The classical and quantum fate of the Little Sibling of the Big Rip in $f(R)$ cosmology

Abstract

The Little Sibling of the Big Rip is a cosmological abrupt event predicted by some phantom cosmological models that could describe our Universe. When this event is approached the observable Universe and its expansion rate grow infinitely, but its cosmic derivative remains finite. In this work we have obtained the group of metric $f(R)$ theories of gravity that reproduce this classical cosmological background evolution. Furthermore, we have considered the quantization of some of the resulting models in the framework of quantum geometrodynamics, showing that the DeWitt criterion can be satisfied. Therefore, as it also happens in General Relativity, this event may be avoided in $f(R)$ quantum cosmology.

arXiv comment10 pages; title changed; 1 table added; 8 references added; no physics changes. This version accepted for publication in Physical Review D

References in corpus (44)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Observation of Gravitational Waves from a Binary Black Hole Merger
• Planck 2015 results. XIII. Cosmological parameters
• Extended Theories of Gravity
• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Phantom Energy and Cosmic Doomsday
• Can the dark energy equation-of-state parameter w be less than -1?
• Properties of singularities in (phantom) dark energy universe
• The final state and thermodynamics of dark energy universe
• Reconciling dark energy models with f(R) theories
• Modified gravity and its reconstruction from the universe expansion history
• Planck 2015 results. XIV. Dark energy and modified gravity
• Extended Gravity Cosmography
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• The Little Rip
• A f(R) gravity without cosmological constant
• More General Sudden Singularities
• On the LCDM Universe in f(R) gravity
• Worse than a big rip?
• Quantum phantom cosmology
• Pseudo-rip: Cosmological models intermediate between the cosmological constant and the little rip
• Classifying and avoiding singularities in the alternative gravity dark energy models
• On the quantum fate of singularities in a dark-energy dominated universe
• On the generalised Chaplygin gas: worse than a big rip or quieter than a sudden singularity?
• The little sibling of the big rip singularity
• A new approach to reconstruction methods in $f(R)$ gravity
• Constraining models of $f(R)$ gravity with Planck and WiggleZ power spectrum data
• Phantom boundary crossing and anomalous growth index of fluctuations in viable f(R) models of cosmic acceleration
• Theoretical and observational constraints of viable f(R) theories of gravity
• Constraints on f(R) theory and Galileons from the latest data of galaxy redshift surveys
• Future Oscillations around Phantom Divide in f(R) Gravity
• Cosmological perturbations in an effective and genuinely phantom dark energy Universe
• One-loop divergences for $f(R)$ gravity
• The quantum realm of the "Little Sibling" of the Big Rip singularity
• Towards the Quantization of Eddington-inspired-Born-Infeld Theory
• Classical and quantum cosmology of the little rip abrupt event
• $f(R)$ quantum cosmology: avoiding the Big Rip
• Can f(R) gravity contribute to (dark) radiation?
• On the Consistency of the Wheeler-DeWitt Equation in the Quantized Eddington-inspired Born-Infeld Gravity
• "Expansion" around the vacuum: how far can we go from Lambda?
• What if gravity becomes really repulsive in the future?

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• Similarity solutions for the Wheeler-DeWitt equation in $f\left(R\right)$-cosmology
• The little rip in classical and quantum $f(R)$ cosmology
• Classical and quantum $f(R)$ cosmology: The big rip, the little rip and the little sibling of the big rip
• $f(R)$ Dual Theories of Quintessence : Expansion-Collapse Duality
• Quantum Einsteinian Cubic Cosmology
• Cosmological models with Big rip and Pseudo rip Scenarios in extended theory of gravity