Classically scale-invariant (and perturbative) theories provide a way to understand large hierarchies, as scales are generated through dimensional transmutation. They always lead to first-order phase transitions, since symmetries are radiatively broken, and they generically feature quasiflat potentials, which are suitable for inflation. We construct a simple but fully realistic model of this kind that accounts for all observational evidence of new physics and is remarkably compatible with the most recent constraints on inflationary observables from both the Planck/BICEP/Keck and the Atacama Cosmology Telescope Collaborations. This model illustrates how classical scale invariance generically leads to a nonstandard cosmology in which inflation occurs in two stages: a slow-roll stage and a thermal stage, separated by a radiation-dominated era.

Italy

Filippo Cutrona

Francesco Rescigno

Alberto Salvio

ACT-Planck data and phase transitions from a viable no-scale Standard Model completion

We examine the impact on the phenomenology of the minimal supersymmetric SU(5) Grand Unified Theory (GUT) of dimension-5 operators with coefficients suppressed by the Planck mass scale, with particular emphasis on predictions for nucleon decay. We incorporate dimension-5 operators in both the Higgs sector and the Yukawa interactions in the theory, and take account of the constraints from gauge coupling measurements, the mass of the Higgs boson, fermion masses and the cold dark matter density. We consider two scenarios for soft supersymmetry breaking: the constrained minimal supersymmetric extension of the Standard Model (CMSSM) and the Non-Universal Higgs Model (NUHM). We present predictions for the nucleon decay modes $$p \rightarrow \pi ^0 e^+, \pi ^0 \mu ^+, K^+ \bar{\nu }, \pi ^+ \bar{\nu }$$ , $$K^0 e^+, K^0 \mu ^+$$ and $$n\rightarrow \pi ^0 \bar{\nu }$$ , $$\pi ^- e^+, K^0 \bar{\nu }$$ , which we compare with both the present experimental sensitivities and those projected for the JUNO and Hyper-Kamiokande experiments. We find that these experiments may have interesting possibilities for discovering several of these decay modes.

Estonia

United Kingdom

Switzerland

John Ellis

China

United States

Jason Evans

Shihwen Hor

Japan

Natsumi Nagata

Keith Olive

Planck-scale effects on nucleon decay in minimal supersymmetric SU(5)

We develop a framework for testing quantum gravity through the stochastic gravitational-wave background produced by evaporating near-Planck-mass primordial black holes. Because gravitons freestream from the emission region without rescattering, they preserve a direct spectral record of the black-hole temperature–mass relation <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo stretchy="false">(</mo><mi>M</mi><mo stretchy="false">)</mo></math>, a relation that is erased for all other Hawking-radiated species by rapid thermalization. We translate six representative phenomenological beyond-semiclassical frameworks (the generalized uncertainty principle, loop quantum gravity, noncommutative geometry, asymptotic safety, string/Hagedorn physics, and tunneling backreaction) into distinct <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo stretchy="false">(</mo><mi>M</mi><mo stretchy="false">)</mo></math> parameterizations and compute the resulting gravitational-wave spectra numerically within a hybrid semiclassical-phenomenological framework. Modifications that suppress <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>T</mi><mo stretchy="false">(</mo><mi>M</mi><mo stretchy="false">)</mo></mrow></math> shift the spectral peak by up to 10 decades in frequency, in some cases into the sensitivity bands of next-generation interferometers or resonant-cavity detectors, while models imposing a hard evaporation cutoff produce distinctive peak morphologies that distinguish between phenomenological classes of modified evaporation. We further discuss the impact of different choices for post-inflationary conditions in the very early Universe and note that breaking the remaining cosmological degeneracies and connecting these signatures to specific quantum-gravity theories requires complementary observables. We find that the relative spectral displacement between the standard Hawking prediction and any modified model is cosmology-independent, and hence spectral shape rather than absolute peak frequency provides the cleanest probe of Planck-scale physics.

Stefano Profumo

Probing Planck-scale physics with high-frequency gravitational waves

Determining whether Planck-scale effects can stabilize black holes addresses fundamental questions about black hole evaporation and quantum gravity consistency. Here, we analyze the thermodynamic topology ofSchwarzschild black holes under Planck-scale modified kinematics, using a cubic entropy correction derived from a well-known phenomenological MDR with leading correction $$\eta E^3/E_P$$ . Enforcing physical constraints ( $$S'(r_h) > 0$$ , $$T > 0$$ ) via the entropy-geometry correspondence, we find a single unstable branch with $$w = -1$$ and $$W = -1$$ for both signs of the correction parameter. A second root suggesting stability ( $$w = +1$$ ) is excluded due to negative mass/temperature and lies outside the perturbative regime. Thus, this class of MDRs does not yield stable Schwarzschild black holes. However, MDRs with different leading-order corrections may behave otherwise, leaving the search for Planck-scale stabilization an open endeavor.

