CMB constraints on the simultaneous variation of the fine structure constant and the electron mass

We study constraints on time variation of the fine structure constant $\alpha$ from cosmic microwave background (CMB) taking into account simultaneous change in $\alpha$ and the electron mass $m_e$ which might be implied in unification theories. We obtain the constraints $-0.097<\Delta \alpha /\alpha <0.034$ at 95% C.L. using WMAP data only, and $-0.042<\Delta \alpha /\alpha <0.026$ combining with the constraint on the Hubble parameter by the HST Hubble Key Project. These are improved by 15% compared with constraints assuming only $\alpha$ varies. We discuss other relations between variations in $\alpha$ and $m_e$ but we do not find evidence for varying $\alpha$.

Figure 1

The ionization fraction $x_e$ as a function of redshift $z$ for no change of $\alpha$ (solid curve), an increase of $\alpha$ by 5% (dashed curve), a decrease of $\alpha$ by 5% (dotted curve).

Figure 2

The ionization fraction $x_e$ as a function of redshift $z$ for no change of $m_e$ (solid curve), an increase of $m_e$ by 5% (dashed curve), a decrease of $m_e$ by 5% (dotted curve).

Figure 3

The visibility function as a function of conformal time for no change of $\alpha$ (solid curve), an increase of $\alpha$ by 5% (dashed curve), a decrease of $\alpha$ by 5% (dotted curve).

Figure 4

The visibility function as a function of conformal time for no change of $m_e$ (solid curve), an increase of $m_e$ by 5% (dashed curve), a decrease of $m_e$ by 5% (dotted curve).

Figure 5

The spectrum of CMB fluctuations for no change of $\alpha$ (solid curve), an increase of $\alpha$ by 5% (dashed curve), a decrease of $\alpha$ by 5% (dotted curve).

Figure 6

The spectrum of CMB fluctuations for no change of $m_e$ (solid curve), an increase of $m_e$ by 5% (dashed curve), a decrease of $m_e$ by 5% (dotted curve).

Figure 7

${\chi }^2$ function for variation in $\alpha$ only (solid curves) and $\alpha$ and $m_e$ simultaneously with the relation of Eq. (25) (dashed curves). The HST prior is imposed for the thinner curves.

Figure 8

${\chi }^2$ function for variation in $\alpha$ and $m_e$ with several values of $p$ defined in Eq. (26). The curves are for, from outside to inside, $p=0,1/2,2$ and 4. The HST prior is imposed.