Quantum field theory, gravity and cosmology in a fractal universe

Abstract

We propose a model for a power-counting renormalizable field theory living in a fractal spacetime. The action is Lorentz covariant and equipped with a Stieltjes measure. The system flows, even in a classical sense, from an ultraviolet regime where spacetime has Hausdorff dimension 2 to an infrared limit coinciding with a standard $D$-dimensional field theory. We discuss the properties of a scalar field model at classical and quantum level. Classically, the field lives on a fractal which exchanges energy-momentum with the bulk of integer topological dimension D. Although an observer experiences dissipation, the total energy-momentum is conserved. The field spectrum is a continuum of massive modes. The gravitational sector and Einstein equations are discussed in detail, also on cosmological backgrounds. We find ultraviolet cosmological solutions and comment on their implications for the early universe.

42 pages, 4 figures. v2: discussion improved.

References in corpus (14)

• Quantum Gravity at a Lifshitz Point
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Fractal universe and quantum gravity
• Lorentz symmetry breaking as a quantum field theory regulator
• Cosmology of the Lifshitz universe
• Fractal properties of quantum spacetime
• Fractional Action-Like Variational Problems
• Renormalization group in Lifshitz-type theories
• Detailed balance in Horava-Lifshitz gravity
• Cosmological Bardeen-Cooper-Schrieffer condensate as dark energy
• The cosmological BCS mechanism and the Big Bang Singularity
• Constants of motion for fractional action-like variational problems
• Power-counting renormalizability of generalized Horava gravity
• Phenomenology of scale-dependent space-time dimension

Cited by in corpus (86)

• Super-renormalizable Quantum Gravity
• Fractal universe and quantum gravity
• Cosmological Evolution With Interaction Between Dark Energy And Dark Matter
• Review of Some Promising Fractional Physical Models
• Geometry and field theory in multi-fractional spacetime
• Vector Calculus in Non-Integer Dimensional Space and its Applications to Fractal Media
• Entropic force, noncommutative gravity and ungravity
• Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data
• Anisotropic Fractal Media by Vector Calculus in Non-Integer Dimensional Space
• Inflation in (Super-)renormalizable Gravity
• The R^2 phase-diagram of QEG and its spectral dimension
• Detecting Vanishing Dimensions Via Primordial Gravitational Wave Astronomy
• Thermodynamics of photons on fractals
• Gravity on a multifractal
• Multifractional theories: an unconventional review
• Multi-scale gravity and cosmology
• Diffusion on $\kappa$-Minkowski space
• Diffusion in multiscale spacetimes
• Asymptotic Safety, Fractals, and Cosmology
• Cosmology under the fractional calculus approach
• Fractional and noncommutative spacetimes
• Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes
• Regular black holes in UV self-complete quantum gravity
• de Sitter Fractional Quantum Cosmology
• Quantum mechanics in fractional and other anomalous spacetimes
• Multiscale spacetimes from first principles
• Discrete to continuum transition in multifractal spacetimes
• Diffusion in quantum geometry
• Thermodynamics of Fractal Universe
• Multifractional theories: an updated review
• Fractional Einstein-Hilbert Action Cosmology
• Cosmic microwave background and inflation in multi-fractional spacetimes
• Pre-inflationary primordial perturbations
• Tsallis holographic dark energy in Fractal Universe
• Revisiting Fractional Cosmology
• Holographic, new agegraphic and ghost dark energy models in fractal cosmology
• Quantum scalar field theories with fractional operators
• Exact solutions and cosmological constraints in fractional cosmology
• Dark energy in multi-fractional spacetimes
• Spectral dimension and diffusion in multi-scale spacetimes
• Does fractal Universe describe a complete cosmic scenario?
• Estimated Age of the Universe in Fractional Cosmology
• Coupling running through the Looking-Glass of dimensional Reduction
• An interacting New Holographic Dark Energy in the framework of fractal cosmology
• Varying electric charge in multiscale spacetimes
• Metric dimensional reduction at singularities with implications to Quantum Gravity
• Dimensional flow and fuzziness in quantum gravity: emergence of stochastic spacetime
• Symmetries and propagator in multifractional scalar field theory
• Study of Tsallis holographic dark energy model in the framework of Fractal cosmology
• Parity violation in pre-inflationary bounce
• Signal propagation on $\kappa$-Minkowski spacetime and non-local two-point functions
• Deformed symmetries in noncommutative and multifractional spacetimes
• Fractional Scalar Field Cosmology
• FRW model with Two -- fluid Source in fractal cosmology
• Standard Model in multiscale theories and observational constraints
• Introduction to multifractional spacetimes
• Emergence of fractal cosmic space from fractional quantum gravity
• Parametrizations of Dark Energy Models in the Background of General Non-canonical Scalar Field in $D$-dimensional Fractal Universe
• Gravitational potential and galaxy rotation curves in multi-fractional spacetimes
• The Geometry of Black Hole singularities
• The Legendre Condition of the Fractional Calculus of Variations
• Conformal and Non-Minimal Couplings in Fractional Cosmology
• Observational constraints on the fractal cosmology
• Fractional Derivative Regularization in QFT
• Unitary Standard Model from Spontaneous Dimensional Reduction and Weak Boson Scattering at the LHC
• Fractal FRW Model within Domain Wall
• Spontaneous Spacetime Reduction and Unitary Weak Boson Scattering at the LHC
• A consistent quantum field theory from dimensional reduction
• Interacting dark energy models in fractal cosmology
• On the depth of quantum space
• Geometry of fractional spaces
• Newtonian Fractional-Dimension Gravity and Galaxies without Dark Matter
• Generalized Ghost Pilgrim Dark Energy Fractal Cosmology with Observational Constraint
• Multifractional spacetimes from the Standard Model to cosmology
• AdS cycles in eternally inflating background
• Gravitational Foundations and Exact Solutions in $n$-Dimensional Fractional Cosmology
• Quantum Field Theory in fractal space-time with negative Hausdorff-Colombeau dimensions.The solution cosmological constant problem
• The Spectrum of Low-$p_T$ $J/\psi$ in Heavy-Ion Collisions in a Statistical Two-Body Fractal Model
• Spacetime Foam Effects on Charged AdS Black Hole Thermodynamics
• Minimal Proper-time in Quantum Field Theory
• Emergent $\Lambda$CDM cosmology from a measure-induced deformation of the Newtonian action
• Inflation and Primordial Perturbations in Fractal Cosmology
• Quantum Field Theory on Multifractal Spacetime: Varying Dimension and Ultraviolet Completeness
• Investigation of Dephasing In an Open Quantum System under Chaotic Influence via a Fractional Kohn-Sham Scheme
• Relativistic Fractional-Dimension Gravity
• Cosmology of fractional gravity