Finite-time Cosmological Singularities and the Possible Fate of the Universe

Abstract

Singularities in any physical theory are either remarkable indicators of the unknown underlying fundamental theory, or indicate a change in the description of the physical reality. In General Relativity there are three fundamental kinds of singularities that might occur, firstly the black hole spacelike crushing singularities, e.g. in the Schwarzschild case and two cosmological spacelike singularities appearing in finite-time, namely, the Big Bang singularity and the Big Rip singularity. In the case of black hole and Big Bang singularity, the singularity indicates that the physics is no longer described by the classical gravity theory but some quantum version of gravity is probably needed. The Big Rip is a future singularity which appears in the context of General Relativity due to a phantom scalar field needed to describe the dark energy era. Apart from the Big Rip singularity, a variety of finite-time future singularities, such as, sudden singularity, Big Freeze singularity, generalized sudden singularity, $w$-singularity and so on, are allowed in various class of cosmological models irrespective of their origin. The occurrence of these finite-time singularities has been intensively investigated in the context of a variety of dark energy, modified gravity, and other alternative cosmological theories. These singularities suggest that the current cosmological scenario is probably an approximate version of a fundamental theory yet to be discovered. In this review we provide a concrete overview of the cosmological theories constructed in the context of Einstein's General Relativity and modified gravity theories that may lead to finite-time cosmological singularities. We also discuss various approaches suggested in the literature that could potentially prevent or mitigate finite-time singularities within the cosmological scenarios.

Invited Review Article from Physics Reports; Published version; 138 pages including 7 tables, 1 figure and the references

References in corpus (289)

• Dynamics of dark energy
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R,T) gravity
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Dark Energy and the Accelerating Universe
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• Einstein's Other Gravity and the Acceleration of the Universe
• Extra force in $f(R)$ modified theories of gravity
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Reconstructing Dark Energy
• Can dark energy evolve to the Phantom?
• The teleparallel equivalent of general relativity
• A New Model of Agegraphic Dark Energy
• The Large Scale Structure of f(R) Gravity
• A Holographic Dark Energy Model from Ricci Scalar Curvature
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• Dark energy cosmology from higher-order, string-inspired gravity and its reconstruction
• Large-scale instability in interacting dark energy and dark matter fluids
• Future of the universe in modified gravitational theories: Approaching to the finite-time future singularity
• Approaches to Understanding Cosmic Acceleration
• Dark Energy-Dark Matter Interaction and putative violation of the Equivalence Principle from the Abell Cluster A586
• Inflationary cosmology in modified gravity theories
• Observational constraints on $f(T)$ theory
• Dark Energy and Gravity
• Loop quantum cosmology of k=1 FRW models
• The Cosmology of f(R) Gravity in the Metric Variational Approach
• String-inspired Gauss-Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy
• The Cosmology of Modified Gauss-Bonnet Gravity
• Dynamics of dark energy with a coupling to dark matter
• f(R) Gravity and Chameleon Theories
• $f(T,\mathcal{T})$ gravity and cosmology
• Hawking Radiation of Apparent Horizon in a FRW Universe
• The Newtonian Limit of F(R) gravity
• Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity
• Modified non-local-F(R) gravity as the key for the inflation and dark energy
• Dynamics of interacting dark energy
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• Consequences of dark matter-dark energy interaction on cosmological parameters derived from SNIa data
• The new form of the equation of state for dark energy fluid and accelerating universe
• Dark Energy: the equation of state description versus scalar-tensor or modified gravity
• Viscous Cosmology for Early- and Late-Time Universe
• Non-linear Evolution of f(R) Cosmologies III: Halo Statistics
• Cosmologies with Energy Exchange
• Cosmology and Astrophysical Constraints of Gauss-Bonnet Dark Energy
• Effects of the interaction between dark energy and dark matter on cosmological parameters
• Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion
• Stability of Cosmological Solution in f(R) Models of Gravity
• Are loop quantum cosmos never singular?
