Context :

Aims : We constrain a hypothetical variation in the fundamental physical constants over the course of cosmic time .

Methods : We use unique observations of the CO ( 7-6 ) rotational line and the [ C i ] ^ { 3 } P _ { 2 } - ^ { 3 } P _ { 1 } fine-structure line towards a lensed galaxy at redshift z = 5.2 to constrain temporal variations in the constant F = \alpha ^ { 2 } / \mu , where \mu is the electron-to-proton mass ratio and \alpha is the fine-structure constant .
The relative change in F between z = 0 and z = 5.2 , \Delta F / F = ( F _ { obs } - F _ { lab } ) / F _ { lab } , is estimated from the radial velocity offset , \Delta V = V _ { rot } - V _ { fs } , between the rotational transitions in carbon monoxide and the fine-structure transition in atomic carbon .

Results : We find a conservative value \Delta V = ( 1 \pm 5 ) km s ^ { -1 } ( 1 \sigma C.L .
) , which when interpreted in terms of \Delta F / F gives \Delta F / F < 2 \times 10 ^ { -5 } .
Independent methods restrict the \mu -variations at the level of \Delta \mu / \mu < 1 \times 10 ^ { -7 } at z = 0.7 ( look-back time t _ { z 0.7 } = 6.4 Gyr ) .
Assuming that temporal variations in \mu , if any , are linear , this leads to an upper limit on \Delta \mu / \mu < 2 \times 10 ^ { -7 } at z = 5.2 ( t _ { z 5.2 } = 12.9 Gyr ) .
From both constraints on \Delta F / F and \Delta \mu / \mu , one obtains for the relative change in \alpha the estimate \Delta \alpha / \alpha < 8 \times 10 ^ { -6 } , which is at present the tightest limit on \Delta \alpha / \alpha at early cosmological epochs .

Conclusions :