Limit on the Cosmological Variation of $m_p/m_e$ from the Inversion Spectrum of Ammonia

We obtain the limit on the space-time variation of the ratio of the proton mass to the electron mass, $\mu =m_p/m_e$, based on comparison of quasar absorption spectra of ${\mathrm{NH}}_3$ with CO, ${\mathrm{HCO}}^{+}$ and HCN rotational spectra. For the inversion transition in ${\mathrm{NH}}_3$ ($\lambda \approx 1.25{\mathrm{cm}}^{-1}$) the relative frequency shift is significantly enhanced: $\delta \omega /\omega =-4.46\delta \mu /\mu$. This enhancement allows one to increase sensitivity to the variation of $\mu$ using ${\mathrm{NH}}_3$ spectra for high redshift objects. We use published data on microwave spectra of the object $B0218+357$ to place the limit $\delta \mu /\mu =(0.6\pm 1.9)\times {10}^{-6}$ at redshift $z=0.6847$; this limit is several times better than the limits obtained by different methods and may be significantly improved. Assuming linear time dependence we obtain $\dot{\mu }/\mu =(-1\pm 3)\times {10}^{-16}{\mathrm{yr}}^{-1}$.