• A Singularity Problem with f(R) Dark Energy
• Inflation and late-time cosmic acceleration in non-minimal Maxwell-$F(R)$ gravity and the generation of large-scale magnetic fields
• Dynamical vacuum energy, holographic quintom, and the reconstruction of scalar-field dark energy
• Non-Singular Bouncing Universes in Loop Quantum Cosmology
• Gauss-Bonnet Quintessence: Background Evolution, Large Scale Structure and Cosmological Constraints
• Interacting Dark Energy and Dark Matter: observational Constraints from Cosmological Parameters
• The Dynamics of Quintessence, The Quintessence of Dynamics
• Cosmological Solutions of $f(T)$ Gravity
• Holographic Ricci dark energy: Current observational constraints, quintom feature, and the reconstruction of scalar-field dark energy
• Reconstructing holographic quintessence
• Loop Quantum Cosmology: An Overview
• Mimetic $F(R)$ gravity: inflation, dark energy and bounce
• Does Bulk Viscosity Create a Viable Unified Dark Matter Model?
• Bulk Viscous Cosmology
• Non-linear evolution of f(R) cosmologies I: methodology
• The evolution of density perturbations in f(R) gravity
• Worse than a big rip?
• Bouncing cosmology in modified Gauss-Bonnet gravity
• Inflationary cosmology and the late-time accelerated expansion of the universe in non-minimal Yang-Mills-$F(R)$ gravity and non-minimal vector-$F(R)$ gravity
• Loop quantum cosmology and the k = - 1 RW model
• Dark Interactions and Cosmological Fine-Tuning
• Dynamical behavior in $f(T,T_G)$ cosmology
• Dark energy from modified F(R)-scalar-Gauss-Bonnet gravity
• Quintessence: a mini-review
• Accelerating cosmologies from non-local higher-derivative gravity
• Cosmological coincidence problem in interacting dark energy models
• Avoidance of future singularities in loop quantum cosmology
• Newton law corrections and instabilities in $f(R)$ gravity with the effective cosmological constant epoch
• Large-scale magnetic fields in the inflationary universe
• Cosmological Evolution of Interacting Phantom Energy with Dark Matter
• Phantom and non-phantom dark energy: The cosmological relevance of non-locally corrected gravity
• Closed FRW model in Loop Quantum Cosmology
• Interacting models may be key to solve the cosmic coincidence problem
• A combined analysis of the $H_0$ late time direct measurements and the impact on the Dark Energy sector
• Toward a solution of the coincidence problem
• Unifying of Inflation with Early and Late Dark Energy Epochs in Axion $F(R)$ Gravity
• Classifying and avoiding singularities in the alternative gravity dark energy models
• Dark energy from modified gravity with Lagrange multipliers
• Viability of f(R) Theories with Additional Powers of Curvature
• The oscillating dark energy: future singularity and coincidence problem
• A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
• Testing the interaction between dark energy and dark matter via latest observations
• Dynamical behavior in mimetic F(R) gravity
• Time-dependent matter instability and star singularity in $F(R)$ gravity
• Brans-Dicke Scalar Field as a Chameleon
• Autonomous Dynamical System Approach for $f(R)$ Gravity
• Agegraphic dark energy as a quintessence
• New observational constraints on $f(R)$ gravity from cosmic chronometers
• Loop quantum cosmology and inhomogeneities
• The phase space view of f(R) gravity
• Stability of the Einstein static universe in modified Gauss-Bonnet gravity
• Matter Bounce Loop Quantum Cosmology from $F(R)$ Gravity
• Dynamics of Quintessence Models of Dark Energy with Exponential Coupling to the Dark Matter
• Quintessence reconstruction of the new agegraphic dark energy model
• Interacting models of soft coincidence
• An Accelerating Cosmology Without Dark Energy
• Modified gravity as an alternative for Lambda-CDM cosmology
• Dynamical analysis of generalized Galileon cosmology
• Dark energy, inflation and dark matter from modified F(R) gravity
• A new interacting two fluid model and its consequences
• Geometric Inflation and Dark Energy with Axion $F(R)$ Gravity
• Can a matter-dominated model with constant bulk viscosity drive the accelerated expansion of the universe?
