uGMRT observations of a Fast and Blue Optical Transient -- AT 2018cow

We present low-frequency radio observations of a fast-rising blue optical transient (FBOT), AT\,2018cow, with the upgraded Giant Metrewave Radio Telescope (uGMRT). Our observations span $t =$ 11 $-$ 570 days post-explosion and a frequency range of 250 $-$ 1450 MHz. The uGMRT light curves are best modeled as synchrotron emission from an inhomogeneous radio-emitting region expanding into an ionized medium. However, due to the lack of information on the source covering factor, which is a measure of the degree of inhomogeneity, we derive various parameters assuming the source covering factor to be unity. These parameters, hence, indicate limits on the actual values in an inhomogeneous model. We derive the lower limit of the shock radius to be $R \sim$ (6.1$-$14.4) $\times$ 10$^{16}$ cm at $t =$ 138$-$257 days post-explosion. We find that the fast-moving ejecta from the explosion are moving with velocity $v$ $>$ 0.2c up to $t =$ 257 days post-explosion. The upper limits of the mass-loss rate of the progenitor are $\dot{M}$ $\sim$ (4.1$-$1.7) $\times$ 10$^{-6}$ $M_{\odot}$\,yr$^{-1}$ at (19.3$-$45.7) years before the explosion for a wind velocity $v_{\rm w}$ = 1000 km\,s$^{-1}$. These $\dot{M}$ values are $\sim$ 100 times smaller than the previously reported mass-loss rate at 2.2 years before the explosion, indicating an enhanced phase of the mass-loss event close to the end-of-life of the progenitor. Our results are in line with the speculation of the presence of a dense circumstellar shell in the vicinity of AT\,2018cow from previous radio, ultra-violet, and optical observations.