Modified Gravity Models Admitting Second Order Equations of Motion

Abstract

The aim of this paper is to find higher order geometrical corrections to the Einstein-Hilbert action that can lead to only second order equations of motion. The metric formalism is used, and static spherically symmetric and Friedmann-Lemaître space-times are considered, in four dimensions. The FKWC-basis are introduced in order to consider all the possible invariant scalars, and both polynomial and non-polynomial gravities are investigated.

16 pages, minor modifications, published version

References in corpus (8)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Classification of Six Derivative Lagrangians of Gravity and Static Spherically Symmetric Solutions
• Weyl gravity as general relativity
• Bianchi I Model: An Alternative Way To Model The Presentday Universe
• Bianchi I meets the Hubble diagram
• Spherically symmetric solutions of Einstein + non-polynomial gravities
• Black hole and de Sitter solutions in a covariant renormalizable field theory of gravity
• FKWC-bases and geometrical identities for classical and quantum field theories in curved spacetime

Cited by in corpus (4)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Non-polynomial Lagrangian approach to Regular Black Holes
• Regular black holes from pure gravity in four dimensions
• All $2D$ generalised dilaton theories from $d\ge 4$ gravities