We obtain constraints on the variation of the fundamental constants from the full shape of the redshift-space correlation function of a sample of luminous galaxies drawn from the Data Release 9 of the Baryonic Oscillations Spectroscopic Survey .
We combine this information with additional data from recent cosmic microwave background , baryon acoustic oscillations and H _ { 0 } measurements .
We focus on possible variations of the fine structure constant \alpha and the electron mass m _ { e } in the early universe , and study the degeneracies between these constants and other cosmological parameters , such as the dark energy equation of state parameter w _ { DE } , the massive neutrinos fraction f _ { \nu } , the effective number of relativistic species N _ { eff } , and the primordial helium abundance Y _ { He } .
In the case when only one of the fundamental constants is varied , our final bounds are \alpha / \alpha _ { 0 } = 0.9957 _ { -0.0042 } ^ { +0.0041 } and m _ { e } / ( m _ { e } ) _ { 0 } = 1.006 _ { -0.013 } ^ { +0.014 } .
For the joint variation of both fundamental constants , our results are \alpha / \alpha _ { 0 } = 0.9901 _ { -0.0054 } ^ { +0.0055 } and m _ { e } / ( m _ { e } ) _ { 0 } = 1.028 \pm 0.019 .
The variations of \alpha and m _ { e } from their present values affects the bounds on other cosmological parameters .
Although when m _ { e } is allowed to vary our constraints on w _ { DE } are consistent with a cosmological constant , when \alpha is treated as a free parameter we find w _ { DE } = -1.20 \pm 0.13 ; more than 1 \sigma away from its standard value .
When f _ { \nu } and \alpha are allowed to vary simultaneously , we find f _ { \nu } < 0.043 ( 95 % CL ) , implying a limit of \sum m _ { \nu } < 0.46 { eV } ( 95 % CL ) , while for m _ { e } variation , we obtain f _ { \nu } < 0.086 ( 95 % CL ) , which implies \sum m _ { \nu } < 1.1 { eV } ( 95 % CL ) .
When N _ { eff } or Y _ { He } are considered as free parameters , their simultaneous variation with \alpha provides constraints close to their standard values ( when the H _ { 0 } prior is not included in the analysis ) , while when m _ { e } is allowed to vary , their preferred values are significantly higher .
In all cases , our results are consistent with no variations of \alpha or m _ { e } at the 1 or 2 \sigma level .