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This is clearly not the case today. The fact that we observe the appropriate fine-tuning today gives us the opportunity to use it as a powerful constraint to test the entire framework and related theories.

As an extension of the Savedoff’s method, Joseph et al. [ 386 ] used the doublet ratios in a sample of 53 bright emission-line QSOs at z=3 to constrain the average value of the fine-structure constant and the relative abundance of metals in QSO absorbing clouds. Bautista et al. [ 172 ] made use of QSO absorption-line spectra to constrain the variation of the proton to electron mass ratio, where they take advantage of the sensitivity of the fine-structure constant to changes in this ratio.

i.e. it is proportional to the baryonic mass. The other term (2), which is directly proportional to the fine structure (see above), was estimated in [4, 9, 10, 389, 389] and gives the proportionality constant

To conclude, we have shown that one can explain the fine-tuning of the constants of Nature by considering the expected value of the constants on the anthropic bound and that the anthropic bound itself is a consequence of the multiverse scenario itself.

The fine-structure (E[1/2, νf,νs], h=1/2, νf=1/2, νs=1/2), which is the difference between the masses of the constituent (up to isotopes) and the rest of the universe, is a combination of two factors

however, even in this case, the fine-structure constant variation is not negligible, since one should deal with a relative variation instead of an absolute one. Further independent calibration data may resolve the issue. d8a7b2ff72

“Anomalies” also occur in the laboratory, and we now have constraints on possible variations of the fine-structure constant [ 4, 24, 25, 26 ] with two possible interpretations, which are not necessarily exclusive [ 43 ]. The deuterium limit and the lattice QCD constraints are reviewed in Particle Physics: Cosmological Phenomenology, and to these we add the laboratory constraints and the constraints from recent data from the Karl G. Jansky Very Large Array (VLA) radio telescope and from the South Pole Telescope [ 5, 6, 7 ].

As discussed in [10] and [89], if the cosmic expansion rate is directly proportional to the ratio H /GUT, the constants GUT /Fand F / Bmust vary inversely as the effective gravitational constant and the fine-structure constant, respectively (for more details see [7, 8, 9, 178, 179, 182, 484]). In particular if the energy density of the universe is due to a constant adiabatic speed of expansion of the order of unity, the effective coupling constant goes to zero, so that H/GUT might approach a constant. This situation would imply that during the cosmological evolution, the fundamental constants remained constant.

where z is the redshift, \u001Bpsilon is the constant small coupling/vacuum expectation value of the scalar field, and where an index d stands for the dimension of the spacetime in which the variation occurs. The result is, obviously, far from being tested. The result obtained in [ 50, 523 ] has a double loophole: first, the data does not reproduce the second index d; second, the dependence on the scale factor z is not small compared to the experimental error bar. Also, the result is contradictory with the other analyses which suggest a different sign for the exponent of the exponential. This being said, the claim that the fine structure constant varies with the scale factor must be regarded as controversial, since it is a violation of the principle of general covariance. Therefore, it relies on a new fundamental constant. In the same way, the spectrum of light has been measured from the stars and has been used to probe the global structure of the universe. Therefore, a violation of the constancy of the fine structure constant is a hint of new physics at the very beginning of the universe, namely, a theory with a new dimension of space. According to the authors of [ 50, 523 ], the dilaton, a scalar field for higher-dimensional theories, generates such a variation. This is, of course, an important result which, however, must be investigated by additional work. It is thus worth mentioning that the general-relativistic theory of gravity predicts the existence of a dilaton, whose vacuum expectation value determines the strength of the gravitational constant [ 50, 523 ].