Table 1
Summary of the 68% confidence limit (CL) bounds on the variation of fundamental constants obtained from previous analyses of cosmological data and more particularly of CMB data.
| Constraint | Data | Other parameters | Reference |
| (α × 102) | |||
|
|
|||
| [−9,2 ] | COBE-BOOMERanG-DASI + BBN | BBN with α only | (Avelino et al. 2001) |
| (Ωc,Ωb,h,ns) | |||
| [−1.4,2 ] | COBE-BOOMERanG-MAXIMA | (Ωc,Ωb,h,ns) | (Landau et al. 2001) |
| [−5,2 ] | WMAP-1 | (Ωch2,Ωbh2,ΩΛh2,τ,ns,dns/ d lnk) | (Rocha et al. 2004) |
| [−6,1 ] | WMAP-1 | Same as above + dns/ d lnk = 0 | (Rocha et al. 2004) |
| [−9.7,3.4 ] | WMAP-1 | (Ωc,Ωb,h,ns,τ,me) | (Ichikawa et al. 2006) |
| [−4.2,2.6 ] | WMAP-1 + HST | (Ωc,Ωb,h,ns,τ,me) | (Ichikawa et al. 2006) |
| [−3.9,1.0 ] | WMAP-3 (TT, TE, EE) + HST | (Ωc,Ωb,h,ns,zre,As) | (Stefanecsu 2007) |
| [−1.2,1.8 ] | WMAP-5 + ACBAR + CBI + 2df | (Ωch2,Ωbh2,Θ∗,τ,ns,As,me) | (Scoccola et al. 2008) |
| [−1.9,1.7 ] | WMAP-5 + ACBAR + CBI + 2df | (Ωch2,Ωbh2,Θ∗,τ,ns,As,me) | (Scoccola et al. 2009) |
| [−5.0,4.2 ] | WMAP-5 + HST | (Ωch2,Ωbh2,h,τ,ns,As) | (Nakashima et al. 2008) |
| [−4.3,3.8 ] | WMAP-5 + ACBAR + QUAD + BICEP | (Ωch2,Ωbh2,h,τ,ns) | (Menegoni et al. 2009) |
| [−1.3,1.5 ] | WMAP-5 + ACBAR + QUAD + BICEP + HST | (Ωch2,Ωbh2,h,τ,ns) | (Menegoni et al. 2009) |
| [−0.83,0.18 ] | WMAP-5 (TT, TE, EE) | (Ωch2,Ωbh2,h,τ,ns,As,me,μ) | (Nakashima et al. 2010) |
| [−2.5,−0.3 ] | WMAP-7 + H0 + SDSS | (Ωch2,Ωbh2,Θ∗,τ,ns,As,me) | (Landau & Scóccola 2010) |
Notes. All assume ΩK = 0, i.e., no spatial curvature. Here Ωb, Ωc, and ΩΛ refer to the density parameters for the baryons, cold dark matter, and cosmological constant, respectively. In addition h is the reduced Hubble constant, τ the reionization optical depth, Θ∗ the angular size of the sound horizon at last scattering, and the spectrum of the initial curvature perturbation is characterized by an amplitude As, a spectral index ns and potentially a running, dns/ dlnk. For comparison, our new analysis, based on the Planck data, uses (Ωch2,Ωbh2,H0,τ,ns,As,α,me).
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