  Cs$_2$AgBiBr$_6$ is a representative halide double perovskite which exhibits
promising photovoltaic and light-emitting properties, making it a candidate for
next-generation solar cells and LED technologies. Here, we study various
possible excited states of this material to understand its absorption and
emission properties. We use Time-Dependent Density Functional Theory (TD-DFT)
coupled with non-empirical hybrid functionals, specifically PBE0($\alpha$) and
dielectric-dependent hybrids (DDH) to explore direct, indirect, and
self-trapped excitons in this material. Based on comparison with experiment, we
show that these methods can give excellent prediction of the absorption
spectrum and that the fundamental band gap has been underestimated in previous
computational studies. We connect the experimental photoluminescence signals at
1.9-2.0 eV to the emission from self-trapped excitons and electron polarons.
Finally, we reveal a complex landscape with energetically competing direct,
indirect, and self-trapped excitons in the material.
