Does Dirac-Born-Infeld Modification Of Quadratic Theories Really Matter?

We study the consequences of further modification of $f(R,R_{\mu\nu} R^{\mu\nu}, R_{\mu\nu\sigma\rho} R^{\mu\nu\sigma\rho}) / f(R)$-theories by means of the Dirac-Born-Infeld deformation procedure, which amounts to the replacement of $f$ by $\lambda(\sqrt{1+2f/\lambda}-1)$ (the free parameter $\lambda$ fixes an additional energy scale). We pay special attention to the definition of masses of the linearized propagating degrees of freedom since these are important to judge about the stability of the linearization around vacuum background spaces. In this context we discuss the subtleties associated with expanding $f(R,R_{\mu\nu} R^{\mu\nu},R_{\mu\nu\sigma\rho} R^{\mu\nu\sigma\rho})$-Lagrangians around maximally symmetric spaces of constant curvature, as well as with equivalence of the linearized Lagrangian to a scalar-tensor theory. Investigation of the consequences of applying the Dirac-Born-Infeld strategy to further modify quadratic theories, on the stability of de Sitter vacuum, as well as its impact on the cosmological dynamics, is the main concern of this paper.