Constraints on variation in $\alpha$ and $m_e$ from WMAP 7-year data

We update the constraints on the time variation of the fine structure constant $\alpha$ and the electron mass $m_e$, using the latest CMB data, including the 7-yr release of WMAP. We made statistical analyses of the variation of each one of the constants and of their joint variation, together with the basic set of cosmological parameters. We used a modified version of CAMB and COSMOMC to account for these possible variations. We present bounds on the variation of the constants for different data sets, and show how results depend on them. When using the latest CMB data plus the power spectrum from Sloan Digital Sky Survey LRG, we find that $\alpha / \alpha_0=0.986 \pm 0.007$ at 1-$\sigma$ level, when the 6 basic cosmological parameters were fitted, and only variation in $\alpha$ was allowed. The constraints in the case of variation in both constants are $\alpha / \alpha_0= 0.986 \pm 0.009$ and $m_e / m_{e0} = 0.999 \pm 0.035$. In the case of only variation in $m_e$, the bound is $m_e /m_{e0}=0.964 \pm 0.025$.