Papers

We explicitly compute the axial anomaly in dense matter and show that its form remains unchanged from that in vacuum, even in the massless limit. This result follows from a subtle cancellation in the anomalous Ward identity between the medium-induced contributions to the divergence of the axial current and to the pseudoscalar density. We then revisit the chiral magnetic effect in a fermionic medium coupled to an axial chemical potential under an external magnetic field. We show that the medium supports a persistent, conserved anomalous current carried by fermions. The current is determined by the axial chemical potential and suppressed by the Fermi velocity, in agreement with anomalous axial-current correlation functions. We finally discuss applications to axion physics, where axion dark matter acts as an effective axial chemical potential.

A nontopological soliton of the Q-ball type in a Chern-Simons-Higgs gauge model is studied using both analytical and numerical methods. The general non-self-dual case is considered. It is shown that the soliton solution is an extremum of the energy functional at a fixed Noether charge. A differential relation between the energy, Noether charge, and the boundary value of the gauge potential of the soliton is derived. A linear relation between the components of the soliton energy is obtained. The parametric domain of existence of the soliton solution is determined. It is established that the soliton properties depend significantly on the form of the self-interaction potential of the scalar field. In particular, the energy and charge of the soliton can take arbitrarily large values only if the self-interaction potential has two degenerate zero minima.

Non-invertible symmetries in quantum many-body systems generally give rise to sequential unitary circuits that move symmetry defects. In this paper, we investigate invariants defined by sequences of such circuits, which move non-invertible defects and generate a Berry phase evaluated on quantum states with defects. We show that this Berry phase generally defines an invariant under local deformations, provided that the sequential circuits preserve the locality of those deformations. This invariant also rules out a short-range-entangled state that preserves the non-invertible symmetry, thereby signaling the 't Hooft anomaly of a non-invertible symmetry purely in terms of unitary operators acting on a state. We then apply this framework to loop excitations in three spatial dimensions and identify a new loop excitation in the (3+1)D $\mathbb{D}_4$ topological order, which we dub a non-Abelian fermionic loop. Using the invariant of sequential circuits, we characterize the statistics of non-Abelian fermionic loops. In addition, we find a new (3+1)D mixed topological order with a single non-Abelian fermionic loop, whose long-range entanglement is protected by an invariant of sequential circuits.

In the Euclidean view one must first require that positivity not be violated, and from this modest demand, together with locality, a great deal follows: starting from a reflection-positive lattice formulation of pure SU(N) Yang-Mills theory we obtain a transfer operator with a uniform gap, while large Wilson loops already show an area law by means of convergent character (polymer) expansions; a finite-range, gauge-covariant multiscale analysis then carries these features from one scale to the next with interlaced inequalities whose small defects can be summed, so that exponential clustering and a strictly positive string tension endure in the continuum; the Osterwalder-Schrader reconstruction turns these Euclidean facts into a Minkowski theory with a self-adjoint Hamiltonian, the spectral gap lying above the vacuum and the linear potential for static charges appearing, which gives a concrete picture of confinement; the construction depends on no special regulator, for a single-scale Lipschitz control and a telescoping argument bind all admissible reflection-positive slicings into a unique limiting measure and thus secure universality; moreover, the same framework admits entry from weak coupling, so that the continuum reached from strong coupling meets the one approached along an asymptotically free trajectory, yielding one and the same theory; in my view this is how mathematical clarity and physical insight cooperate: positivity, locality, and renormalization working together so that the mass gap and confinement are not marvels to be assumed, but natural properties of the non-Abelian vacuum.

