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We present the results of a uniform search for additional planets around allstars with confirmed hot Jupiters observed by the Transiting Exoplanet SurveySatellite (TESS) in its Cycle 1 survey of the southern ecliptic hemisphere. Oursearch comprises 184 total planetary systems with confirmed hot Jupiters with$R_{p}$ > 8$R_\oplus$ and orbital period < 10 days. The Transit Least Squares(TLS) algorithm was utilized to search for periodic signals that may have beenmissed by other planet search pipelines. While we recovered 169 of theseconfirmed hot Jupiters, our search yielded no new statistically-validatedplanetary candidates in the parameter space searched (P < 14 days). A lack ofplanet candidates nearby hot Jupiters in the TESS data supports results fromprevious transit searches of each individual system, now down to thephotometric precision of TESS. This is consistent with expectations from a higheccentricity migration formation scenario, but additional formation indicatorsare needed for definitive confirmation. We injected transit signals into thelight curves of the hot Jupiter sample to probe the pipeline's sensitivity tothe target parameter space, finding a dependence proportional to$R_{p}^{2.32}P^{-0.88}$ for planets within 0.3$\leq$$R_{p}$$\leq$4 $R_\oplus$and 1$\leq$$P$$\leq$14 days. A statistical analysis accounting for thissensitivity provides a median and $90\%$ confidence interval of$7.3\substack{+15.2 \\ -7.3}\%$ for the rate of hot Jupiters with nearbycompanions in this target parameter space. This study demonstrates how TESSuniquely enables comprehensive searches for nearby planetary companions tonearly all the known hot Jupiters.

A Uniform Search for Nearby Planetary Companions to Hot Jupiters in TESS Data Reveals Hot Jupiters are Still Lonely