• On the large-scale instability in interacting dark energy and dark matter fluids
• Matter creation and cosmic acceleration
• Novel approach towards the large-scale stable Interacting Dark-Energy models and their Astronomical Bounds
• Dynamical dark energy after Planck CMB final release and $H_0$ tension
• Translation of Einstein's Attempt of a Unified Field Theory with Teleparallelism
• Dynamics of Interacting Quintessence Models: Observational Constraints
• Quantum cosmology with big-brake singularity
• Exploring a matter-dominated model with bulk viscosity to drive the accelerated expansion of the Universe
• On the quantum fate of singularities in a dark-energy dominated universe
• The Cosmology of Ricci-Tensor-Squared Gravity in the Palatini Variational Approach
• Interacting Dark Energy in a closed universe
• Barotropic index w-singularities in cosmology
• Disformal couplings and the dark sector of the universe
• Can f(R) Modified Gravity Theories Mimic a LCDM Cosmology?
• The Einstein static universe in Loop Quantum Cosmology
• Cosmological Inflation in f(Q, T) Gravity
• Holographic dark energy in the DGP braneworld with GO cutoff
• Unifying inflation with dark energy in modified F(R) Horava-Lifshitz gravity
• Is Emergent Universe a Consequence of Particle Creation Process?
• Delicate f(R) gravity models with disappearing cosmological constant and observational constraints on the model parameters
• Dynamical behavior of generic quintessence potentials: constraints on key dark energy observables
• Constraining $f(R)$ Gravity Theory Using Weak Lensing Peak Statistics from the Canada-France-Hawaii-Telescope Lensing Survey
• Searching for dark matter - dark energy interactions: going beyond the conformal case
• Stepping out of Homogeneity in Loop Quantum Cosmology
• Constraints on f(R) Cosmology in the Palatini Formalism
• Phantom field dynamics in loop quantum cosmology
• On the generalised Chaplygin gas: worse than a big rip or quieter than a sudden singularity?
• Testing coupled dark energy models with their cosmological background evolution
• Deceleration versus Acceleration Universe in Different Frames of $F(R)$ Gravity
• CMB and Matter Power Spectra of Early f(R) Cosmology in Palatini Formalism
• Spherically symmetric brane spacetime with bulk $f(\mathcal{R})$ gravity
• The little sibling of the big rip singularity
• Inflationary solutions in asymptotically safe f(R) theories
• Classical Stability of Sudden and Big Rip Singularities
• A Consistent View of Interacting Dark Energy from Multiple CMB Probes
• Constraining a dark matter and dark energy interaction scenario with a dynamical equation of state
• Gravitationally Induced Particle Production: Thermodynamics and Kinetic Theory
• Non-adiabatic dark fluid cosmology
• Phantom behavior via cosmological creation of particles
• Phase Space Analysis of the Accelerating Multi-fluid Universe
• Dynamics of interacting phantom scalar field dark energy in Loop Quantum Cosmology
• Dynamical systems analysis of anisotropic cosmologies in $R^n$-gravity
• Inflationary universe in loop quantum cosmology
• Late time interacting cosmologies and the Hubble constant tension
• Open FRW model in Loop Quantum Cosmology
• Inflation with a quartic potential in the framework of Einstein-Gauss-Bonnet gravity
• Inevitable ghost and the degrees of freedom in f(R,G) gravity
• Quintessence reconstructed: new constraints and tracker viability
• Turbulence and Little Rip Cosmology
• Emergent Universe in Brane World Scenario with Schwarzschild-de Sitter Bulk
• In search of the dark matter dark energy interaction: a kinematic approach
• Interacting Dark Energy in f(T) cosmology : A Dynamical System analysis
• Singular fate of the universe in modified theories of gravity
• Coupled dark energy with perturbed Hubble expansion rate
• Gaussian processes and effective field theory of $f(T)$ gravity under the $H_0$ tension
• Data-driven Reconstruction of the Late-time Cosmic Acceleration with f(T) Gravity
• On dynamical systems approaches and methods in $f(R)$ cosmology
• First law of thermodynamics and Friedmann-like equations in braneworld cosmology
• Dark degeneracy I: Dynamical or interacting dark energy?
