Phantom menace in Palatini f(R,ϕ) theories: Ghost instabilities in the quadratic curvature limit

Abstract

We investigate general f(R,ϕ) theories in the Palatini formalism with the aim of describing both inflation and late-time cosmic acceleration within a unified framework. Imposing weak-gravity consistency, we show that a tractable Einstein-frame description arises for a R + R2 curvature sector, leading to an effective k-essence theory. We perform a dynamical systems analysis of the post-inflationary evolution and identify a class of critical points associated with accelerated expansion. To close the autonomous dynamical system governing post-inflationary evolution, we employ a late-time adiabatic approximation by imposing that parameters related to scalar potentials remain constant. While this restricts the trajectory as well as observational analysis to a specific class of scalar potentials and non-minimal couplings, we identify a continuous set of non-hyperbolic critical points associated with accelerated expansion. The late-time behavior is, therefore, found to be sensitive to initial conditions. Using late-time observational datasets, including DESI BAO, Cosmic Chronometers, and Type Ia supernovae, we constrain the model and find that while a wide range of trajectories can reproduce the observed expansion history, most suffer from ghost instabilities due to the non-canonical kinetic structure. The only physically viable solution corresponds to a potential-dominated de Sitter phase, which is not dynamically selected as a preferred attractor. These results indicate that perturbative stability significantly restricts Palatini f(R,ϕ) models, challenging their ability to provide a unified cosmological description.