Cosmological variability of fundamental physical constants

Gamow was one of the pioneers who studied the possible variability of fundamental physical constants. Some versions of modern Grand Unification theories do predict such variability. The paper is concerned with three of the constants: the fine-structure constant, the ratio of the proton mass m(p) to the electron mass m(e), and the ratio of cu the neutron mass m(p), to m(e). It is shown on the basis of the quasar spectra analysis, that all the three constants revealed no statistically significant variation over the last 90% of the life time of the Universe. At the 2 sigma significance level, the following upper bounds are obtained for the epoch corresponding to the cosmological redshifts z similar to 2 - 3: Delta alpha/alpha < 1.5 x 10(-3), Delta m(p)/m(p) < 2 x 10(-3), and Delta m/m < 3 x 10(-4), where Delta x is a possible deviation of a quantity x from its present value, m = m(p)+m(n), and the nucleon masses are in units of m(e). (According to new observational data which became known most recently, Delta m(p)/m(p) < 2 x 10(-4)). In addition a possible anisotropy of the high-redshift fine splitting over the celestial sphere is checked. Within the relative statistical error 3 sigma < 1% the values of alpha turned out to be the same in various quadrants of the celestial sphere, which corresponds to their equality in causally disconnected areas. However, at the 2 sigma level a tentative anisotropy of estimated Delta alpha/alpha values is found in directions that approximately coincide with the direction of the relic microwave background anisotropy. The revealed constraints serve as criteria for selection of those theoretical models which predict variation of alpha, m(p) or m(n) with the cosmological time.