Iran

Azerbaijan

Mohsen Khodadi

Kazakhstan

Nosratolla Jafari

Shahin Mamedov

A winding number analysis of Schwarzschild black hole stability in light of Planck-scale modified kinematics

We consider a Universe with a three-torus topology, which before inflation is devoid of any matter or radiation. Its preinflationary evolution is driven solely by Casimir energies of the existing fields, with a radiationlike equation of state. We show that, under natural assumptions and with the appropriate number of fermions and bosons in the theory, such a Universe can start its evolution from a Planck size at the Planck time. Moreover, assuming typical parameters for inflation and reheating, the three-torus Universe can be several Hubble radii across at present time, which is precisely the size hinted by the anomaly in the cosmic microwave background observed at low multipole moments. We derive a relation between the size of the Universe, the number of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>e</mi></mrow></math>-folds of inflation, and the energy density decrease during reheating, which we then use to determine the parameter values consistent with the anomaly and the lower bound on the size of the Universe from the Planck satellite.

Bartosz Fornal

Universe originating from an empty Planck-size torus

In this paper, a generalized Dunkl-Fokker-Planck equation in <math altimg='si1.svg'><mrow><mo>(</mo><mn>1</mn><mo linebreak='goodbreak'>+</mo><mn>1</mn><mo>)</mo></mrow></math> dimensions is formulated within a fractional calculus setting based on the Riemann-Liouville (RL) derivative. In this case, the construction employs reflection-deformed operators to represent parity-dependent structures together with nonlocal memory contributions characteristic of fractional evolution. Also, the associated Wigner-Dunkl supersymmetric (SUSY) framework is developed, providing a consistent algebraic structure that extends standard supersymmetry under fractional dynamics. Moreover, the system is examined for a harmonic oscillator potential combined with a centrifugal-type interaction, where the coupling between Dunkl deformation and fractional order produces modified dynamical behavior and effective transport properties. By applying an exact Foldy-Wouthuysen (FW) transformation, a nonlocal relativistic operator form of the system is obtained, yielding a closed fractional Dunkl structure governed by RL dynamics. In addition, a higher-order Foldy-Wouthuysen reduction is used to derive effective Dunkl-Fokker-Planck evolution equations from reflection-deformed relativistic quantum systems. In this context, the resulting formulation establishes a unified description of fractional diffusion, relativistic corrections, and Dunkl symmetry within an operator-based framework, with applications to generalized quantum transport and deformed statistical systems.

Algeria

Abdelmalek Bouzenada

Fractional Dunkl-Fokker-Planck operators in supersymmetric (SUSY) quantum state under Foldy-Wouthuysen (FW) transformation

Employing the generalized free energy landscape and solving the associated Fokker–Planck equation, we obtain the time-dependent probability evolution of the order parameter for the RN-AdS black hole phase transitions. Our analysis reveals two distinct kinetic regimes, namely relaxation dynamics initialized at the unstable maximum and phase transition from the metastable state. Furthermore, we characterize the non-equilibrium irreversibility and macroscopic uncertainty using the entropy production rate and the Shannon entropy. The results demonstrate that the phase transition synchronizes exactly with a prominent peak in the entropy production rate, identifying the barrier crossing event as a process fundamentally driven by maximum thermodynamic dissipation.

Chao Wang

Chen Ma

Meng-Ci He

Bin Wu

Probabilistic evolution of black hole thermodynamic states via Fokker–Planck equation

Quantum gravity (QG) has a natural cutoff given by the Planck scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>pl</mi></msub></math>. However, it is known that the effective field theory (EFT) of gravity can break down at a lower scale, the species scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>s</mi></msub><mo>≲</mo><msub><mi>M</mi><mi>pl</mi></msub></math>, if there are light species of particles. Here we point out that there is a third scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub><mo>≲</mo><msub><mi mathvariant="normal">Λ</mi><mi>s</mi></msub><mo>≲</mo><msub><mi>M</mi><mi>pl</mi></msub></math>, which marks the inverse length (or the temperature) of the smallest black hole where the EFT gives a correct description of its entropy and free energy. This latter scale is hard to detect from the viewpoint of EFT as it represents a phase transition to a state with lower free energy. We illustrate this using examples drawn from consistent QG landscape. In particular <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub></math> gets related to Gregory-Laflamme transition in the decompactification limits of quantum gravity and to the Horowitz-Polchinski solution in the light perturbative string limits. We propose the existence of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub></math> marking the temperature at which neutral black holes undergo a phase transition, as a new Swampland condition for all consistent quantum theories of gravity. In the asymptotic regimes of field space <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub></math> is close to the mass scale of the lightest tower but deviates from it as we move inwards in the moduli space.

