Ab initio calculations
are employed to generate the rigid rotor (RR) potential energy surface
(PES) describing the interaction of the linear molecular cation HeHHe
+
, at its equilibrium geometry, with the neutral He atom. The
resulting interaction is employed to investigate the efficiency of
rotational state-changing collisions at the temperatures relevant
to the early universe conditions, where the latter molecule has been
postulated to exist, albeit not yet observed. The inelastic rate coefficients
are found to be fairly large and are compared with those found for
another important cation just recently observed in the interstellar
medium: the HeH
+
polar molecule. The possibility for this
cation to provide new options to energy dissipation routes under early
universe conditions after the recombination era is briefly discussed.