The Cauchy problem of f(R) gravity

Abstract

The initial value problem of metric and Palatini f(R)gravity is studied by using the dynamical equivalence between these theories and Brans-Dicke gravity. The Cauchy problem is well-formulated for metric f(R)gravity in the presence of matter and well-posed in vacuo. For Palatini f(R)gravity, instead, the Cauchy problem is not well-formulated.

16 latex pages, to appear in Class. Quantum Grav; typographical errors corrected, new references added

References in corpus (10)

• The Newtonian Limit of F(R) gravity
• Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity
• Stability of Cosmological Solution in f(R) Models of Gravity
• de Sitter space and the equivalence between f(R) and scalar-tensor gravity
• f(R) gravity theories in Palatini formalism: cosmological dynamics and observational constraints
• Newton law corrections and instabilities in $f(R)$ gravity with the effective cosmological constant epoch
• Ghost Constraints on Modified Gravity
• Can f(R) Modified Gravity Theories Mimic a LCDM Cosmology?
• How (Not) to Palatini
• Rippled Cosmological Dark Matter from Damped Oscillating Newton Constant

Cited by in corpus (6)

• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• The viability of theories with matter coupled to the Ricci scalar
• Hyperbolicity of scalar-tensor theories of gravity
• Palatini f(R) gravity as a fixed point
• Problems with Modified Theories of Gravity, as Alternatives to Dark Energy