Ratio Of Proton Mass To Electron Mass Unchanged For 11.5 Billion Years

A recent paper observed that the proton-electron mass ratio has been unchanged since at least z=3.025 (about 11.5 billion years ago). The observed ratio of the difference in this ratio to the ratio itself at that redshift is(0.120±0.144)× 10⁸. This is consistent with null hypothesis of zero at the one sigma level. All previous efforts to determine changes in physical constants in the distant past using astronomy observations have likewise seen no statistically significant difference.

Here is a chart converting redshift z to look back time (i.e. how long ago that z occurred). Note the shift from z amount in the left body of the table, to look back time in billions of years in the right body of the table, starting at z=6.