• Astronomical bounds on future big freeze singularity
• Modified cosmology from the thermodynamics of apparent horizon
• Exact solutions for Big Bounce in loop quantum cosmology
• Cosmic acceleration without dark energy: Background tests and thermodynamic analysis
• Cosmological constant, brane tension and large hierarchy in a generalized Randall-Sundrum braneworld scenario
• Dynamics of Quintom and Hessence Energies in Loop Quantum Cosmology
• Inflation and dark energy from f(R) gravity
• Testing the quasi-static approximation in $f(R)$ gravity simulations
• Realistic simulations of galaxy formation in f(R) modified gravity
• How far is it to a sudden future singularity of pressure?
• $w$-cosmological singularities
• Speeding up $N$-body simulations of modified gravity: Chameleon screening models
• Dynamics and cosmological evolution in Λ-varying cosmology
• Testing the equation of state for viscous dark energy
• Did the Universe Experienced a Pressure non-Crushing Type Cosmological Singularity in the Recent Past?
• Turning Big Bang into Big Bounce: I. Classical Dynamics
• Interacting 3-form dark energy models: distinguishing interactions and avoiding the Little Sibling of the Big Rip
• Quintessential inflation in Palatini $f(R)$ gravity
• Holographic Ricci dark energy in Randall-Sundrum braneworld: Avoidance of big rip and steady state future
• Probing the imprints of generalized interacting dark energy on the growth of perturbations
• Tachyon cosmology, supernovae data and the Big Brake singularity
• On the dynamics of a dark sector coupling
• Tolman-Oppenheimer-Volkoff Equations in Modified Gauss-Bonnet Gravity
• Type I singularities and the Phantom Menace
• $\nu$Galileon: modified gravity with massive neutrinos as a testable alternative to $\Lambda$CDM
• Cosmic acceleration and crossing of $\omega =-1$ in non-minimal modified Gauss-Bonnet gravity
• The interrelation between the generation of large-scale electric fields and that of large-scale magnetic fields during inflation
• Is the continuous matter creation cosmology an alternative to $\Lambda$CDM?
• Fast full N-body simulations of generic modified gravity: conformal coupling models
• Little Rip, $\Lambda$CDM and singular dark energy cosmology from Born-Infeld-$f(R)$ gravity
• Kinetic Axion $F(R)$ Gravity Inflation
• Exploration of interacting dynamical dark energy model with interaction term including the equation-of-state parameter: alleviation of the $H_0$ tension
• Gravitational lensing in braneworld gravity: formalism and applications
• Cosmological singularities in Born-Infeld determinantal gravity
• Logamediate Inflation in f(T) Teleparallel Gravity
• The imprint of $f(R)$ gravity on weak gravitational lensing II : Information content in cosmic shear statistics
• Observational Constraints on $f(T)$ Gravity from Model-Independent Data
• Parameters of cosmological models and recent astronomical observations
• Fast full $N$-body simulations of generic modified gravity: derivative coupling models
• A general framework to test gravity using galaxy clusters II: A universal model for the halo concentration in $f(R)$ gravity
• Non-parametric reconstruction of interaction in the cosmic dark sector
• Braneworld gravitational collapse from a radiative bulk
• Statefinder diagnosis for holographic dark energy in the DGP braneworld
• Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars
• Effects of Quantized Scalar Fields in Cosmological Spacetimes with Big Rip Singularities
• Analytical solutions in $R+q{R}^n$ cosmology from singularity analysis
• Transcending Big Bang in Loop Quantum Cosmology: Recent Advances
• Nonlinear bulk viscosity and the stability of accelerated expansion in FRW spacetime
• Structure formation on the brane: A mimicry
• Dynamical Systems analysis of an interacting dark energy model in the Brane Scenario
• IWDM: The fate of an interacting non-cold dark matter $-$ vacuum scenario
• Reconstruction of $f(R)$ gravity models for an accelerated universe using Raychaudhuri equation
• New integrable models and analytical solutions in $f(R)$~cosmology with an ideal gas
• Bounces, turnarounds and singularities in bimetric gravity
• de Sitter branes with a bulk scalar
• Archimedean-type force in a cosmic dark fluid: III. Big Rip, Little Rip and Cyclic solutions
• Viscous Generalized Chaplygin Gas as a Unified Dark Fluid: Including Perturbation of Bulk Viscosity
• Do we need soft cosmology?
