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Fractal universe and quantum gravity
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We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.
Forward citations
Cited by 8 Pith papers
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Cosmology of fractional gravity
Fractional gravity yields stable de Sitter expansion and exact bouncing solutions driven by phantom (w < -1) or ghost (negative energy) fluids, with results independent of the form-factor representation.
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Tests of General Relativity with the Binary Black Hole Signals from the LIGO-Virgo Catalog GWTC-1
Binary black hole signals in GWTC-1 are consistent with general relativity predictions, with an improved graviton mass bound of mg ≤ 4.7 × 10^{-23} eV/c² at 90% credible level.
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Noether charges and the first law of thermodynamics for multifractional Schwarzschild black hole in the q-derivative theory
Multi-fractional Schwarzschild black holes have profile-insensitive Noether mass and geometric area-law entropy, but require an extended first law with work terms for the q-profile parameters to restore integrability ...
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Quantum-Deformed Phase-Space Geometry and Emergent Inflation in Effective Four-Dimensional Spacetime
Quantum deformation of projective phase-space geometry induces a conformally deformed FLRW metric whose time-dependent corrections modify inflationary background equations, slow-roll parameters, and perturbations in a...
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Probing modified gravitational-wave dispersion with bursts from eccentric black-hole binaries
Applies parameterized dispersion to eccentric BBH burst waveforms, deriving a 2.5PN time-delay correction and Bessel amplitude modulation, then uses Fisher matrix to project LIGO constraints that are stronger than cur...
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Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog
No evidence for deviations from general relativity is found in LIGO-Virgo binary black hole events, with improved constraints on waveform parameters, graviton mass, and ringdown properties.
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Fractional-Dimension Gravity and the Milky Way Galaxy
Fractional-Dimension Gravity reproduces Milky Way rotation curves via a variable dimension D(R) fitted to Gaia data without dark matter.
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Tests of General Relativity with GWTC-3
No evidence for physics beyond general relativity is found in the analysis of 15 GW events from GWTC-3, with consistency in residuals, PN parameters, and remnant properties.
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