2 G ⇒ λ 2 $_{G}$G (2) Δ α α = Q Δ G G (1) Y$_{p}$ = 0 . 250 ± 0 . 003 (3) D/H = (2 . 87 +0 . 22 $_{−}$0 . $_{21}$) · 10 $_{−}$5 (4) In Table I we report the constraints on the α/α 0 and the λ$_{G}$ parameters obtained from the COSMOMC anal- ysis, using the the different combinations of the datasets described in the previous section, and in Figure 1 we show the 68% and 95% c.l. constraints on the α/α 0 vs λ$_{G}$ for the different datasets. We allow for a possible variation in the fine structure constant and in the Newton’s constant during recombi- nation using the method described in [13] and [26], mod- ifying the publicly available RECFAST ([29]) routine in the CAMB ([30]) CMB code. As in [26] we consider vari- ations in the Newton’s constant G by introducing a new dimensionless parameter λ$_{G}$ such that Constraints on λ$_{G}$ and α are also computed using stan- dard BBN theoretical predictions as provided by the nu- merical code described in [40], which includes a full up- dating of all rates entering the nuclear chain based on the most recent experimental results on nuclear cross sections. The BBN predictions are compared with the experimental determinations of the $^{4}$He mass fraction Y$_{p}$ and D/H abundance ratio, as discussed in [41] In the rest of the paper we briefly sketch out analysis pipeline in Sec. II and present our results in Sec. III. Finally we will discuss the implications of our results and present some conclusions. We emphasize that the key assumption of the present analysis is that the particle masses are kept constant, and there are no changes to the strong sector. A more general analysis, without this assumption, will be presented elsewhere. In what follows, we also combine the CMB data with the recent UNION catalog of supernovae type Ia lumi- nosity distances and with the improved constraint on the Hubble constant of h = 0 . 747 ± 0 . 036 at 68% c.l.. from the recent analysis of [39]. with Q a free parameter that can be positive or negative, but not much larger than unity in absolute value (we will conservatively assume that − 10 < Q < 10). As an illus- tration of the range of values allowed in some represen- tative models, Kaluza-Klein-type theories typically have 1 < Q ≤ 3, Einstein-Yang-Mills has Q = 1, and Randall- Sundrum type models have very small positive Q s (say Q ∼ 0 . 01). These examples are discussed in more detail in [2, 28]—note that all of them have Q > 0. However, one can equally easily find models with Q < 0: for exam- ple string theory dilaton-type models have Q ∼ − 1 [10], while the BSBM-Brans-Dicke model has Q = − 1 exactly [11]. Our basic data set is the five–year WMAP data [32, 33] (temperature and polarization) with the routine for com- puting the likelihood supplied by the WMAP team. In addition to the WMAP data we also consider the fol- lowing CMB datasets: ACBAR ([34]), QUAD ([35]) and BICEP ([36]), as well as the older datasets from BOOMERanG ([37]) and CBI ([38]). For all these ex- periments we marginalize over a possible contamina- tion from Sunyaev-Zeldovich component, rescaling the WMAP template at the corresponding experimental fre- quencies. The interesting point is that the CMB is an observ- able potentially sensitive to variations in both fundamen- tal constants. It is therefore timely to perform a com- bined analysis of CMB data considering simultaneous variations in α and G in order to investigate the possible correlations and deviations from the standard values. Specifically, we will consider that the variations of α and G are related by We sample the following ten-dimensional set of cosmo- logical parameters, adopting flat priors on each of them: the baryon and cold dark matter densities ω b and ω c , the Hubble constant H 0 , the scalar spectral index n$_{s}$ , the overall normalization of the spectrum A$_{s}$ at k = 0 . 05 Mpc $^{$_{−}$1}$, the optical depth to reionization, τ and, finally, the variations in the fine structure constant α/α 0 and in the Newton’s constant λ$_{G}$ . Furthermore, we consider purely adiabatic initial conditions and we impose spatial flatness. The analysis method we adopt is based on the publicly available Markov Chain Monte Carlo package cosmomc [31] with a convergence diagnostics done through the Gel- man and Rubin statistics. while we constrain variations in the fine structure con- stant by considering the dimensionless parameter α/α 0 where α 0 is the fine structure constant today. gravity. Indeed, in the past two decades our knowledge of its value didn’t substantially improve from the precision of 0 . 05% reached in 1942 (see [22]). Recent laboratory measurements (see e.g. [23]) point towards an uncer- tainty at the level of ∼ 0 . 4%, while other works claim an improved precisions below 0 . 01% ([24]). Analysis of the secular variation of the period of nonradial pulsations of the white dwarf G117-B15A ([25]) has produced comple- mentary constraints at ∼ 0 . 1% level. On the other hand, as shown in [26] a variation in the gravitational constant could also affect the CMB anisotropy spectra, with current bounds of the order of ∼ 10% (se e.g. [27]) and constraints at level of ∼ 1% achievable with future CMB experiments as Planck. III. RESULTS II. ANALYSIS METHOD