Colloquium: Search for a drifting proton-electron mass ratio from H2

An overview is presented of the H₂ quasar absorption method to search for a possible variation of the proton-electron mass ratio μ =m_p/m_e on a cosmological time scale. The method is based on a comparison between wavelengths of absorption lines in the H₂ Lyman and Werner bands as observed at high redshift with wavelengths of the same lines measured at zero redshift in the laboratory. For such comparison sensitivity coefficients to a relative variation of μ are calculated for all individual lines and included in the fitting routine deriving a value for Δ μ /μ . Details of the analysis of astronomical spectra, obtained with large 8-10 m class optical telescopes, equipped with high-resolution echelle grating based spectrographs, are explained. The methods and results of the laboratory molecular spectroscopy of H₂, in particular, the laser-based metrology studies for the determination of rest wavelengths of the Lyman and Werner band absorption lines, are reviewed. Theoretical physics scenarios delivering a rationale for a varying μ are discussed briefly, as well as alternative spectroscopic approaches to probe variation of μ , other than the H₂ method. Also a recent approach to detect a dependence of the proton-to-electron mass ratio on environmental conditions, such as the presence of strong gravitational fields, are highlighted. Currently some 56 H₂ absorption systems are known and listed. Their usefulness to detect μ variation is discussed, in terms of column densities and brightness of background quasar sources, along with future observational strategies. The astronomical observations of ten quasar systems analyzed so far set a constraint on a varying proton-electron mass ratio of |Δ μ /μ |<5 ×1 0^-6 (3 σ ), which is a null result, holding for redshifts in the range z =2.0 - 4.2 . This corresponds to look-back times of (10 - 12.4 )×10⁹ years into cosmic history. Attempts to interpret the results from these ten H₂ absorbers in terms of a spatial variation of μ are currently hampered by the small sample size and their coincidental distribution in a relatively narrow band across the sky.