Necessary and sufficient conditions for big bangs, bounces, crunches, rips, sudden singularities, and extremality events

Abstract

The physically relevant singularities occurring in FRW cosmologies had traditionally been thought to be limited to the "big bang", and possibly a "big crunch". However, over the last few years, the zoo of cosmological singularities considered in the literature has become considerably more extensive, with "big rips" and "sudden singularities" added to the mix, as well as renewed interest in non-singular cosmological events such as "bounces" and "turnarounds". In this article we present a complete catalogue of such cosmological milestones, both at the kinematical and dynamical level. First, using generalized power series, purely kinematical definitions of these cosmological events are provided in terms of the behaviour of the scale factor a(t). The notion of a "scale-factor singularity'" is defined, and its relation to curvature singularities (polynomial and differential) is explored. Second, dynamical information is extracted by using the Friedmann equations (without assuming even the existence of any equation of state) to place constraints on whether or not the classical energy conditions are satisfied at the cosmological milestones. We use these considerations to derive necessary and sufficient conditions for the existence of cosmological milestones such as bangs, bounces, crunches, rips, sudden singularities, and extremality events. Since the classification is extremely general, the corresponding results are to a high degree model-independent: In particular, we provide a complete characterization of the class of bangs, crunches, and sudden singularities for which the dominant energy condition is satisfied.

arXiv comment20 pages, uses iopart.cls; several references added

References in corpus (37)

• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• Phantom Energy and Cosmic Doomsday
• Properties of singularities in (phantom) dark energy universe
• Inhomogeneous Equation of State of the Universe: Phantom Era, Future Singularity and Crossing the Phantom Barrier
• Jerk, snap, and the cosmological equation of state
• The Emergent Universe: inflationary cosmology with no singularity
• Sudden Future Singularities
• Cosmography: Cosmology without the Einstein equations
• Quantum escape of sudden future singularity
• The Emergent Universe: An Explicit Construction
• Twilight for the energy conditions?
• Bouncing Braneworlds
• You need not be afraid of phantom energy
• More General Sudden Singularities
• Geodesic behavior of sudden future singularities
• "Expansion" around the vacuum equation of state - sudden future singularities and asymptotic behavior
• On the Construction of Nonsingular Pre-Big-Bang and Ekpyrotic Cosmologies and the Resulting Density Perturbations
• New Cosmological Singularities in Braneworld Models
• New Isotropic and Anisotropic Sudden Singularities
• Dark energy cosmology with generalized linear equation of state
• Cosmological perturbations through a simple bounce
• Minimal conditions for the creation of a Friedman-Robertson-Walker universe from a "bounce"
• On big rip singularities
• Escaping the Big Rip?
• Sudden future singularities in FLRW cosmologies
• Cosmological perturbations across a curvature bounce
• Did the Universe loiter at high redshifts ?
• Non-singular big-bounces and evolution of linear fluctuations
• Tolman wormholes violate the strong energy condition
• Cosmological Perturbations Through a General Relativistic Bounce
• A Model for the Big Bounce
• Power laws, scale invariance, and generalized Frobenius series: Applications to Newtonian and TOV stars near criticality
• Quantum fields and "Big Rip" expansion singularities
• Bigger Rip with No Dark Energy
• Recollapse of the closed Tolman spacetimes
• Causal Entropy Bound for Non-Singular Cosmologies
• Anatomy of a Bounce

Cited by in corpus (119)