In this paper, we investigate the sparsity of black hole radiation, the Bekenstein entropy loss, and the total particle emission of a Schwarzschild black hole (SBH) within the framework of non-commutative (NC) gauge theory of gravity. First, we provide a brief review of black hole (BH) thermodynamics, computing both the deformed Hawking temperature and entropy. In this geometry, the divergent behavior of the temperature is removed, and a logarithmic correction to the entropy emerges. We then present the NC corrections to the Bekenstein entropy loss of the SBH alongside the total number of emitted particles. Our results show that the total number of emitted particles is proportional to the entropy behavior of the NC SBH, which is consistent with non-thermal radiation. Finally, we analyze the sparsity of Hawking radiation in this geometry, finding that the NC SBH exhibits extremely sparse radiation ($\hat{\eta} \gg 1$), which diverges at the final stage of evaporation as the black hole ceases to radiate.

Infinitesimal deformations of $\text{AdS}_5 \times \mathbb{S}^5$ form a representation of the AdS supersymmetry algebra. The structure of this representation has not yet been completely described in the literature. Some information can be obtained just from the fact that the space of deformations is the cohomology of a nilpotent BRST operator. We can consider the bicomplex formed by the BRST operator and the Lie cohomology differential, and its two spectral sequences. Their matching imposes some constraints on the structure of representations, which we start exploring in this paper. In particular, we clarify the structure of ghost number three zero modes.

We perform a Hamiltonian constraint analysis of metric $f(R)$ gravity in the Jordan frame and show that the regular constraint classification degenerates on singular phase-space surfaces located at $f'(R)\!=\!0$ and $f''(R)\!=\!0$. We then study the perturbative implications of these surfaces. For exact backgrounds satisfying $f(R)\!=\!0$ and $f'(R)\!=\!0$, the linearized spectrum is empty; the known pure $R^2$ result is therefore a special case of a more general degeneracy in $f(R)$ gravity. We also show that FLRW trajectories in the Starobinsky model can cross the surface $f'(R)=0$, but that inhomogeneous perturbations develop a degenerate constraint structure at the crossing. The resulting crossing condition is better interpreted as a regularity condition for perturbative evolution than as an ordinary constraint within the Dirac–Bergmann algorithm. Together, these results distinguish backgrounds that lie entirely on a singular surface from backgrounds that cross one dynamically, and show that the two situations lead to different perturbative degeneracies.

We recast Einstein's equations as ordinary integro-differential equations for the worldlines, integrating out the gravitational field by means of the Schwinger-Keldysh path integral. The same framework allows the gravitational waveform to be computed for unspecified orbits. The two computations are independent: solutions of the equations of motion can then be inserted to reconstruct the waveform for generic orbits. The derivation of the equations of motion does not require a map between scattering and bound-orbit observables. Thus, it could be implemented within an Effective One-Body-inspired framework, with the advantage that retardation and radiation effects are automatically included: no separation between potential and radiation modes is required. Conversely, the waveform computation may provide an alternative to the Effective One-Body approach, if supplemented by suitable resummation schemes. We emphasise that computations in this framework bypass the need for integration-by-parts identities, which are the main technical bottleneck in the computation of observables. In this paper, we outline the general framework and present a computational strategy at leading and next-to-leading order in the weak-field expansion.

Wormholes that are traversable in principle offer fascinating insights into general relativity, yet they typically require exotic matter and suffer from stability issues. We construct a thin-shell wormhole by gluing two copies of a quantum-corrected, regular spacetime obtained from string T-duality. This regularisation replaces the classical curvature singularity with a smooth core and introduces a fundamental length scale $l_0$. For the static configuration, we derive the surface stresses and show that, unlike the Schwarzschild case, the null and strong energy conditions can be satisfied for sufficiently large throat radii. A linearised stability analysis reveals a rich landscape: close to the minimum allowed throat radius the configuration is unstable; at intermediate radii ($a \sim l_0$) the geometric stability threshold becomes negative, yielding a window of unconditional stability where any convex surface mass function suffices; at large radii the wormhole recovers Schwarzschild-like behaviour and stability requires a stiff equation of state. The T-duality scale $l_0$ is thus not merely a regulariser but a key physical parameter that opens a novel region of unconditional stability absent in classical thin-shell wormholes. Our results suggest that quantum-gravity-motivated modifications can simultaneously cure singularities and make traversable wormholes dynamically viable, providing new targets for gravitational-wave astronomy and theoretical studies of exotic compact objects.

