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 $m_e /m_{e0}=0.964 \pm 0.025$.
