  The recently suggested generalized unimodular gravity theory, which was
originally put forward as a model of dark energy, can serve as a model of
cosmological inflation driven by the effective perfect fluid -- the dark purely
gravitational sector of the theory. Its excitations are scalar gravitons which
can generate, in the domain free from ghost and gradient instabilities, the red
tilted primordial power spectrum of CMB perturbations matching with
observations. The reconstruction of the parametric dependence of the action of
the theory in the early inflationary Universe is qualitatively sketched from
the cosmological data. The alternative possibilities of generating the
cosmological acceleration or quantum transition to the general relativistic
phase of the theory are also briefly discussed.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory