  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 uJy 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.
