Fundamental physics with ESPRESSO: Precise limit on variations in the fine-structure constant towards the bright quasar HE 0515?4414

The strong intervening absorption system at redshift 1.15 towards the very bright quasar HE 0515?4414 is most studied absorber for measuring possible cosmological variations in fine-structure constant, ? . We observed 16.1 h with Very Large Telescope and present here first constraint on relative parts-per-million (ppm) precision from new ESPRESSO spectrograph: ? / = 1.3 ± stat 0.4 sys ppm. statistical uncertainty (1 ? ) similar to ensemble of previous large samples absorbers derives high signal-to-noise ratio achieved (?105 per km s ?1 pixel). ESPRESSO’s design, calibration our observations its laser frequency comb, effectively removed wavelength errors measurement. resolving power spectrum ( R 145 000) enabled identification narrow components within profile, allowing a more robust analysis evidence corroborated by their correspondence previously detected molecular hydrogen neutral carbon. main remaining systematic arise ambiguities profile modelling, effects redispersing individual exposures, convergence parameter estimation algorithm. All analyses spectrum, including error estimates, were initially blinded avoid human biases. make reduced publicly available further analysis. Combining result 28 measurements, other spectrographs, which have been mitigated yields weighted mean ?0.5 0.5 ppm redshifts 0.6?2.4.