Breakdown of the initial value formulation of scalar-tensor gravity and its physical meaning

Abstract

We revisit singularities of two distinct kinds in the Cauchy problem of general scalar-tensor theories of gravity (previously discussed in the literature), and of metric and Palatini f(R) gravity, in both their Jordan and Einstein frame representations. Examples and toy models are used to shed light onto the problem and it is shown that, contrary to common lore, the two conformal frames are equivalent with respect to the initial value problem.

14 pages, LaTex, to appear in Phys. Rev. D

References in corpus (69)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution
• Discovery of a Supernova Explosion at Half the Age of the Universe and its Cosmological Implications
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Coupled Quintessence
• New Hubble Space Telescope Discoveries of Type Ia Supernovae at z > 1: Narrowing Constraints on the Early Behavior of Dark Energy
• Cosmological Results from High-z Supernovae
• New Constraints on ${\Omega }_M$, ${\Omega }_{\Lambda }$, and w from an Independent Set of Eleven High-Redshift Supernovae Observed with HST
• Late-time cosmology in (phantom) scalar-tensor theory: dark energy and the cosmic speed-up
• Unifying phantom inflation with late-time acceleration: scalar phantom-non-phantom transition model and generalized holographic dark energy
• Reconstruction of a scalar-tensor theory of gravity in an accelerating universe
• String Solitons
• 1/R gravity and Scalar-Tensor Gravity
• The final state and thermodynamics of dark energy universe
• Cosmological scaling solutions of non-minimally coupled scalar fields
• 23 High Redshift Supernovae from the IfA Deep Survey: Doubling the SN Sample at z>0.7
• Scalar-tensor gravity in an accelerating universe
• Extended Quintessence
• Extended Gravity Theories and the Einstein-Hilbert Action
• f(R) Gravity and scalar-tensor theory
• 1/R Curvature Corrections as the Source of the Cosmological Acceleration
• Quantum escape of sudden future singularity
• Nonminimal coupling and quintessence
• Quintessence, the Gravitational Constant, and Gravity
• The conformal frame freedom in theories of gravitation
• Metric-affine f(R) theories of gravity
• Inflation and quintessence with nonminimal coupling
• Dark Energy: the equation of state description versus scalar-tensor or modified gravity
• Reconstructing the universe history, from inflation to acceleration, with phantom and canonical scalar fields
• The (pseudo)issue of the conformal frame revisited
• Cosmological observations in scalar-tensor quintessence
• Quintessence, super-quintessence and observable quantities in Brans-Dicke and non-minimally coupled theories
• Scalar fields, energy conditions, and traversable wormholes
• Superquintessence
• Born-Infeld Quantum Condensate as Dark Energy in the Universe
• A Preliminary Indication of Evolution of Type Ia Supernovae from their Risetimes
• Einstein and Jordan frames reconciled: a frame-invariant approach to scalar-tensor cosmology
• Quintessence and Gravitational Waves
• Tracking Extended Quintessence
• The Cauchy problem of scalar-tensor theories of gravity
• A no-go theorem for polytropic spheres in Palatini f(R) gravity
• Perturbations in a coupled scalar field cosmology
• A Quintessence Scalar Field in Brans-Dicke Theory
• Self interacting Brans Dicke cosmology and Quintessence
• Superinflation, quintessence, and nonsingular cosmologies
• A Two-Field Quintessence Model
• Curvature singularities, tidal forces and the viability of Palatini f(R) gravity
• Dark energy and the Boomerang data
• The Cauchy problem of f(R) gravity
• de Sitter attractors in generalized gravity
• Tracker fields from nonminimally coupled theory
• Phase space geometry in scalar-tensor cosmology
• Big smash of the universe
• Extended quintessence and the primordial helium abundance
• Extended Quintessence and its Late-time Domination
• Coupled oscillators as models of phantom and scalar field cosmologies
• Approaching Lambda without fine-tuning
• Quintessence, scalar-tensor theories and non-Newtonian gravity
• On the singularities of gravity in the presence of non-minimally coupled scalar fields
• Extended quintessence, inflation, and stable de Sitter spaces
• Energy conditions and classical scalar fields
• Non-chaotic dynamics in general-relativistic and scalar-tensor cosmology
• Hyperextended Scalar-Tensor Gravity
• Singularities in scalar-tensor gravity
• Local transformations of units in Scalar-Tensor Cosmology
• Sub-horizon Perturbation Behavior in Extended Quintessence
• Conformal quantum effects and the anisotropic singularities of scalar-tensor theories of gravity

Cited by in corpus (12)

• Modified gravity with R-matter couplings and (non-)geodesic motion
• Axially symmetric solutions in f(R)-gravity
• Charged spherically symmetric black holes in $f(R)$ gravity and their stability analysis
• A new framework for studying spherically symmetric static solutions in f(R) gravity
• The Jebsen-Birkhoff theorem in alternative gravity
• A general solution in the Newtonian limit of f(R)- gravity
• Asymptotically FRW black holes
• Scalar-tensor cosmologies: fixed points of the Jordan frame scalar field
• Scalar field mass in generalized gravity
• Geodesic Congruences in the Palatini f(R) Theory
• Trapped surfaces and nature of singularities in Lyra's geometry
• Superradiant (In)stability, Greybody Radiation, and Quasinormal Modes of Rotating Black Holes in non-linear Maxwell f (R) Gravity