CMB } ( z ) = T _ { 0 } ( 1 + z ) ^ { 1 - \beta } to be \beta = 0.004 \pm 0.016 up to a redshift z \sim 3 .
We also discuss how , with the next generation of space and ground-based experiments , these constraints can be improved by more than one order of magnitude .