• A general framework to test gravity using galaxy clusters IV: Cluster and halo properties in DGP gravity
• Galaxy-galaxy weak gravitational lensing in $f(R)$ gravity
• Constraining interacting dark energy models with the halo concentration-mass relation
• A late time acceleration of the universe with two scalar fields : many possibilities
• Exact spherically symmetric solutions in modified Gauss-Bonnet gravity from Noether symmetry approach
• Dynamical system analysis for DBI dark energy interacting with dark matter
• (Compactified) black branes in four dimensional f(R)-gravity
• Dynamical Systems Analysis of K-essence Model
• On thermodynamics second law in the modified Gauss Bonnet gravity
• Brane singularities and their avoidance
• Future dynamics in f(R) theories
• Little Rip cosmological models with time-dependent equation of state
• Dissipative Universe-Inflation with Soft Singularity
• Cosmological model with time varying deceleration parameter in $F(R,G)$ gravity
• Observational constraints on the interacting dark energy - dark matter (IDM) cosmological models
• Observational constraints on soft dark energy and soft dark matter: challenging $\Lambda$CDM
• The fate of bound systems through Sudden Future Singularities
• Stability of Hyperbolic and Matter-Dominated Bounce Cosmologies From F(R,G) Modified Gravity at Late Evolution Stages
• Updating constraints on phantom crossing $f(T)$ gravity
• Scalar field cosmological models with finite scale factor singularities
• Structure formation in dark energy cosmologies described by PADE parameterization
• Finite time future singularities in the interacting dark sector
• Shocks and finite-time singularities in Hele-Shaw flow
• Revisiting the screening mechanism in $f(R)$ gravity
• Vanishing Cosmological Constant in Modified Gauss-Bonnet Gravity with Conformal Anomaly
• Semi-classical gravity phenomenology under the causal-conditional quantum measurement prescription
• Holographic dark energy interacting with dark matter in a Closed Universe
• Covariant action for bouncing cosmologies in modified Gauss-Bonnet gravity
• Singularity formation in asymptotically safe cosmology with inhomogeneous equation of state
• Initial directional singularity in inflationary models
• Holographic dark energy and validity of the generalized second law of thermodynamics in the dgp brane world
• Holographic energy density, dark energy sound speed, and tensions in cosmological parameters: $H_0$ and $S_8$
• Analytic solutions in Einstein-aether scalar field cosmology
• Exploring bulk viscous unified scenarios with Gravitational Waves Standard Sirens
• Similarity solutions for the Wheeler-DeWitt equation in $f\left(R\right)$-cosmology
• Van der Waals Universe with Adiabatic Matter Creation
• Brane cosmology, Weyl fluid, and density perturbations
• No "big trips" for the universe
• Emergent Universe in Brane World Scenario
• Alternative approach to the Starobinsky model for inflation scenarios
• A general framework to test gravity using galaxy clusters VI: Realistic galaxy formation simulations to study clusters in modified gravity
• Modified Equations of State for Dark Energy and Observational Limitations
• A general framework to test gravity using galaxy clusters V: A self-consistent pipeline for unbiased constraints of $f(R)$ gravity
• New futures for cosmological models
• Integrability and Cosmological Solutions in Einstein-aether-Weyl theory
• Sudden Future Singularities in Quintessence and Scalar-Tensor Quintessence Models
• Type V singularities with inhomogeneous equations of state
• New Anisotropic Sudden Singularities and Dimensional Reduction
• Evolving Cosmic Scenario in Modified Chaplygin Gas with Adiabatic Matter Creation
• Cosmological future singularities in massive gravity and massive bigravity
• Future soft singularities, Born-Infeld-like fields and particles
