Fundamental Constant Evolution

(Jayaram N. Chengalur, Nissim Kanekar)

Coupling constants like the fine structure constant (alpha), the ratios of particle masses (e.g. the ratio of the proton mass to the electron mass, mu = m_p/m_e), and other dimensionless quantities, are not expected to change with space or time in the standard model of particle physics or General relativity. Tests of temporal variation of such low-energy fundamental constants are thus tests of the basic assumption of the standard model and relativity, similar to tests of violations of the weak equivalence principle, Lorentz invariance, local position invariance, etc. However, besides the above pragmatic view of tests of fundamental constant evolution, a generic prediction of higher-dimensional theories that attempt to unify the standard model and relativity is that low energy fundamental constants like alpha and mu should evolve with time. As such, tests of fundamental constant evolution allow a low-energy probe of such higher-dimensional theories. This is very interesting as most other predictions of these theories lie at very high energies (the unification scale), far beyond our reach in the foreseeable future.

Laboratory studies of fundamental constant evolution, using atomic clocks, provide an excellent approach to probe changes on relatively short timescales, up to a few years. Indeed, such studies have yielded very sensitive constraints on changes in alpha on timescales of a year (e.g. Rosenband et al. 2008, Science). However, such studies are not sensitive to changes in the constants on cosmological timescales. Astronomical studies allow one to probe such evolution on timescales of billions of years, and to thus test the validity of the standard model on cosmological timescales. The most important of these studies are based on a comparison between the redshifts of a galaxy lying along the line of sight to a background quasar, as measured from multiple spectral lines detected in absorption in the quasar spectrum. If the different lines arise from different physical mechanisms (e.g. fine structure, hyperfine structure, rotation, lambda-doubling, inversion, etc.), the line frequencies would have different dependences on quantities like alpha and mu. If alpha and/or mu change with cosmological time, the rest frequency of each line would be different at the galaxy's redshift from the value measured in the laboratory today. However, one uses the laboratory rest wavelength to infer the galaxy's redshift from the observed line in the quasar spectrum, thus making the implicit assumption that the rest wavelength does not change with time. As such, if the constants do change with time, and the line rest wavelengths change as well, the effect is that one would infer an incorrect galaxy redshift. And, if one uses two lines, with different frequency dependences on alpha, mu, etc., one would infer different redshifts for the same galaxy! 

Researchers at NCRA-TIFR have come up with new techniques to probe fundamental constant evolution, based on radio spectral lines. They also use radio telescopes to carry out accurate measurements of the redshifts of atomic and molecular radio spectral lines, including those of neutral hydrogen, hydroxyl, ammonia, methanol, etc, to carry out amongst the most accurate tests of cosmological changes in the fine structure constant and the proton-electron mass ratio.

Recent Results
Stringent constraints on fundamental constant evolution over 3 billion years
Kanekar, Ghosh and Chengalur used the mighty Arecibo Telescope to carry out one of its deepest-ever observing runs, 125 hours on the hydroxyl (OH) lines from a gas cloud close to the z=0.247 active galactic nucleus PKS1413+135. The satellite OH lines, at rest frequencies of 1720 MHz and 1612 MHz, are ``conjugate'' in this system, mirror images of each other, with the 1720 MHz line in emission and the 1612 MHz line in absorption. Since the 1720 and 1612 MHz line frequencies have different dependences on the fine structure constant, alpha, and the ratio of the proton mass to the electron mass, mu, this expected perfect cancellation makes the two lines ideal to probe changes in alpha and mu out to z~0.247, i.e. a lookback time of nearly 3 billion years. If alpha and/or mu change with time, the lines would shift relative to each other, and would not cancel out. Kanekar et al. found that the OH satellite line remain conjugate within the measurement errors, with no evidence for a shift between the two lines. They used this perfect cancellation to place stringent constraints on changes in alpha and mu with cosmological time, limiting fractional changes in the two quantities to less than a few parts in a million. This is the most sensitive constraint on fractional changes in alpha in the literature, and with no known systematic effects. The top two panels of the figure show the two OH satellite lines from PKS1413+135 at z=0.247, with the 1720 MHz in the upper panel and the 1612 MHz line in the middle panel. The bottom panel shows the sum of the two line optical depths. It is clear that this is consistent with Gaussian noise, as expected if the lines are mirror images of each other.
Stringent constraints on changes in the proton-electron mass ratio over 7.5 Gyrs from methanol lines
Kanekar et al. used the Karl G. Jansky Very Large Array (VLA) to obtain deep absorption spectra in four methanol (CH3OH) lines from the z=0.88582 gravitational lens towards PKS1830-211. Three of the four CH3OH lines have very different sensitivity coefficients to changes in the proton-electron mass ratio mu=m_p/m_e. A comparison between the redshifts of these lines thus allows one to test for temporal evolution in mu. Kanekar et al. compared the line shapes of the three CH3OH lines that have similar rest frequencies, 48.372, 48.377 and 60.531 GHz, and found their line profiles to be in excellent agreement. This yielded a robust constraint of ~4 parts in ten million on fractional changes in mu; this is the most stringent current constraint on changes in mu. Kanekar et al. thus find no evidence for changes in the proton-electron mass ratio over a lookback time of ~7.5 Gyr. The figure to the right shows the four CH3OH lines detected in the z=0.88582 lens with the VLA (two of the lines are in the middle panel, blended with each other); the line rest frequencies in Ghz are listed on the top left of each panel. The dashed blue curve in each panel shows a single Gaussian fit to each line.
Constraints on fundamental constant evolution from HI 21cm and OH 18cm lines
Kanekar et al. used the Green Bank Telescope to carry out spectroscocpy in the redshifted neutral hydrogen (HI) 21cm and hydroxyl (OH) 18cm lines from the z=0.765 absorption system toward the quasar PMN J0134-0931. A comparison between the ``satellite'' OH 18cm line redshifts, or between the redshifts of the HI 21cm and ``main'' OH 18 cm lines, is sensitive to changes in different combinations of the fine structure constant (alpha) and the proton-electron mass ratio (mu = m_p/m_e). A comparison between the redshifts of the HI 21cm and the OH 18cm lines, via a multi-Gaussian fit, yielded strong constraints on changes in a combination of alpha and mu, and no evidence for a change in the constants between z=0.765 and the present epoch. Incorporating the independent constraints on fractional changes in mu from another absorber at a similar redshift, Kanekar et al. found that fractional changes in alpha are less than ~3 parts in a million (at 2 sigma significance) over a look-back time of 6.7 Gyr. The top panels of the figure to the right show the HI 21cm and 18cm lines detected with the Green Bank Telescope, with the multi-Gaussian fit shown in blue. The lower panels show the residuals from each fit, which can be seen to be consistent with noise.