These lecture notes are intended as a coherent introduction to conformal field theory in general, and composite operators in particular, through a semiclassical framework for computing scaling dimensions, with emphasis on operators of the form $\phi^n$. In doing so, they aim to fill a gap in the literature and to help decode some of the relevant concepts. The physical idea is that at large $n$ an (heavy) operator creates a highly occupied state. Through the state-operator correspondence, this state lives on the cylinder $\mathbb{R}\times S^{d-1}$, and its scaling dimension is the corresponding energy of the theory on the cylinder. The notes are organized as a self-contained route from conformal symmetry to semiclassical dynamics. Part I reviews the conformal group, primary operators, radial quantization, the state-operator correspondence, and operator mixing. Part II builds the semiclassical framework, first in the free scalar theory, where the dimension of $\phi^n$ is recovered in three independent ways, and then through the double-scaling limit, the action variable, and Bohr-Sommerfeld quantization. Part III develops the general machinery of periodic saddles, Floquet theory, fluctuation determinants, the Gel'fand-Yaglom method, and the Gutzwiller trace formula. Part IV applies the framework to the $O(N)$ $\phi^4$ theory in $d=4-\epsilon$ at the Wilson-Fisher fixed point, deriving the classical elliptic solution, the Lamé fluctuation spectrum, the zero modes, and the one-loop contribution to the large-$n$ scaling dimensions. Beyond the explicit computation, the notes emphasize the role of composite operators as probes of collective sectors of quantum field theory, with extensions to gauge theories, conformal windows, and asymptotically safe field theories.

Exact results using dual-unitarity largely rely on nearest-neighbor structures, while finite-range interactions typically lead to complications. Going beyond the usual nearest-neighbor setting, we introduce an analytically tractable family of finite-range kicked Ising models that admit exact closed-form entanglement dynamics. The construction is based on a staggered structure in which dual-unitarity is present on sublattices that are then coupled to each other. The central observation is that these inter-sublattice couplings do not obstruct the dual-unitarity of the resulting model. For the minimal interaction range of $r= 2$, we derive exact expressions for all the $n-$Rényi entanglement entropies at all times and show that the result is the sum of the two coupled sublattice contributions. Our framework extends naturally to larger finite interaction ranges and to systems with heterogeneous local Hilbert spaces, without additional assumptions. It thus provides a controlled setting for studying exact entanglement growth beyond strictly nearest-neighbor dual-unitary models.

This work proposes a new terrestrial probe for millicharged particles (mCPs) and demonstrates promising discovery prospects. mCPs can be copiously produced in core-collapse supernovae (SNe), and a fraction may escape, travel to Earth and yield distinct signals. The mCP mass induces a time-of-flight (ToF) delay relative to the SN neutrino burst, opening a clean search window after the neutrino signal has passed. We compute the mCP-induced electron-recoil signals at XENONnT, JUNO, DUNE, and Hyper-Kamiokande for benchmark SN scenarios, and find that for $\varepsilon = 10^{-9}$ and sub-MeV to MeV-scale masses, more than 10 events per year can be detected. This search can improve upon existing SN cooling bound on $\varepsilon$ by up to an order of magnitude.

We investigate the existence and implications of “bouncing geodesics” in asymptotically flat Schwarzschild and Schwarzschild–de Sitter black holes. These trajectories, which probe the high-curvature regions near the black hole singularity, correspond to specific “bouncing singularities” in the bulk retarded Green's function. We provide a precise description of these singularities by combining the local Hadamard form with the global propagation of singularities theorem. We then derive the critical times at which the bulk retarded correlator becomes singular, considering all possible anchorings of the bouncing geodesics, including null infinity and the cosmological horizon. Finally, for black holes enclosed in a reflecting cavity, we establish a universal connection between the locations of the bouncing singularities and the spectrum of cavity quasinormal modes (QNMs) by deriving a cavity version of the thermal product formula, analogous to the one known for anti-de Sitter black holes. This relation allows one to extract information about the black hole interior from the asymptotic QNM spectrum measured at a reflecting hypersurface, even when the cosmological constant is zero or positive. We confirm this prediction through explicit examples by computing the cavity QNMs of scalar and electromagnetic fields, as well as gravitational waves, in spacetimes with asymptotically flat and de Sitter black holes.

