  We study the red-optical photometry of the ultra-hot Jupiter WASP-121 b as
observed by the Transiting Exoplanet Survey Satellite (TESS) and model its
atmosphere through a radiative transfer simulation. Given its short orbital
period of $\sim1.275$ days, inflated state and bright host star, WASP-121 b is
exceptionally favorable for detailed atmospheric characterization. Towards this
purpose, we use \texttt{allesfitter} to characterize its full red-optical phase
curve, including the planetary phase modulation and the secondary eclipse. We
measure the day and nightside brightness temperatures in the TESS passband as
$3012\substack{+40 \\ -42}$ K and $2022\substack{+254 \\ -602}$ K,
respectively, and do not find a statistically significant phase shift between
the brightest and substellar points. This is consistent with an inefficient
heat recirculation on the planet. We then perform an atmospheric retrieval
analysis to infer the dayside atmospheric properties of WASP-121 b such as its
bulk composition, albedo and heat recirculation. We confirm the temperature
inversion in the atmosphere and suggest H$^-$, TiO and VO as potential causes
of the inversion, absorbing heat at optical wavelengths at low pressures.
Future HST and JWST observations of WASP-121 b will benefit from its first full
phase curve measured by TESS.
