  We advance a class of unitary higher derivative theories of gravity that
realize an ultraviolet completion of Einstein general relativity in any
dimension. This range of theories is marked by an entire function, which averts
extra degrees of freedom (including poltergeists) and improves the high energy
behavior of the loop amplitudes. It is proved that only one-loop divergences
survive and the theory can be made super-renormalizable regardless of the
spacetime dimension. Moreover, using the Pauli-Villars regularization procedure
introduced by Diaz-Troost-van Nieuwenhuizen-van Proeyen (DTPN) and applied to
Einstein's gravity by Anselmi, we are able to remove the divergences also at
one-loop, making the theory completely finite in any dimension as expected by
Anselmi and Asorey-Lopez-Shapiro.