A new type of Yang-Baxter equation (YBE) for $R$-operators depending on three spectral parameters is constructed from the star-triangle relation for the chiral Potts model. As the $Z_N$ symmetric generalization to the Ising model, its Boltzmann weights are known to depend on two variables describing a curve with genus larger than one for $N>2$, except for the self-dual point corresponding to the Fateev-Zamolodchikov chain. Combined with the fact that quantum Hamiltonians of edge-type models such as the Ising model contain both nearest-neighbor interaction and onsite potential terms, this leads naturally to an additional spectral parameter in the associated $R$-operator. The construction extends the edge-vertex correspondence of solvable lattice models, and provides a bridge between the Bazhanov-Stroganov four-parameter $R$-matrix—realized as an intertwiner of cyclic representations of $U_q(\mathfrak{sl}_2)$ at a root of unity—and Shastry's two-parameter $R$-operator obtained from the decorated YBE.

We examine supersymmetry of charged and accelerating black holes embedded in a Bertotti-Robinson universe, in the context of $N=2$, $D=4$ supergravity. After a review of the solution, we study the constraints that guarantee supersymmetry and explicitly compute the Killing spinors of the spacetime. We show that the supersymmetric solution saturates the BPS bound, and we use this result to compute the mass of the black hole and to analyze the thermodynamics of the solution. Finally, we present a generalization of the extremal solution to include the cosmological constant.

We present Ph-$\Lambda_{\rm s}$CDM, a phantom-scalar realization within General Relativity of the sign-switching cosmological-constant idea, $\Lambda_{\rm s}$CDM, in which a phantom scalar evolving on a bounded hyperbolic-tangent potential induces a smooth mirror AdS-to-dS transition in the late-time dark-energy density. The wrong-sign kinetic term, usually viewed as pathological, becomes the mechanism lifting the field from a negative- to a positive-energy vacuum-like regime. The construction also shows that the field can become repulsive while its energy density is still negative. The cosmology nevertheless remains controlled: total energy stays positive, the late-time attractor is de Sitter rather than a Big Rip, and the dynamics remain safely infrared. Ph-$\Lambda_{\rm s}$CDM thus offers a concrete late-time mechanism with the potential to address multiple cosmological tensions.

We discuss a theoretical approach to discriminate whether two states of a many-body quantum system belong or not to different topology classes. This approach is based on expressing a strange correlator - a recently established tool for quantum topology discrimination - between the states as a function of Kirkwood-Dirac quasiprobabilities (KDQs). KDQs provide a first-principles representation of two-time quantum correlators. The link between strange correlators and KDQs allows to establish that strange correlators are weak values of an observable converting an initial trivial state into a topologically non-trivial one. We thus propose a quantum topology witness that is achievable measuring the prior and subsequent effects on a many-body system of a sudden quench transformation that realizes the transition between trivial and topological phases. The witness is evaluated on a probe quantum state whose main features are detailed within the paper. Finally, directly exploiting schemes that allows for the complete reconstruction of KDQs, we address an interferometric protocol for topology discrimination, along with a general discussion of the main lines and challenges towards its implementation.

