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.
Calcagni,Multifractional theories: an unconventional review,JHEP03(2017) 138; Erratum-ibid.06(2017) 020 [arXiv:1612.05632]
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abstract
We answer to 72 frequently asked questions about theories of multifractional spacetimes. Apart from reviewing and reorganizing what we already know about such theories, we discuss the physical meaning and consequences of the very recent flow-equation theorem on dimensional flow in quantum gravity, in particular its enormous impact on the multifractional paradigm. We will also get some new theoretical results about the construction of multifractional derivatives and the symmetries in the yet-unexplored theory $T_\gamma$, the resolution of ambiguities in the calculation of the spectral dimension, the relation between the theory $T_q$ with $q$-derivatives and the theory $T_\gamma$ with fractional derivatives, the interpretation of complex dimensions in quantum gravity, the frame choice at the quantum level, the physical interpretation of the propagator in $T_\gamma$ as an infinite superposition of quasiparticle modes, the relation between multifractional theories and quantum gravity, and the issue of renormalization, arguing that power-counting arguments do not capture the exotic properties of extreme UV regimes of multifractional geometry, where $T_\gamma$ may indeed be renormalizable. A careful discussion of experimental bounds and new constraints are also presented.
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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 of the Clausius relation.
If Hawking's area law is taken as exact, nonlocal and Stelle quantum-gravity theories are forced to drop R^2 and (Riemann)^2 terms (or use singular Ricci-flat black holes), and the standard entropy-area law follows as a consequence.
Fractional-Dimension Gravity reproduces Milky Way rotation curves via a variable dimension D(R) fitted to Gaia data without dark matter.
citing papers explorer
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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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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 of the Clausius relation.
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Hawking area law in quantum gravity
If Hawking's area law is taken as exact, nonlocal and Stelle quantum-gravity theories are forced to drop R^2 and (Riemann)^2 terms (or use singular Ricci-flat black holes), and the standard entropy-area law follows as a consequence.
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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.