Comparing these with the results of the recent studies for the two individual parameters [21, 27] we see only a mild changes in the best fit and confidence intervals for α , while the changes are somewhat larger for G . More importantly, a degeneracy is clearly present be- tween λ$_{G}$ and the fine structure constant. The underly- ing reason is easy to understand. A change in α shifts the recombination epoch, affecting the angular diameter distance at recombination and the peaks position in the CMB anisotropy angular spectra. A similar effect can be obtained by changing the value of λ$_{G}$ and the two pa- rameters are therefore degenerate. Both parameters are degenerate with the Hubble constant H 0 as we can see from Figures 2 and 3. From the above it follows that including the recent HST measurements of H 0 has an important effect: it breaks the α - H 0 and λ$_{G}$ - H 0 degeneracies and thereby provides a stronger bound on those parameters. This is clearly shown in the third row of Table 1. the behavior of the Q parameter, which in terms of our analysis pipeline is defined as Obviously, since the current data doesn’t show any ev- idence for variations in G or α it is not possible to rule out any of the models discussed before. The CMB data, however, does show a clear correlation between α and λ$_{G}$ that could be fitted with a linear relation. Considering the models that are inside the 95% confidence level we found constraints on the best-fit Q parameter as reported in Table II. As already mentioned in the introduction, from the perspective of mode-building it is interesting to consider The data therefore prefers a value of Q whose value is significantly larger than zero, and again we see that the HST prior has a very strong effect. Taken at face value, this result would therefore strongly disfavor the models we mentioned in the introduction as having Q negative for λ$_{G}$ ∼ 0 . 1 in absolute value. In other words, if there are any variations at or around the percent level, then the variations of the two parameters must have the same FIG. 3: 68% and 95% c.l. constraints on the λ G vs H 0 for different datasets. The contours regions come from CMB data (blue), CMB data and SN-Ia (red), and CMB+HST (green). FIG. 1: 68% and 95% c.l. constraints on the α/α 0 vs λ G for different datasets. The contours regions come from CMB data (blue), CMB data and SN-Ia (red), and CMB+HST (green). α α 0 − 1 = Q ( λ 2 $_{G}$− 1) . (5) G $_{/}$α 0 0.5 1 1.5 0.9 0.95 1 1.05 1.1 G H 0 0.5 1 1.5 40 60 80 100 / 0 H 0 0.95 1 1.05 40 60 80 100 FIG. 2: 68% and 95% c.l. constraints on the α/α 0 vs H 0 for different datasets. The contours regions come from CMB data (blue), CMB data and SN-Ia (red), and CMB+HST (green). TABLE I: Limits on α/α 0 and λ G from CMB data only (first row), from CMB+SN-Ia (second row), from CMB plus the HST prior on the Hubble constant, h = 0 . 748 ± 0 . 036 (third row), from CMB plus BBN (fourth row) and for simulated mock data for the Planck experiment. We report errors at 68% confidence level. Experiment α/α 0 68% c.l. λ G 68% c.l. All CMB 0 . 999 ± 0 . 017 1 . 04 ± 0 . 12 All CMB+SN-Ia 0 . 989 ± 0 . 012 1 . 04 ± 0 . 11 All CMB+HST 1 . 003 ± 0 . 008 1 . 13 ± 0 . 09 ALL CMB+BBN 0 . 985 ± 0 . 009 1 . 01 ± 0 . 01 Planck only 1 . 000 ± 0 . 015 1 . 02 ± 0 . 09 3