The Cauchy problem in hybrid metric-Palatini f(X)-gravity

Abstract

The well-formulation and the well-posedness of the Cauchy problem is discussed for {\it hybrid metric-Palatini gravity}, a recently proposed modified gravitational theory consisting of adding to the Einstein-Hilbert Lagrangian an $f(R)$ term constructed {\it à la} Palatini. The theory can be recast as a scalar-tensor one predicting the existence of a light long-range scalar field that evades the local Solar System tests and is able to modify galactic and cosmological dynamics, leading to the late-time cosmic acceleration. In this work, adopting generalized harmonic coordinates, we show that the initial value problem can always be {\it well-formulated} and, furthermore, can be {\it well-posed} depending on the adopted matter sources.

7 pages

References in corpus (7)

• Dynamics of dark energy
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Wormholes supported by hybrid metric-Palatini gravity
• Cosmology of hybrid metric-Palatini f(X)-gravity
• Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke
• The Cauchy problem for metric-affine f(R)-gravity in presence of perfect-fluid matter
• The Cauchy problem for metric-affine f(R)-gravity in presence of a Klein-Gordon scalar field

Cited by in corpus (20)

• Generalized curvature-matter couplings in modified gravity
• Hybrid metric-Palatini gravity
• Cosmological solutions in generalized hybrid metric-Palatini gravity
• A dynamical system analysis of hybrid metric-Palatini cosmologies
• Invariant solutions and Noether symmetries in Hybrid Gravity
• Beyond Einstein's General Relativity: Hybrid metric-Palatini gravity and curvature-matter couplings
• Hybrid metric-Palatini stars
• Born-Infeld-$f(R)$ gravity
• Spherically symmetric static vacuum solutions in hybrid metric-Palatini gravity
• Bianchi type I cosmological models in Eddington-inspired Born-Infeld gravity
• Thick brane structures in generalized hybrid metric-Palatini gravity
• Homogeneous Gödel-type solutions in hybrid metric-Palatini gravity
• Sudden singularities in generalized hybrid metric-Palatini cosmologies
• Junction conditions of Palatini $f\left(\mathcal{R},T\right)$ gravity
• Black Hole Perturbations and Quasinormal Modes in Hybrid Metric-Palatini Gravity
• Cosmic strings in generalized hybrid metric-Palatini gravity
• Hybrid metric-Palatini brane system
• On the Hyperbolicity and Stability of $3+1$ Formulations of Metric $f(R)$ Gravity
• Novel electrically charged wormhole, black hole and black bounce exact solutions in hybrid metric-Palatini gravity
• Extended Theories of Gravity in cosmological and astrophysical applications