We investigate the pion gravitational form factors (GFFs) at intermediate and large momentum transfer within the framework of QCD factorization. Our analysis centers on the non-Abelian $TJJ$ correlator, which couples the local QCD energy-momentum tensor to two external gluon fields and explicitly encodes the perturbative effects of the trace anomaly. We demonstrate how this quantum anomaly induces a scalar, dilaton-like contribution to the hard-scattering kernel. To ensure field-theoretic consistency, a careful separation of the quark and gluon sectors is performed, accounting for the modifications introduced by gauge-fixing terms and Slavnov-Taylor identities on the off-shell gluonic structure. To obtain realistic phenomenological predictions and regulate soft-gluon endpoint divergences in the hard kernel, we implement the Sudakov resummation framework coupled with a Gaussian model for the pion's transverse-momentum-dependent wave function. We show that the resulting anomaly-induced corrections significantly modify the behavior of the pion GFFs at large momentum transfer, leaving a unique imprint on the trace sector and the $D$-term.

Under suitable assumptions, geometric objects such as the spacetime metric and curvature tensor can be reconstructed from the algebra of operators of quantized matter fields in the limit of vanishing Newton's constant. In this framework, the full non-linear Einstein equations can be expressed in the language of operator algebras, extending Jacobson's derivation without invoking the area law for Bekenstein-Hawking entropy. These assumptions can then be used as a criterion for determining whether the semiclassical limit of a given quantum theory admits an emergent gravitational description. Going in the other direction, the discrete spectrum of a holographic theory at finite N can be modelled by adding non-perturbative corrections to semiclassical operator algebras. The type III von Neumann algebra that arises in the vanishing Newton's constant limit can be enlarged by adjoining its modular Hamiltonian. A random matrix theory completion of this enlarged algebra, followed by ensemble averaging, results in a type I von Neumann algebra whose minimal projectors approximate those of the underlying microstates. In the case of an eternal black hole, the dimension of the type I algebra equals the Bekenstein-Hawking entropy with universal logarithmic corrections. The complexity of probe operators in the boundary theory provides a diagnostic of the validity of the corresponding bulk semiclassical effective field theory.

The conjecture that compact trapped submanifolds (CTMs) of any codimension greater than one cannot intersect the domain of outer communications of a black hole is tested in symmetrically collapsing spacetimes of $n+1$ dimensions, $n \geq 2$, and on the entire Kerr-Newman sub-extreme family. The results provide evidence to the idea that CTMs of lower dimension, such as trapped loops, should be ragarded as black hole signatures.

Fibre inflation, Poly-instanton inflation and (Loop) Blow-up inflation are among the most popular Kähler moduli based inflationary models realized in the standard LARGE volume scenarios (LVS). In this article, we present a unified framework in which all these three LVS inflationary models can be realized by using (different orientifolds of) a single Calabi-Yau (CY) threefold. In fact, the desired CY threefold needs to have a K3- or ${\mathbb T}^4$-fibration structure along with two diagonal del Pezzo divisors, and a so-called `Wilson' divisor which corresponds to a surface realized as a ${\mathbb P}^1$ fibration over ${\mathbb T}^2$s. For classification purpose, we perform a detailed scan of the CY geometries with $1 \leq h^{1,1}({\rm CY}) \leq 6$ that arise from the triangulation of the four-dimensional reflexive polytopes of the Kreuzer-Skarke database. In this regard, after scanning around 100,000 CY geometries and the corresponding topologies of around a million of toric divisors, we find two CY threefolds satisfying these requirements for $1 \leq h^{1,1}({\rm CY}) \leq 4$, while there are 14 and 45 candidate CY geometries for $h^{1,1}({\rm CY}) = 5$ and $h^{1,1}({\rm CY}) = 6$, respectively. We discuss the extended applications of such CY threefolds for cosmological model building in string theoretic frameworks.

We study the pair creation phenomenon for a real scalar field $\varphi$ in the presence of a surface that undergoes time-dependent deformations, while imposing Dirichlet-like boundary conditions. Including terms up to fourth order in the departure of the surface from an infinite plane, we present results for the angular dependence of the emission rate for the vacuum-to-pair process as a function of the geometry and the dynamics of the surface, as well as of the momenta of the emitted pair. We check the consistency of the leading contribution with previous results obtained from the imaginary part of the effective action, and clarify how the relation between exclusive probabilities and the imaginary part of the effective action is modified at fourth order by the opening of a two-pair channel.