• Dynamics of dark energy
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Finite-time future singularities in modified Gauss-Bonnet and $\mathcal{F}(R,G)$ gravity and singularity avoidance
• Future of the universe in modified gravitational theories: Approaching to the finite-time future singularity
• Reconstruction of $f(T)$ gravity: Rip cosmology, finite-time future singularities and thermodynamics
• Quantum gravity without Lorentz invariance
• G-Bounce
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• The Little Rip
• Constraints on the sum of the neutrino masses in dynamical dark energy models with $w(z)\ge -1$ are tighter than those obtained in $\Lambda$CDM
• Are loop quantum cosmos never singular?
• A Primer on Energy Conditions
• On the theory and applications of modern cosmography
• Singular Bouncing Cosmology from Gauss-Bonnet Modified Gravity
• Classification of cosmological milestones
• Crossing of the phantom divide in modified gravity
• Bouncing cosmology with future singularity from modified gravity
• Classifying and avoiding singularities in the alternative gravity dark energy models
• Constraining f(R) theories with the energy conditions
• Cosmological bouncing solutions in f(T,B) gravity
• Hawking-like radiation from evolving black holes and compact horizonless objects
• Observational constraints on phantom-like braneworld cosmologies
• Singular Inflationary Universe from $F(R)$ Gravity
• On the quantum fate of singularities in a dark-energy dominated universe
• Barotropic index w-singularities in cosmology
• Correspondence of $F(R)$ Gravity Singularities in Jordan and Einstein Frames
• On the generalised Chaplygin gas: worse than a big rip or quieter than a sudden singularity?
• Extended matter bounce scenario in ghost free $f(R,\mathcal{G})$ gravity compatible with GW170817
• Classical Stability of Sudden and Big Rip Singularities
• Quantum effects, soft singularities and the fate of the universe in a braneworld cosmology
• Is the future universe singular: Dark Matter versus modified gravity?
• Scalar dark energy models mimicking $\Lambda$CDM with arbitrary future evolution
• Modified first-order Horava-Lifshitz gravity: Hamiltonian analysis of the general theory and accelerating FRW cosmology in power-law F(R) model
• Singular Inflation
• Turbulence and Little Rip Cosmology
• A quantitative analysis of singular inflation with scalar-tensor and modified gravity
• Consequences of a Cosmic Scalar with Kinetic Coupling to Curvature
• Cardy-Verlinde formula in FRW Universe with inhomogeneous generalized fluid and dynamical entropy bounds near the future singularity
• Phantom-like behaviour in dilatonic brane-world scenario with induced gravity
• Dark Energy and Dark Matter from an additional adiabatic fluid
• The cosmology of an holographic induced gravity model with curvature effects
• Quantum cosmology and late-time singularities
• From a Bounce to the Dark Energy Era with $F(R)$ Gravity
• How far is it to a sudden future singularity of pressure?
• $w$-cosmological singularities
• A General Sudden Cosmological Singularity
• Quantum Particle Production at Sudden Singularities
• Null Energy Condition violations in bimetric gravity
• Local conditions separating expansion from collapse in spherically symmetric models with anisotropic pressures
• Sudden singularities survive massive quantum particle production
• Hidden past of dark energy cosmological models
• Screening of cosmological constant for De Sitter Universe in non-local gravity, phantom-divide crossing and finite-time future singularities
• Non-singular Bounce Cosmology from Lagrange Multiplier $F(R)$ Gravity
• Bounce cosmology in $f(\mathcal{R})$ gravity
• The holographic induced gravity model with a Ricci dark energy: smoothing the little rip and big rip through Gauss-Bonnet effects?
• Quasi-Rip: A New Type of Rip Model without Cosmic Doomsday
• Cosmological Hysteresis and the Cyclic Universe
• ISCOs and OSCOs in the presence of positive cosmological constant
• Singularity of spherically-symmetric spacetime in quintessence/phantom dark energy universe
• Confronting dark energy models mimicking $\Lambda$CDM epoch with observational constraints: future cosmological perturbations decay or future Rip?
• Decomposition of total stress-energy for the generalised Kiselev black hole
• Phantom singularities and their quantum fate: general relativity and beyond
• Gordon and Kerr-Schild ansatze in massive and bimetric gravity
• Phantom evolving wormholes with big rip singularities
• Cosmological tests of sudden future singularities
• Resolution of type IV singularities in quantum cosmology
• Effects of Quantized Scalar Fields in Cosmological Spacetimes with Big Rip Singularities
• Recent advances in cosmological singularities
• Is the accelerated expansion evidence of a forthcoming change of signature on the brane?
• Grand Rip and Grand Bang/Crunch cosmological singularities
• Cosmological evolution, future singularities, Little Rip and Pseudo-Rip in viable f(R) theories and their scalar-tensor counterpart
• Future singularities if the universe underwent Starobinsky inflation in the past
• Cosmodynamics: Energy conditions, Hubble bounds, density bounds, time and distance bounds
• Bounces, turnarounds and singularities in bimetric gravity
• Cyclic cosmology in modified gravity
• New perspectives on the TOV equilibrium from a dual null approach
• Archimedean-type force in a cosmic dark fluid: III. Big Rip, Little Rip and Cyclic solutions
• Dark Energy: The Shadowy Reflection of Dark Matter?
• A generalized Kasner transition for bouncing Bianchi I models in modified gravity theories
• Singular deformations of nearly $R^2$ inflation potentials
• Reconstruction of mimetic gravity in a non-singular bouncing universe from quantum gravity
• Equation-of-state formalism for dark energy models on the brane and the future of brane universes
• Cosmological milestones and energy conditions
• The fate of bound systems through Sudden Future Singularities
• Geodesics of McVittie Spacetime with a Phantom Cosmological Background
• Scalar field cosmological models with finite scale factor singularities
• Singularities in Isotropic Non-Minimal Scalar Field Models
• Singular Accelerated Evolution in Massive $F(R)$ Bigravity
• A dual null formalism for the collapse of fluids in a cosmological background
• Initial directional singularity in inflationary models
• Periodic Cosmological Evolutions of Equation of State for Dark Energy
• New non-singular cosmological solution of non-local gravity
• Big Bang Singularity Resolution In Quantum Cosmology
• Quintessence and (Anti-)Chaplygin Gas in Loop Quantum Cosmology
• Rip Brane Cosmology from 4d Inhomogeneous Dark Fluid Universe
• Viable non-singular cosmic bounce in holonomy improved F(R) gravity endowed with a Lagrange multiplier
• Knot Universes in Bianchi Type I Cosmology
• Geodesic Behaviour around Cosmological Milestones
• Tachyon field in loop quantum cosmology: An example of traversable singularity
• New futures for cosmological models
• Dark Energy and Cosmological Horizon Thermal Effects
• Spacetime averaging of exotic singularity universes
• Effects of a Late Gravitational Transition on Gravitational Waves and Anticipated Constraints
• Expansion-contraction duality breaking in a Planck-scale sensitive cosmological quantum simulator
• Wave asymptotics at a cosmological time-singularity: classical and quantum scalar fields
• Loop Quantum Cosmology: Physics of Singularity Resolution and its Implications
• Quantum fields near phantom-energy `sudden' singularities
• $w$-singularities in cosmological models
• Future soft singularities, Born-Infeld-like fields and particles
• The general scalar-tensor Hamiltonian with deformed covariance
• Singularities in inflationary cosmological models
• Equation of state and singularities in FLRW cosmological models
• Regularizing future cosmological singularities with varying speed of light
• Accelerating expansion and change of signature
• Bounding the Hubble flow in terms of the w parameter
• Is it possible to separate baryonic from dark matter within the $\Lambda$-CDM formalism?
• Cosmic anisotropic doomsday in Bianchi type I universes