We report on an analysis of the Extended Chandra Deep Field South ( E-CDFS ) region using archival data from the Very Large Array , with the goal of studying radio variability and transients at the sub-mJy level .
The 49 epochs of E-CDFS observations at 1.4 GHz sample timescales from one day to 3 months .
We find that only a fraction ( 1 % ) of unresolved radio sources above 40 \mu Jy are variable at the 4 \sigma level .
There is no evidence that the fractional variability changes along with the known transition of radio source populations below one milliJansky .
Optical identifications of the sources show that the variable radio emission is associated with the central regions of an active galactic nucleus or a star-forming galaxy .
After a detailed comparison of the efficacy of various source-finding algorithms , we use the best to carry out a transient search .
No transients were found .
This implies that the areal density of transients with peak flux density greater than 0.21 mJy is less than 0.37 deg ^ { -2 } ( at a confidence level of 95 % ) .
This result is approximately an order of magnitude below the transient rate measured at 5 GHz by Bower et al . ( 2007 ) but it is consistent with more recent upper limits from Frail et al . ( 2012 ) .
Our findings suggest that the radio sky at 1.4 GHz is relatively quiet .
For multi-wavelength transient searches , such as the electromagnetic counterparts to gravitational waves , this frequency may be optimal for reducing the high background of false positives .