  We study a novel class of higher curvature gravity models in $n$ spacetime
dimensions which we call Ricci polynomial gravity. The action is consisted
purely of a polynomial in Ricci curvature of order $N$. In the absence of the
second order terms in the action, the models are ghost free around the
Minkowski vacuum. By appropriately choosing the coupling coefficients in front
of each terms in the action, it is shown that the models can have multiple
vacua with different effective cosmological constants, and can be made free of
ghost and scalar degrees of freedom around at least one of the maximally
symmetric vacua for any $n>2$ and any $N\geq 4$. We also discuss some of the
physical implications of the existence of multiple vacua in the contexts of
black hole physics and cosmology.