Alek Bedroya

Cumrun Vafa

David H. Wu

Tale of three scales: The Planck, the species, and the black hole scales

The maximum number of irreversible bit operations a Schwarzschild black hole can support is computed from Landauer’s principle applied at the asymptotic Hawking temperature, the frame in which the ADM mass-energy and the thermal radiation spectrum are both defined. The result is exact: <math altimg='si1.svg'><mrow><msub><mi>N</mi><mi>max</mi></msub><mo linebreak='goodbreak'>=</mo><mn>2</mn><mspace width='0.16em' /><msub><mi>N</mi><mtext>BH</mtext></msub></mrow></math>, where <italic>N</italic> <inf>BH</inf> is the Bekenstein&#8211;Hawking entropy measured in bits. The factor of two follows algebraically from the Smarr formula <math altimg='si2.svg'><mrow><mi>M</mi><msup><mi>c</mi><mn>2</mn></msup><mo linebreak='goodbreak'>=</mo><mn>2</mn><mspace width='0.16em' /><msub><mi>T</mi><mi>H</mi></msub><msub><mi>S</mi><mtext>BH</mtext></msub></mrow></math> and requires no assumptions beyond semiclassical black hole thermodynamics and Landauer&#8217;s principle. This identity admits a natural interpretation through the chiral structure of the two-dimensional horizon: a compact surface supports independent left-moving and right-moving excitations, doubling the processing capacity relative to single-sector storage. For Kerr black holes, the Kerr/CFT correspondence maps the rotational work term in the Smarr formula entirely to the right-moving chiral sector, yielding an asymmetric decomposition <math altimg='si3.svg'><mrow><msub><mi>N</mi><mi>max</mi></msub><mo linebreak='goodbreak'>=</mo><mn>2</mn><mspace width='0.16em' /><msub><mi>N</mi><mi>L</mi></msub><mo linebreak='goodbreak'>+</mo><mn>2</mn><mspace width='0.16em' /><msub><mi>N</mi><mi>R</mi></msub><mspace width='0.16em' /><msup><mi>M</mi><mn>2</mn></msup><mo linebreak='goodbreak'>/</mo><mrow><mo>(</mo><msup><mi>M</mi><mn>2</mn></msup><mo linebreak='badbreak'>&#8722;</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math> in which the left-moving processing capacity is independent of spin. The processing-to-storage ratio exceeding unity has a direct bearing on the information paradox: it ensures sufficient throughput for complete information processing during Hawking evaporation.

Kurtis Kemple

A Landauer bound on black hole information processing: <math altimg='si1.svg'><mrow><msub><mi>N</mi><mi>max</mi></msub><mo linebreak='goodbreak'>=</mo><mn>2</mn><mspace width='0.16em' /><msub><mi>N</mi><mtext>BH</mtext></msub></mrow></math>

We investigate the thermodynamic behavior of a spherically symmetric Anti-de Sitter black hole in Mod(A)Max electrodynamics surrounded by a cloud of strings. Within the extended phase-space framework, we treat the cosmological constant as a pressure and interpret the black-hole mass as enthalpy, which enables a unified discussion of local stability, global phase structure, and Joule–Thomson expansion. We analyze the Hawking temperature, Gibbs free energy, and heat capacity, and show how the string-cloud parameter, the Mod(A)Max deformation, and the electric charge reshape the physical domain, the stability windows, and the small/large black-hole transition pattern. We further characterize the critical behavior and demonstrate that a van der Waals–like phase structure arises only in the physical sector, while the alternate branch does not admit a genuine critical point. For the Joule-Thomson process, we determine the inversion curve and the corresponding isenthalpic trajectories, highlighting how the model parameters control the cooling/heating regimes and can generate terminating isenthalpic behavior at sufficiently large charge. Finally, we examine the sparsity of Hawking radiation and discuss how the underlying parameters influence the temporal discreteness of the emitted flux, particularly near extremality and in the large-radius AdS regime.

India

Faizuddin Ahmed

Jordan

Ahmad Al-Badawi

Brazil

Edilberto O. Silva

Thermal analysis, Joule-Thomson expansion and Hawking sparsity of Mod(A)Max-AdS black hole immersed in a cloud of strings