Effective Action of Vacuum: Semiclassical Approach

Abstract

We present brief, to great extent pedagogical review on renormalization in curved space-time and of some recent results on the derivation and better understanding of quantum corrections to the action of gravity. The paper is mainly devoted to the semiclassical approach, but we also discuss its importance for quantum gravity and string theory.

54 pages, 2 figures, invited review paper partially based on various lecture courses, accepted in Classical and Quantum Gravity as topical review. A few changes compared to the original version: some relevant comments on black hole case and references added, typos corrected

References in corpus (70)

• Cosmological Constant - the Weight of the Vacuum
• The Case for a Positive Cosmological Lambda-term
• Cosmology and the Fate of Dilatation Symmetry
• The Cosmological Constant
• The Standard Model Higgs boson as the inflaton
• Relativistic gravitation theory for the MOND paradigm
• Nonperturbative Evolution Equation for Quantum Gravity
• Heat kernel expansion: user's manual
• Extra force in $f(R)$ modified theories of gravity
• Twenty Years of the Weyl Anomaly
• Study of the anomalous acceleration of Pioneer 10 and 11
• Energy in Generic Higher Curvature Gravity Theories
• Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity
• Cosmology of the Planck Era from a Renormalization Group for Quantum Gravity
• The scaling evolution of cosmological constant
• Weyl Cohomology and the Effective Action for Conformal Anomalies
• On the scaling behavior of the cosmological constant and the possible existence of new forces and new light degrees of freedom
• Some remarks on high derivative quantum gravity
• Trace anomaly driven inflation
• Cosmology with Self-Adjusting Vacuum Energy Density from a Renormalization Group Fixed Point
• Variable Cosmological Constant as a Planck Scale Effect
• Running G and Λat low energies from physics at M_X: possible cosmological and astrophysical implications
• Are Nonrenormalizable Gauge Theories Renormalizable?
• Nonlocal action for long-distance modifications of gravity theory
• Non-perturbative effects of vacuum energy on the recent expansion of the universe
• Dark energy: a quantum fossil from the inflationary Universe?
• Renormalization Group and Decoupling in Curved Space
• Matter density perturbations in interacting quintessence models
• A cosmological constant from the QCD trace anomaly?
• Testing the running of the cosmological constant with Type Ia Supernovae at high z
• The one-loop effective action and trace anomaly in four dimensions
• Renormalization-group running cosmologies - a scale-setting procedure
• On the stability of the anomaly-induced inflation
• Covariant methods for the calculation of the effective action in quantum field theory and investigation of higher-derivative quantum gravity
• Universality and Ambiguities of the Conformal Anomaly
• On 4D-Hawing Radiation from Effective Action
• Anomaly induced effective actions and Hawking radiation
• Vacuum polarization in Schwarzschild space-time by anomaly induced effective actions
• Renormalization Group and Decoupling in Curved Space: II. The Standard Model and Beyond
• Cosmological constant, renormalization group and Planck scale physics
• Massive fields temper anomaly-induced inflation: the clue to graceful exit?
• The Running of the Cosmological and the Newton Constant controlled by the Cosmological Event Horizon
• Renormalization Group and Decoupling in Curved Space: III. The Case of Spontaneous Symmetry Breaking
• Hawking radiation by effective two-dimensional theories
• Density Perturbations for Running Cosmological Constant
• Stress Tensor from the Trace Anomaly in Reissner-Nordstrom Spacetimes
• Quantum Effects in Softly Broken Gauge Theories in Curved Space-Times
• Studying the decay of the vacuum energy with the observed density fluctuation spectrum
• Energy-momentum tensor for scalar fields coupled to the dilaton in two dimensions
• On the inflationary solutions in higher-derivative gravity with dilaton field
• Quantum discontinuity between zero and infinitesimal graviton mass with a Lambda term
• Acceleration of the universe, vacuum metamorphosis, and the large-time asymptotic form of the heat kernel
• Cosmological significance of one-loop effective gravity
• On the gravitational waves on the background of anomaly-induced inflation
• The graceful exit from the anomaly-induced inflation: Supersymmetry as a key
• On the renormalization group for the interacting massive scalar field theory in curved space
• Vacuum effects of ultra-low mass particle account for Recent Acceleration of Universe
• The Pioneer anomaly in the context of the braneworld scenario
• Running of Newton's constant and non integer powers of the d'Alembertian
• Quantum M^2 -> 2Lambda/3 discontinuity for massive gravity with a Lambda term
• Particle production from nonlocal gravitational effective action
• Renormalization Ambiguities and Conformal Anomaly in Metric-Scalar Backgrounds
• Backreaction of the Hawking radiation
• Radiation equations for black holes
• On the high derivative fermionic operator and trace anomaly
• 'Steckbrief' Lambda
• Kinematics of evaporating black holes
• Stability issues in the modified Starobinsky model
• Strong limits on the possible decay of the vacuum energy into CDM or CMB photons
• The Anomalous Trajectories of the Pioneer Spacecraft

