  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.
