Ricci polynomial gravity

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.