Modified gravity in Arnowitt-Deser-Misner formalism

TL;DR

This paper develops two modified gravity theories within the ADM formalism inspired by Horava-Lifshitz gravity, showing they can address cosmic acceleration and singularities while remaining consistent with solar system tests.

Contribution

It introduces f(R) and K-essence modified gravity models in ADM formalism, demonstrating their potential to explain cosmic acceleration and resolve singularities.

Findings

UV and IR modifications to Friedmann equations prevent singularities.

IR modification accounts for current cosmic acceleration.

Solutions include Schwarzschild and Schwarzschild-de Sitter metrics.

Abstract

Motivated by Horava-Lifshitz gravity theory, we propose and investigate two kinds of modified gravity theories, the f(R) kind and the K-essence kind, in the Arnowitt-Deser-Misner (ADM) formalism. The f(R) kind includes one ultraviolet (UV) term and one infrared (IR) term together with the Einstein-Hilbert action. We find that these two terms naturally present the ultraviolet and infrared modifications to the Friedmann equation. The UV and IR modifications can avoid the past Big-Bang singularity and the future Big-Rip singularity, respectively. Furthermore, the IR modification can naturally account for the current acceleration of the Universe. The Lagrangian of K-essence kind modified gravity is made up of the three dimensional Ricci scalar and an arbitrary function of the extrinsic curvature term. We find the cosmic acceleration can also be naturally interpreted without invoking any kind of dark energy. The static, spherically symmetry and vacuum solutions of both theories are Schwarzschild or Schwarzschild-de Sitter solution. Thus these modified gravity theories are viable for solar system tests.