• Eternal vs singular observers in interacting dark energy-dark matter models
• Modified Brans-Dicke cosmology with Minimum Length Uncertainty
• Brane world solutions of perfect fluid in the background of a bulk containing dust or cosmological constant
• Finite scale factor and future singularities

Cited by in corpus (44)

• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• Quasi-static evolution of axially and reflection symmetric large-scale configuration
• Combining pre- and post-recombination new physics to address cosmological tensions: case study with varying electron mass and sign-switching cosmological constant
• Thermodynamic topology of black Holes in f(R) gravity
• Transition dynamics in the ${\Lambda }_{\mathrm{s}}$CDM model: Implications for bound cosmic structures
• Fractional Holographic Dark Energy
• III. Interacting Dark Energy: Summary of Models, Pathologies, and Constraints
• Cosmological model with linear equation of state parameter in f(R, Lm) gravity
• Conformal Killing cosmology -- Geometry, dark sector, growth of structures, and big rip
• Tsallis holographic dark energy with power law ansatz approach
• Primordial regular black holes as all the dark matter. III. Covariant canonical quantum gravity models
• Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields
• Decay of $f(R)$ quintessence into dark matter: mitigating the Hubble tension?
• Reconstruction of the singularity-free $f(\mathcal{R})$ gravity via Raychaudhuri equations
• I. Linear Interacting Dark Energy: Analytical Solutions and Theoretical Pathologies
• A new approach to $P-V$ phase transitions: Einstein gravity and holographic type dark energy
• Anisotropic Born-Infeld-f(R) Cosmologies
• New perspectives on future rip scenarios with holographic dark energy
• Cosmology of unimodular Born-Infeld-$f(R)$ gravity
• A comprehensive data-driven odyssey to explore the equation of state of dark energy
• Gravitational Slip parameter and Gravitational Waves in Einstein-Cartan theory
• Gauge Invariant Lagrangian Formulations for Mixed Symmetry Higher Spin Bosonic Fields in AdS Spaces
• Observational constraints using Bayesian statistics and Deep Learning in $f(Q)$ gravity
• Rips and regular future scenario with Holographic Dark Energy: A comprehensive look
• An innovative black hole solution and thermodynamic properties in higher-order curvature gravity with a scalar field
• Solutions of Maxwell equations for admissible electromagnetic fields, in spaces with simply transitive four-parameter groups of motions
• Stability of Relativistic Spheres Powered by Energy Profile in Einstein Gauss-Bonnet Gravity
• Sudden cosmological singularities in Aether scalar-tensor theories
• Cosmological singularities in non-canonical models of dark energy
• Dynamical Systems Analysis of $f(R,L_m)$ Gravity Model
• Gauss-Bonnet entropy and thermal dynamics of RN-AdS black holes
• Reheating constraints and the $H_0$ tension in Quintessential Inflation
• Cosmological Singularities in Brane Gravity
• On rips and cosmological singularities in a universe merging with baby universes
• Again About Singularity Crossing In Gravitation And Cosmology
• Individual halo bias in models of $f(R)$ gravity
• Cosmological Implications of Thermodynamic Split Conjecture
• Crunching, Bouncing, and Cyclical Cosmologies from Dark Sector Interactions
• The $f(Q)$ gravity and affine EoS: Compatibility and observational constraints
• Singularity softening and avoidance by the action of thermal radiation in a generalized entropic cosmology
• Conformal structure of singularities in some varying fundamental constants bimetric cosmologies
• Fermionic quantum cosmology as a framework for resolving type IV singularities
• Towards Lagrangian dynamics for constrained mixed-symmetric interacting higher-spin fields
• Thermodynamic Split Conjecture and an Observational Test for Cosmological Entropy