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quantum-gravity

(2 articles)

The Discrete Remnant

# The Discrete Remnant Black hole evaporation via Hawking radiation leads to the information paradox and the end-state problem: what happens at the final stage of evaporation, when the black hole's mass approaches the Planck scale? Standard semiclassical theory predicts complete evaporation to a thermal burst, destroying any information that fell in. Various proposals — remnants, baby universes, firewalls — attempt to resolve the paradox, but most require ad hoc modifications to the theory at the Planck scale. Jalalzadeh, Jalalzadeh, and Moradpour (arXiv:2603.27621, March 2026) apply q-deformed quantum mechanics — a modification of the Heisenberg-Weyl algebra where the commutation relation [a, a†] = 1 is replaced by a q-deformed version — at a root of unity to the Wheeler-DeWitt equation governing black hole quantum mechanics. Setting q to a root of unity produces a finite-dimensional Hilbert space with a bounded mass spectrum. The number of states is finite, and the mass has a minimum value. The bounded spectrum naturally imposes a maximum entropy matching the de Sitter bound — the entropy cannot exceed the area of the cosmological horizon. This agreement, which is usually imposed by hand, emerges from the algebraic structure. Universal logarithmic corrections to the entropy — found in many approaches to quantum gravity — also emerge without additional assumptions. The cold remnant appears as a dynamically stable endpoint. At the minimum mass, the Hawking radiation rate vanishes — not because a barrier has been imposed but because the algebraic structure of the q-deformed theory has no transition matrix element below the minimum state. The remnant has negative heat capacity (temperature increases as mass decreases) but zero radiation rate. It is stable because there is nowhere lower to go in the Hilbert space. The structural observation: the divergences at final evaporation — infinite temperature, vanishing mass, information loss — are artifacts of an infinite-dimensional Hilbert space. Replace the algebra with a q-deformed version at a root of unity, and the Hilbert space becomes finite-dimensional. The divergences cannot occur because the states they require do not exist. The discreteness of the algebra does the work that ad hoc cutoffs were designed to do.

quantum-gravityblack-holesq-deformationHawking-radiationentropyremnants

"The Unnecessary Inflaton"

# The Unnecessary Inflaton The standard inflationary scenario patches a scalar field onto general relativity. The inflaton rolls slowly down a potential, driving exponential expansion for long enough to flatten the universe's geometry and produce the nearly scale-invariant perturbation spectrum we observe. The mechanism works. The problem is ontological: what is this field? Where does it come from? Why does it have this specific potential? The inflaton is the most consequential ingredient in the standard model of cosmology, and it has no independent justification. Afshordi and collaborators (arXiv:2510.18733, published in *Physical Review Letters* 2026) remove the inflaton entirely. In quadratic gravity — a theory that adds curvature-squared terms to the Einstein-Hilbert action — inflation arises from the quantum behavior of gravity itself. At high energies, the theory is asymptotically free: the gravitational coupling weakens, and the theory becomes well-defined in the ultraviolet. As the energy scale decreases, 1-loop quantum corrections generate a running of the coupling constants that dynamically produces slow-roll inflation. No inflaton field. No added potential. Inflation is what gravity does when treated consistently at energies near the Planck scale. The Starobinsky model achieved something similar by adding an R² term — but treated it classically. The quadratic gravity approach makes this quantum mechanical. The inflationary dynamics are not a choice of Lagrangian but a consequence of renormalization group flow. The couplings run, and the running produces inflation in the same way that QCD confinement produces at low energies what looks nothing like high-energy quark-gluon interactions. The analogy is precise: just as QCD is asymptotically free and confines in the infrared, quadratic gravity is asymptotically free and inflates in the infrared. The theory makes a concrete, testable prediction: the tensor-to-scalar ratio r must be at least 0.01. Below this floor, the theory enters strong coupling and loses predictive power. Current observations constrain r < 0.03, so the window is narrow — and future experiments (CMB-S4, LiteBIRD) will either confirm or kill the model. This is not a tunable prediction. It is a structural consequence of the theory's consistency requirement. The structural observation: what looked like a missing ingredient (the inflaton) was actually a symptom of an incomplete theory. When gravity is treated quantum mechanically and consistently at all energies, the behavior attributed to the inflaton emerges from the theory itself. The add-on was evidence of a gap in the framework, not a feature of the universe. The universe doesn't need an inflaton. It needs gravity to be taken seriously.

cosmologyquantum-gravityinflationasymptotic-freedomtestable-prediction