The status of searches for possible variation in the constants of nature from astronomical observation of molecules is reviewed , focusing on the dimensionless constant representing the proton-electron mass ratio \mu = m _ { p } / m _ { e } .
The optical detection of H _ { 2 } and CO molecules with large ground-based telescopes ( as the ESO-VLT and the Keck telescopes ) , as well as the detection of H _ { 2 } with the Cosmic Origins Spectrograph aboard the Hubble Space Telescope is discussed in the context of varying constants , and in connection to different theoretical scenarios .
Radio astronomy provides an alternative search strategy bearing the advantage that molecules as NH _ { 3 } ( ammonia ) and CH _ { 3 } OH ( methanol ) can be used , which are much more sensitive to a varying \mu than diatomic molecules .
Current constraints are | \Delta \mu / \mu| < 5 \times 10 ^ { -6 } for redshift z = 2.0 - 4.2 , corresponding to look-back times of 10-12.5 Gyrs , and | \Delta \mu / \mu| < 1.5 \times 10 ^ { -7 } for z = 0.88 , corresponding to half the age of the Universe ( both at 3 \sigma statistical significance ) .
Existing bottlenecks and prospects for future improvement with novel instrumentation are discussed .