  We study inflationary solution in an extension of mimetic gravity with the
higher derivative interactions coupled to gravity. Because of the higher
derivative interactions, the setup is free from the ghost and gradient
instabilities while it hosts a number of novel properties. The dispersion
relation of scalar perturbations develops quartic momentum correction similar
to the setup of ghost inflation. Furthermore, the tilt of tensor perturbations
can take either signs with a modified consistency relation between the tilt and
the amplitude of tensor perturbations. Despite the presence of higher
derivative interactions coupled to gravity, the tensor perturbations propagate
with a speed equal to the speed of light as required by the LIGO observations.
Furthermore, the higher derivative interactions induce non-trivial interactions
in cubic Hamiltonian, generating non-Gaussianities in various shapes such as
the equilateral, orthogonal, and squeezed configurations with observable
amplitudes.

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