In this paper, we use machine learning to discover a new seeding strategy for integration-by-parts reduction of Feynman integrals, which is a frequent bottleneck in state-of-the-art calculations in theoretical particle and gravitational-wave physics. Our strategy allows us to reduce multi-loop integrals with large numerator powers via essentially the standard Laporta algorithm but with a sparse selection of seed integrals that grows only linearly with the numerator power, whereas existing strategies lead to growth with a polynomial power that increases with the complexity of the integral being reduced. The seeds are restricted to a thin tube-like region that connects the target integral to the master integrals along a zigzag path. We demonstrate the power of our approach by reducing non-planar 2-loop 5-point integrals of rank 20 with numerical kinematics over a finite field, which is prohibitively difficult for the Laporta algorithm with conventional seeding. Going beyond individual integrals, we further demonstrate the reduction of a complete set of top-level rank-10 integrals by dividing the target integrals into several chunks, each of which can be solved by our sparse seeding strategy with considerably less time and a significantly lower memory footprint than other state-of-the-art strategies, making the approach well-suited for phenomenological applications. We provide a proof-of-principle implementation on GitHub at https://github.com/andreslunagodoy/tube_seeding.

Chiral plasma appears in several areas of physics, historically starting from primordial plasma in the early Universe, then in quark-gluon plasma produced in heavy ion collisions, and, more recently, in Dirac and Weyl semimetals. The major signature of the plasma is the non-conservation of the axial current due to the chiral anomaly and the emergence of new, anomaly-induced transport phenomena. In this paper, we study the plasma exposed to arbitrarily strong constant magnetic and weak electric fields. Employing all-order gradient resummation, we write down constitutive relations for electric and axial currents parameterized by thirteen momentum- and magnetic- field-dependent transport coefficient functions. The latter are computed utilizing a theoretical lab for a realistic plasma, namely a holographic $U(1)_V \times U(1)_A$ Maxwell–Chern–Simons theory in Schwarzschild–AdS$_5$, in the probe limit. As an application, we revisit the phenomena of negative magnetoresistance and chiral magnetic waves, beyond the naive hydrodynamic limit.

We reconsider the Hawking–Page transition using the common thermodynamic vector field whose zeros include the Davies and Hawking–Page points. In the elementary AdS branch their winding numbers are $w_{\rm D}=-1$ and $w_{\rm HP}=+1$, so the pair has zero total charge but a non-zero signed first moment. After normalization by the Davies scales this moment gives the familiar universal ratios $C_S$ and $C_T$; in four dimensions $C_S=2$ and $C_T=2/\sqrt{3}-1$. We check the construction for Schwarzschild–AdS, grand-canonical Reissner–Nordström–AdS, charged non-rotating black holes in arbitrary dimension, and Kerr–AdS at fixed angular velocity. The same reduced geometry gives a barrier $B=1/3$ in four dimensions and $B(d)=1/[(d-1)(d-3)]$. Finally we propose a formulation involving a defect-resolved version for categorical or non-invertible symmetry sectors.

We investigate the thermodynamic properties of static, spherically symmetric Anti-de Sitter (AdS) black holes, focusing on the interplay between characteristic temperatures, as well as on the universality of Ruppeiner scalar curvature at the Hawking-Page (HP) phase transition. In particular, we study the relation between the minimum temperature and the HP phase transition temperature for static, spherically symmetric AdS black holes in pure Lovelock gravity. For the electromagnetically neutral case in Einstein gravity, the minimum temperature in $(d+1)$ dimensions coincides with the HP transition temperature in $d$ dimensions, while in higher pure Lovelock theories this relation is modified by a dimension- and order-dependent factor, reducing to the Einstein result in appropriate limits. For charged AdS black holes, in the grand canonical ensemble, in general relativity, the two temperatures differ by a simple dimension-dependent factor, whereas no universal relation persists in higher curvature pure Lovelock theories. We further analyze the normalized Ruppeiner scalar curvature at the HP transition and show that it is a universal constant depending only on the spacetime dimension for electromagnetically neutral black holes in pure Lovelock theories. The normalized scalar curvature remains a constant, under appropriate conditions, even for the charged static spherically symmetric black holes in the grand canonical ensemble for the Einstein theory case, whereas in general pure Lovelock theories it depends on thermodynamic parameters such as pressure and electrostatic potential, asymptotically approaching a constant in the large-pressure or simultaneous large-potential and large-pressure limits.

