Fundamental constants

Do fundamental physical constants vary?

General relativity and the standard model of particle physics depend on many (~ 27) independent numerical parameters that determine the strengths of the different forces and the relative masses of all known fundamental particles. There is no theoretical explanation for their actual values, but they nevertheless determine the properties of atoms, cells, stars and the whole Universe. They are commonly referred to as the fundamental constants of Nature, although most of the modern extensions of the Standard Model predict a variation of these constants at some level. For instance, in any theory involving more than four space-time dimensions, the constants we observe are merely four-dimensional shadows of the truly fundamental high dimensional constants. The four dimensional constants will then be seen to vary as the extra dimensions change slowly in size during their cosmological evolution. An attractive implication of quintessence models for the dark energy is that the rolling scalar field producing a negative pressure and therefore the acceleration of the universe may couple with other fields and be revealed by a change in the fundamental constants.

Earth-based laboratories have so far revealed no variation in their values. For example, the constancy of the fine structure constant stability is ensured to within a few parts per 10-17 over a ∼1 year period. Hence its status as truly “constants” is amply justified. Astronomy has a great potential in probing their variability at very large distances and in the early Universe. In fact, the transition frequencies of the narrow metal absorption lines observed in the spectra of distant quasars are sensitive to α and those of the raremolecular hydrogen clouds are sensitive to μ, the proton-to-electron mass ratio.

With the advent of 10-m class telescopes, observations of spectral lines in distant QSOs gave the first hints that the fine structure constant might change its value over time, being lower in the past by about 6 ppm. The addition of other 143 VLT-UVES absorbers (Figure 1) has revealed a 4-σ evidence for a dipole-like variation in α across the sky at the 10 ppm level. Several other constraints from higher-quality spectra of individual absorbers exist but none directly support or strongly conflict with the α dipole evidence and a possible systematic producing opposite values in the two hemispheres is not easy to identify.

Figure 1. All-sky spatial dipole with the combined VLT (squares) and Keck (circles) α measurements from Webb et al. (2012). Triangles are measures in common to the two telescopes. The blue dashed line shows the equatorial region of the dipole.

In order to probe μ, the H2 absorbers need to be at a redshift z > 2-2.5 to place the Lyman and Werner H2 transitions redward of the atmospheric cut-off. Only five systems have been studied with no current indication of variability at the level of ~10 ppm. At lower redshifts precise constraints on μ-variation are available from radio- and millimeter-wave spectra of cool clouds containing complex molecules like ammonia and methanol. These molecules are quite abundant in the Galactic dark clouds leading to a stringent limit of ~ 10-8. Other techniques involving radio spectra typically constrain combinations of constants by comparing different types of transitions (e.g. electronic, hyperfine, rotational etc.)

Extraordinary claims require extraordinary evidence and a confirmation of variability with high statistical significance is of crucial importance. Only a high -resolution spectrograph that combines a large collecting area with extreme wavelength precision can provide definitive clarification. A relative variation in α or μ of 1 ppm leads to velocity shifts of about 20 m s−1 between typical combinations of transitions. ESPRESSO is expected to provide an increase in the accuracy of the measurement of these two constants by at least 1order of magnitude compared to VLT/UVES or Keck/HIRES. More stringent bounds are also important and the ones provided already constrain the space of the parameters of various theoretical models that predict their variability.

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