We present continued radio follow-up observations of PTF11qcj, a highly energetic broad-lined Type Ic supernova (SN), with a radio peak luminosity comparable to that of the $gamma$-ray burst (GRB) associated SN 1998bw. The latest observations, carried out with the Karl G. Jansky Very Large Array (VLA), extend up to $sim$5 years after the PTF11qcj optical discovery. The radio light curve shows a double-peak profile, possibly associated with density variations in the circumstellar medium (CSM), or with the presence of an off-axis GRB jet. Optical spectra of PTF11qcj taken during both peaks of the radio light curve do not show the broad H$alpha$ features typically expected from H-rich circumstellar interaction. Modeling of the second radio peak within the CSM interaction scenario requires a flatter density profile and an enhanced progenitor mass-loss rate compared to those required to model the first peak. Although our radio data alone cannot rule out the alternative scenario of an off-axis GRB powering the second radio peak, the implied off-axis GRB parameters are unusual compared to typical values found for cosmological long GRBs. Deep X-ray observations carried out around the time of the second radio peak could have helped distinguish between the density variation and off-axis GRB scenarios. Future VLBA measurements of the PTF11qcj radio ejecta may unambiguously rule out the off-axis GRB jet scenario.
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