We consider quantization techniques with a particular emphasis on the phase space quantization, as encountered in quasi-probabilistic descriptions and in string theory. We investigate what is lost by adopting the normal ordering prescription, by revisiting fundamental quantization concepts and the correspondence rules that define the well-known quasi-distributions: the Wigner, Q, and P functions, some of which are inherently ordering dependent. The actual quantum state dictates the necessity of employing discrete countable structures or, alternatively, the complex phase space formulation based on coherent states, and the quasi-distributions depict the existence of the phase space dynamics, of the wave translations and the propagating directions.

We derive new 3d $\mathcal{N}=2$ dualities with $\mathrm{U}(N)$ gauge groups involving pairs of two-index tensors interacting through a quartic superpotential, (anti)-fundamentals and possibly an adjoint. A strong hint for their validity follows from T-duality on brane setups with O6 planes and stacks of multiple NS fivebranes. These setups engineer two families of 4d models known in the literature as mezzanine and balcony of type $A_k$ and $D_{k+2}$. In 4d these models admit a generalization of Seiberg duality, tested also at the brane level. We study the reduction of such dualities from both the brane and the field theory perspective and we establish the matching of the three-sphere partition functions, assuming the validity of the 4d superconformal indices. The latter is achieved through a double scaling limit, whose structure is dictated by the brane picture, and it requires the validity of new 3d confining dualities for quivers with two gauge nodes. Moreover we provide a proof of these confining dualities via the tensor deconfinement technique.

In this work, we investigate a cosmic inflation model based on a cosine-type potential with a negative cosmological constant. This model originates from a classical solution of the Wheeler-DeWitt equation. The equation of motion for the inflaton field can be solved analytically without relying on approximation schemes, such as the slow-roll conditions. The predictions of the spectral index, the tensor-to-scalar ratio, and the running spectral index are calculated and compared with experimental constraints from Planck Collaboration, Atacama Cosmology Telescope Collaboration (ACT), and Dark Energy Spectroscopic Instrument (DESI).

We investigate the spectral dynamics of a rotating black hole embedded in a Dehnen $(1,4,\gamma)$ dark matter halo, where quasibound states and superradiant scattering jointly characterize the physical response of the system. Starting from an exact Schwarzschild–Dehnen solution, we construct its rotating counterpart via the Newman–Janis algorithm, yielding a consistent axisymmetric geometry that incorporates the influence of a structured halo. The Dehnen profile, through its inner slope parameter $\gamma$, introduces a controlled deformation of both the near-horizon and asymptotic regions of the spacetime. Using the analytical asymptotic matching method, we derive the quasibound-state spectrum and show that the real part of the frequency retains a hydrogen-like structure, but is systematically shifted by the halo through the effective mass scale $\rho_0 r_0^3/(\gamma-3)$. In particular, denser, more extended, and more cuspy halos enhance the binding energy, lower the critical mass required for the onset of instability, and typically suppress the growth rate of the black hole bomb. In the scattering sector, we obtain an analytic expression for the superradiant amplification factor and find that the same halo properties that strengthen binding effects also tend to narrow the superradiant window. These results demonstrate that quasibound states and superradiant scattering are complementary manifestations of a unified spectral structure, with the Dehnen halo acting as an environmental tuner that imprints its properties directly onto both the resonance spectrum and the energy-extraction channels of the rotating black hole.