ExoMol line lists -- XXXIX. Ro-vibrational molecular line list for CO$_2$

A new hot line list for the main isotopologue of CO$_2$ is presented. The line list consists of almost 2.5 billion transitions between 3.5 million rotation-vibration states of CO$_2$ in its ground electronic state, covering the wavenumber range 0-20000 cm$^{-1}$ ($\lambda >0.5$ $\mu$m) with the upper and lower energy thresholds of 36 000 cm$^{-1}$ and 16 000 cm$^{-1}$, respectively. The ro-vibrational energies and wavefunctions are computed variationally using the Ames-2 accurate empirical potential energy surface. The ro-vibrational transition probabilities in the form of Einstein coefficients are computed using an accurate ab initio dipole moment surface using variational program TROVE. A new implementation of TROVE which uses an exact nuclear-motion kinetic energy operator is employed. Comparisons with the existing hot line lists are presented. The line list should be useful for atmospheric retrievals of exoplanets and cool stars. The UCL-4000 line list is available from the CDS and ExoMol databases.