We develop techniques of analyzing the unitarity of general Born-Infeld (BI)
gravity actions in D-dimensional spacetimes. Determinantal form of the action
allows us to find a compact expression quadratic in the metric fluctuations
around constant curvature backgrounds. This is highly nontrivial since for the
BI actions, in principle, infinitely many terms in the curvature expansion
should contribute to the quadratic action in the metric fluctuations around
constant curvature backgrounds, which would render the unitarity analysis
intractable. Moreover in even dimensions, unitarity of the theory depends only
on finite number of terms built from the powers of the curvature tensor. We
apply our techniques to some four-dimensional examples.Comment: 26 pages, typos corrected, version to appear in Phys. Rev.
