  In this Letter, we consider original Nash theory of gravity. In terms of the
scalar fields representation, Nash gravity is equivalent to the action of
bi-scalar tensor gravity with four derivative terms of metric tensor. We then
quantify the ghost in the theory. In order to study the gravitational wave
modes of the theory, we perform a small perturbation over a fixed Minkowski
background. We discover the standard wave equation and obtain the solutions as
those of the standard general relativity. In order to satisfy the GR in the
weak field limit, we further modify the original Nash theory by adding the
Einstein-Hibert term called modified Nash gravity. In this theory, we once
study the gravitational wave modes. We derive equations of motion and examine
the solutions. We discover the two-mode solutions: the massless graviton and
the massive one. Using a uniform prior probability on the graviton mass, we can
constrain mass parameter.
