Dark Energy Dominance and Cosmic Acceleration in First Order Formalism

TL;DR

This paper investigates dark energy and cosmic acceleration within a Palatini (first-order) formulation of non-linear gravity coupled to a scalar field. By adopting a Lagrangian of the form $L = \sqrt{g}(F(R)+f(R)L_d)+\kappa L_{mat}$ and treating the metric and connection as independent, the authors derive a bi-metric, second-order framework that modifies the FRW dynamics and yields effective quintessence or phantom behavior without introducing negative kinetic energies. They solve several exactly solvable cases, notably $F(R)=R$ with $f(R)=\alpha R^n$ and generalizations $F(R)=R$ plus $\mu G(R)$, showing acceleration occurs for certain parameter ranges and highlighting Big Bang/Big Rip singularities in different regimes. The work also demonstrates that a dynamical mechanism to address the cosmological constant problem, previously developed in metric theories, remains viable in the Palatini approach, with stable radiative corrections and consistent low-energy behavior. Overall, the Palatini formulation provides tractable second-order dynamics that reproduce key late-time cosmological phenomena while preserving compatibility with solar-system tests, and it opens avenues for further quantum and spinor-gravity investigations.

Abstract

The current accelerated universe could be produced by modified gravitational dynamics as it can be seen in particular in its Palatini formulation. We analyze here a specific non-linear gravity-scalar system in the first order Palatini formalism which leads to a FRW cosmology different from the purely metric one. It is shown that the emerging FRW cosmology may lead either to an effective quintessence phase (cosmic speed-up) or to an effective phantom phase. Moreover, the already known gravity assisted dark energy dominance occurs also in the first order formalism. Finally, it is shown that a dynamical theory able to resolve the cosmological constant problem exists also in this formalism, in close parallel with the standard metric formulation.