Variations in the fundamental constants in the QSO host J1148+5251 at z=6.4 and the BR1202-0725 system at z=4.7

We use sensitive observations of three high-redshift sources: [C II] P-2(3/2) -> P-2(1/2) fine-structure and CO (J = 2 -> 1) rotational transitions for the z = 6.4 quasar (QSO) host galaxy J1148+5251 taken with the Plateau de Bure Interferometer (PdBI) and Jansky Very Large Array, respectively, and [C II] and CO (J = 5 -> 4) transitions from the QSO BR1202-0725 and its companion sub-millimetre galaxy (SMG) at z = 4.7 taken with the Atacama Large Millimeter Array and the PdBI. We use these observations to place constraints on the quantity Delta z = z(CO) - z(C II) for each source where z(CO) and z(C II) are the observed redshifts of the CO rotational transition and [C II] fine-structure transition, respectively, using a combination of approaches: (1) modelling the emission line profiles using 'shapelets' - a complete orthonormal set of basis functions that allow us to recreate most physical line shapes - to compare both the emission redshifts and the line profiles themselves, in order to make inferences about the intrinsic velocity differences between the molecular and atomic gas, and (2) performing a marginalization over all model parameters in order to calculate a non-parametric estimate of Delta z. We derive 99 per cent confidence intervals for the marginalized posterior of Delta z of (-1.9 +/- 1.3) x 10(-3), (-3 +/- 8) x 10(-4) and (-2 +/- 4) x 10(-3) for J1148+5251, and the BR1202-0725 QSO and SMG, respectively. We show that the [C II] and CO (J = 2 -> 1) line profiles for J1148+5251 are consistent with each other within the limits of the data, whilst the [C II] and CO (J = 5 -> 4) line profiles from the BR1202-0725 QSO and SMG, respectively, have 65 and >99.9 per cent probabilities of being inconsistent, with the CO (J = 5 -> 4) lines similar to 30 per cent wider than the [C II] lines. Therefore, whilst the observed values of Delta z can correspond to variations in the quantity Delta F/F with cosmic time, where F = alpha(2)/mu, with alpha the fine-structure constant and mu the proton-to-electron mass ratio, of both (-3.3 +/- 2.3) x 10(-4) for a look-back time of 12.9 Gyr and of (-5 +/- 15) x 10(-5) for a look-back time of 12.4 Gyr, we propose that they are the result of the two species of gas being spatially separated as indicated by the inconsistencies in their line profiles.