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• Islands in Non-Minimal Dilaton Gravity: Exploring Effective Theories for Black Hole Evaporation
• Recent Progress in Fighting Ghosts in Quantum Gravity
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• Renormalization group flows and fixed points for a scalar field in curved space with nonminimal $F(\varphi )R$ coupling
• Violating the Quantum Focusing Conjecture and Quantum Covariant Entropy Bound in $d\ge 5$ dimensions
• Gravitational form factors and decoupling in 2D
• Cosmological framework for renormalization group extended gravity at the action level
• Implications on the cosmic coincidence by a dynamical extrinsic curvature
• Dark energy and dimensional transmutation in $R^2$ gravity
• Non-local gravity in bouncing cosmology scenarios
• An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions
• One-loop conformal anomaly in an implicit momentum space regularization framework
• Trace anomaly and induced action for a metric-scalar background
• Structure Formation in Non-local Bouncing Models
• Four-point functions of gravitons and conserved currents of CFT in momentum space: testing the nonlocal action with the TTJJ
• Polemic Notes On IR Perturbative Quantum Gravity
• Vacuum contribution of photons in the theory with Lorentz and CPT-violating terms
• Solar System constraints on Renormalization Group extended General Relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect
• Quantum corrections to gravity and their implications for cosmology and astrophysics
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• Vacuum driven accelerated expansion
• On analytical solutions of f(R) modified gravity theories in FLRW cosmologies
• Primordial universe with the running cosmological constant
• A Unified Universe
• Reduced quantum electrodynamics in curved space
• Scale-dependent cosmology from effective quantum gravity in the invariant framework
• Endowing $\mathbf{\Lambda }$ with a dynamic nature: constraints in a spatially curved Universe
• Spherically Symmetric Solutions in Higher-Derivative Theories of Gravity
• Gravi-Natural Higgs and Conformal New Physics
• Polymer quantization, stability and higher-order time derivative terms
• On the vector conformal models in an arbitrary dimension
• Infinite statistics, symmetry breaking and combinatorial hierarchy
• Stochastic quantization of a self-interacting nonminimal scalar field in semiclassical gravity
• Unveiling horizons in quantum critical collapse
• Quantum vacuum and accelerated expansion
• Propagator of a scalar field on a stationary slowly varying gravitational background
• Gravitational Bounce from the Quantum Exclusion Principle
• Nonlocality of quantum matter corrections and cosmological constant running
• Velocity dispersion of dark matter deficient ultra-diffuse galaxies: A case for modified gravity
• An Ultra-compact Object from Semi-classical Gravity
• Sp(2) Renormalization
• Viscosity bound versus the universal relaxation bound
• Emergent gravity and Dark Energy
• Two-loop superfield effective potential for a $\mathcal{N}=2$, $d=3$ supersymmetric quantum electrodynamics with higher derivatives
• Possibility of Spontaneous Symmetry Breaking in the Nambu-Jona-Lasinio model with torsion
• Nonlocal stress-energy tensor in time-dependent gravitational backgrounds
• Stability issues of nonlocal gravity during primordial inflation
• Two-loop effective potential for general higher-derivative superfield models
• Influence of conformal symmetry on the amplitude ratios for O($N$) models
• Spacetime Instability and Quantum Gravity as Low Energy Effective Field Theory
• Trans-Planckian quantum corrections and inflationary vacuum fluctuations of non-minimally coupled scalar fields
• Bounce and stability in the early cosmology with anomaly-induced corrections
• Anomaly Induced Inflation in the Minimal Quartic Extension of Einstein's Gravity
• Effective quantum gravity, cosmological constant and the Standard Model of particle physics
• On the functional renormalization group for the scalar field on curved background with non-minimal interaction
• NLO critical exponents of O($N$) lambda ${\varphi }^4$ scalar field theories in curved spacetime
• Introduction to Higher Order Classical Dynamics: Pais-Uhlenbeck Model and Coupled Oscillators
• Higher-derivative $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetric Maxwell-Chern-Simons theories at one loop in superspace
• Geometry-Induced Vacuum Polarization and Mode Shifts in Maxwell-Klein-Gordon Theory
• Field theory aspects of cosmology and black holes
• Anomaly-induced vacuum effective action with torsion: covariant solution and ambiguities
• Cosmology from a gauge induced gravity
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• Fermions in worldline holography
• Diffusion method in field theories with fakeons