Non-singular gravity with regulator ℓ induces a PBH mass gap ~c²ℓ/G and a stronger Carr criterion δ_H > 2GM_gap/R_H - 1 when R_H ~ ℓ.
Quadratic Gravity
8 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Adding terms quadratic in the curvature to the Einstein-Hilbert action renders gravity renormalizable. This property is preserved in the presence of the most general renormalizable couplings with (and of) a generic quantum field theory (QFT). The price to pay is a massive ghost, which is due to the higher derivatives that the terms quadratic in the curvature imply. In this paper the quadratic gravity scenario is reviewed including recent progress on the related stability problem of higher derivative theories. The renormalization of the theory is also reviewed and the final form of the full renormalization group equations in the presence of a generic renormalizable QFT is presented. The theory can be extrapolated up to infinite energy through the renormalization group if all matter couplings flow to a fixed point (either trivial or interacting). Moreover, besides reviewing the above-mentioned topics some further insight on the ghost issue and the infinite energy extrapolation is provided. There is the hope that in the future this scenario might provide a phenomenologically viable and UV complete relativistic field theory of all interactions.
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Extra spin-2 in quadratic gravity is a dual inverted harmonic oscillator with vanishing Källén–Lehmann density, fixing a principal-value propagator and preserving unitarity with renormalizability.
Complex poles in the ghost propagator induce persistent interactions at asymptotic times, rendering negative-norm ghost states indistinguishable from superpositions of positive-norm multi-particle states and eliminating free asymptotic ghost particles.
Ghosts lack asymptotic particle interpretation due to interference and different Riemann-sheet pole structures compared to decaying unstable particles, with finite-time effects producing narrower resonances and higher peaks.
Tree-level amplitudes in agravity-coupled QED produce differential cross sections scaling universally as dσ/dΩ ∝ 1/s at ultra-Planckian energies across multiple channels.
Apparent exponential growth of metric perturbations in the Newtonian gauge for quadratic-gravity inflation is gauge-dependent and non-generic; other gauges remain well-behaved.
The inverted harmonic oscillator and its dual are argued to underpin a unique unitary renormalizable quantum gravity in four dimensions, yielding a non-singular universe and Starobinsky inflation.
Generalized Einsteinian cubic gravity admits a de Sitter solution from the P cubic term alone; stability analysis is incomplete until the R^2 term is added, which leaves the solution value unchanged.
citing papers explorer
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Carr criterion and mass gaps in non-singular primordial black hole formation
Non-singular gravity with regulator ℓ induces a PBH mass gap ~c²ℓ/G and a stronger Carr criterion δ_H > 2GM_gap/R_H - 1 when R_H ~ ℓ.
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Unitary Quadratic Quantum Gravity in 4D
Extra spin-2 in quadratic gravity is a dual inverted harmonic oscillator with vanishing Källén–Lehmann density, fixing a principal-value propagator and preserving unitarity with renormalizability.
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Asymptotic Quantum Dynamics of Ghost Fields
Complex poles in the ghost propagator induce persistent interactions at asymptotic times, rendering negative-norm ghost states indistinguishable from superpositions of positive-norm multi-particle states and eliminating free asymptotic ghost particles.
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Ghosts versus Unstable Particles in Quantum Field Theory
Ghosts lack asymptotic particle interpretation due to interference and different Riemann-sheet pole structures compared to decaying unstable particles, with finite-time effects producing narrower resonances and higher peaks.
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Scattering amplitudes in dimensionless quadratic gravity coupled to QED
Tree-level amplitudes in agravity-coupled QED produce differential cross sections scaling universally as dσ/dΩ ∝ 1/s at ultra-Planckian energies across multiple channels.
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Gauge-independent approach to inflation in quadratic gravity
Apparent exponential growth of metric perturbations in the Newtonian gauge for quadratic-gravity inflation is gauge-dependent and non-generic; other gauges remain well-behaved.
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The Saddle Point of Everything
The inverted harmonic oscillator and its dual are argued to underpin a unique unitary renormalizable quantum gravity in four dimensions, yielding a non-singular universe and Starobinsky inflation.
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Effect of $R^2$ on the stability of de Sitter solution of the generalized Einsteinian cubic gravity
Generalized Einsteinian cubic gravity admits a de Sitter solution from the P cubic term alone; stability analysis is incomplete until the R^2 term is added, which leaves the solution value unchanged.