Classical and quantum $f(R)$ cosmology: The big rip, the little rip and the little sibling of the big rip

Abstract

The big rip, the little rip and the little sibling of the big rip are cosmological doomsdays predicted by some phantom dark energy models that could describe the future evolution of our Universe. When the universe evolves towards either of these future cosmic events all bounded structures and, ultimately, space-time itself are ripped apart. Nevertheless, it is commonly belief that quantum gravity effects may smooth or even avoid these classically predicted singularities. In this review, we discuss the classical and quantum occurrence of these riplike events in the scheme of metric $f(R)$ theories of gravity. The quantum analysis is performed in the framework of $f(R)$ quantum geometrodynamics. In this context, we analyse the fulfilment of the DeWitt criterion for the avoidance of these singular fates.

arXiv commentInvited review submitted to Universe for the Special Issue on "Quantum Cosmology", ed. by Prof. Paulo Vargas Moniz, 32 pages, 3 tables. v2: typos fixed, references added, matches published version

References in corpus (96)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Planck 2015 results. XIII. Cosmological parameters
• Dynamics of dark energy
• The Cosmological Constant and Dark Energy
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Cosmological Imprint of an Energy Component with General Equation of State
• Extended Theories of Gravity
• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• Cosmological Constant - the Weight of the Vacuum
• f(R,T) gravity
• An alternative to quintessence
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Phantom Energy and Cosmic Doomsday
• Generalized Chaplygin Gas, Accelerated Expansion and Dark Energy-Matter Unification
• A Model of Holographic Dark Energy
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Kinetically Driven Quintessence
• Modified Gauss-Bonnet theory as gravitational alternative for dark energy
• Properties of singularities in (phantom) dark energy universe
• Dark torsion as the cosmic speed-up
• Loop Quantum Cosmology: A Status Report
• Accelerated expansion of the universe driven by tachyonic matter
• Late-time cosmology in (phantom) scalar-tensor theory: dark energy and the cosmic speed-up
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Quintessence: A Review
• The final state and thermodynamics of dark energy universe
• Cosmological Evolution of the Rolling Tachyon
• Cosmology in $f(Q)$ geometry
• Dark Matter and Dark Energy
• Beyond $\Lambda$CDM: Problems, solutions, and the road ahead
• Reconciling dark energy models with f(R) theories
• Loop Quantum Cosmology
• Sudden Future Singularities
• Modified gravity and its reconstruction from the universe expansion history
• Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change
• Dark Energy Dominance and Cosmic Acceleration in First Order Formalism
• Gravity assisted dark energy dominance and cosmic acceleration
• Quantum escape of sudden future singularity
• Solar System constraints to general f(R) gravity
• Galaxy Clusters Selected with the Sunyaev-Zel'dovich Effect from 2008 South Pole Telescope Observations
• Dark energy two decades after: Observables, probes, consistency tests
• Dynamically Triangulating Lorentzian Quantum Gravity
• The Newtonian Limit of F(R) gravity
• Aspects of the cosmological "coincidence problem"
• First Cosmology Results using Type Ia Supernovae from the Dark Energy Survey: Constraints on Cosmological Parameters
• The Little Rip
• Modified Gravity and Cosmology: An Update by the CANTATA Network
• Stability of Cosmological Solution in f(R) Models of Gravity
• A f(R) gravity without cosmological constant
• Dark energy in Horndeski theories after GW170817: A review
• More General Sudden Singularities
• Constraining Dark Energy Dynamics in Extended Parameter Space
• A non-perturbative Lorentzian path integral for gravity
• On the LCDM Universe in f(R) gravity
• "Expansion" around the vacuum equation of state - sudden future singularities and asymptotic behavior
• Worse than a big rip?
• The Atacama Cosmology Telescope: Cosmology from Galaxy Clusters Detected via the Sunyaev-Zel'dovich Effect
• A Vacuum Phase Transition Solves $H_0$ Tension
• PPN-limit of Fourth Order Gravity inspired by Scalar-Tensor Gravity
• Quantum phantom cosmology
• Models for Little Rip Dark Energy
• Quantum cosmology with big-brake singularity
• On the quantum fate of singularities in a dark-energy dominated universe
• Sudden future singularities in FLRW cosmologies
• Reconstruction and deceleration-acceleration transitions in modified gravity
• On the generalised Chaplygin gas: worse than a big rip or quieter than a sudden singularity?
• The little sibling of the big rip singularity
• Constraining cosmic deceleration-acceleration transition with type Ia supernova, BAO/CMB and H(z) data
• A new approach to reconstruction methods in $f(R)$ gravity
• Cosmological constraints from baryon acoustic oscillations and clustering of large-scale structure
• The Future of Primordial Features with 21 cm Tomography
• Phantom-like behaviour in dilatonic brane-world scenario with induced gravity
• Cosmological constraints of phantom dark energy models
• From Big to Little Rip in modified F(R,G) gravity
• Testing an exact $f(R)$-gravity model at Galactic and local scales
• Cosmological perturbations in an effective and genuinely phantom dark energy Universe
• Phantom singularities and their quantum fate: general relativity and beyond
• Accelerated Expansion of the Universe in Gauss-Bonnet Gravity
• The quantum realm of the "Little Sibling" of the Big Rip singularity
• Solar system tests of f(R) gravity
• Cosmological test with the QSO Hubble diagram
• Grand Rip and Grand Bang/Crunch cosmological singularities
• Classical and quantum cosmology of the little rip abrupt event
• $f(R)$ quantum cosmology: avoiding the Big Rip
• Solar System tests and chameleon effect in f (R) gravity
• Doomsdays in a modified theory of gravity: A classical and a quantum approach
• Can f(R) gravity contribute to (dark) radiation?
• Initial directional singularity in inflationary models
• The classical and quantum fate of the Little Sibling of the Big Rip in $f(R)$ cosmology
• On the Consistency of the Wheeler-DeWitt Equation in the Quantized Eddington-inspired Born-Infeld Gravity
• Constraints On Dark Energy Models From Galaxy Clusters and Gravitational Lensing Data
• The little rip in classical and quantum $f(R)$ cosmology
• Notes on the post-Newtonian limit of massive Brans-Dicke theory
• $\gamma$ gravity: Steepness control
• Solar System Tests of a New Class of $f(z)$ Theory

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