A bstract The matrix models are non-perturbative formulations of string theory, from which many believe that spacetime arises. The matrix fluctuations around the spacetime thus created should represent both matter and gravitational fields. In this paper, we discuss how the gravitational field emerges from the IIB matrix model. In particular, we consider how diffeomorphism invariance arises and how unitarity is guaranteed in this theory. Specifically, we consider matrices as bilocal fields and discuss how the Lorentz-invariant vacuum and low-energy excitations around it can be expressed. We then discuss how the conditions for the theory to be unitary can be written in terms of bilocal fields. We argue that in the low-energy limit, the bilocal fields are reduced to local fields consisting of a finite number of massless fields and an infinite number of massive fields, satisfying unitarity.

Cattell–Horn–Carroll models of intelligence frequently show that, at the group-factor level, G f is most strongly related to g , whereas at the subtest level, G c -associated measures exhibit the highest g loadings. One proposed solution to this “ g paradox” holds that Stratum-III g and Stratum-II G f are identical, and that the sizeable g loadings of crystallized subtests merely reflect the investment of G f into learning. Investment theory is weakly evidenced, however. We argue that the “ g paradox” results from subtests measuring facets of G f exhibiting pronounced specificity for cognitive entities. Capturing everything that goes into G f is difficult on a single-measure basis, hence lower Stratum-I g loadings. The G f group factor is nonetheless reflective of the composite of these entities and therefore is uniquely (at Stratum II) associated with g . Subtests measuring G c broadly index the quality of global systems involving many cognitive processes, not entities, and so relate to factors that have formative effects on g , which are Stratum-I specific. We posit the existence of two distinguishable sources of general covariance: a formative g (associated primarily with G c ) and a reflective g (associated primarily with G f ), with the latter hierarchically superordinate to the former. Network analysis of “pure” psychometric measures of the G c and G f domains indicates that the former exhibits significantly greater network integrity than the latter, consistent with this formative/reflective model. Random effects meta-analysis of SEM contrast parameters, derived from four large genetically informed studies, finds that subtests assigned to a “ G c ” category are associated with higher-magnitude direct (formative) genetic paths relative to those in a “ G f ” category, suggesting a weak but discriminable and broad Stratum-I g in the residual covariance structure. Given the theorized phylogenetic histories of these two g s, we term the formative (“bottom-up”) g “proto g ” ( g p ), and the reflective (“top-down”) g “neo g ” ( g n ).

This paper focuses on a large-dimensional approximate factor model with a general covariance matrix assumption of the idiosyncratic components when both the crosssection N and the time dimension T tend to infinity. First, a bias-corrected estimator for noise variance is proposed using random matrix theory, and its asymptotic normality is also established, which is free of the population distribution of the observations. Second, based on this bias-corrected noise variance estimator, the new information criteria are constructed to determine the number of factors. The consistency of the estimators for the number of factors is also proved as both N and T approach infinity. Finally, simulations and real data analysis are conducted to show the superiority and generality of our proposed estimators.

We demonstrate that there are no scale-invariant one-loop corrections to the superhorizon tensor perturbations from small-scale (potentially enhanced) scalar perturbations, irrespective of the details of inflationary background time evolution.For this purpose we derive a soft tensor effective field theory at leading order in the gradient expansion by integrating out small-scale scalar fluctuations in a general time-dependent background over the Schwinger-Keldysh contour, i.e., we perform loop calculations in the soft limit of external momentum.The absence of scale-invariant corrections originates from the diffeomorphism invariance of general relativity and is therefore unavoidable.

Abstract In physics geometrical connections are the mean to create models with local symmetries (gauge connections), as well as general diffeomorphisms invariance (affine connections). Here we study the irreducible tensor decomposition of connections on the tangent bundle of an affine manifold as used in the polynomial affine model of gravity (Castillo-Felisola et al. in Universe 11(3):102, 2025. https://doi.org/10.3390/universe11030102 ). This connection is the most general linear connection, which allows us to build metric independent, diffeomorphism invariant models. This set up includes parts of the connection that are associated with conformal and projective transformations.

Abstract A class of gravity theories respecting spatial covariance and in the presence of non-dynamical auxiliary scalar fields with only spatial derivatives is investigated. Generally, without higher temporal derivatives in the metric sector, there are 3 degrees of freedom (DOFs) propagating due to the breaking of general covariance. Through a Hamiltonian constraint analysis, we examine the conditions to eliminate the scalar DOF such that only 2 DOFs, which correspond the tensorial gravitational waves in a homogeneous and isotropic background, are propagating. We find that two conditions are needed, each of which can eliminate half degree of freedom. The second condition can be further classified into two cases according to its effect on the Dirac matrix. We also apply the formal conditions to a polynomial-type Lagrangian as a concrete example, in which all the monomials are spatially covariant scalars containing two derivatives. Our results are consistent with the previous analysis based on the perturbative method.

In this work, we develop a unified framework for Conformal Gravity and Noncommutative (Fuzzy) Gravity incorporating internal interactions. Our approach relies on two fundamental observations: first, the dimensions of a curved manifold and those of its tangent group need not coincide, and second, both gravitational models can be formulated as gauge theories. We begin with a discussion of the gauge-theoretic formulation of gravitational dynamics, emphasizing the role of diffeomorphism invariance. We then outline the constructions of Conformal Gravity and Fuzzy Gravity within this formalism. Building on an extension of the four-dimensional tangent group, we propose a scheme that unifies the two theories while naturally incorporating internal degrees of freedom. We further investigate the low-energy limits that emerge after appropriate spontaneous symmetry-breaking mechanisms, and we comment on potential observational signatures—particularly those associated with cosmic strings and their imprint on gravitational-wave spectra.

Motivated by the phenomenology of MOND, we propose a theory based on a fundamental non-Abelian Yang-Mills gauge field with gravitational coupling constant (a “graviphoton”) emerging in a regime of weak acceleration, i.e. below the MOND acceleration scale. Using the formalism of the effective field theory and invoking a mechanism of gravitational polarization of the dark matter medium, we show that generic solutions of this theory reproduce the deep MOND limit without having to introduce in an ad hoc way an arbitrary function in the action. In this framework, MOND is due to the existence of a new sector of the standard model of particle physics. Furthermore, the model involves a violation of the local Lorentz invariance in the low acceleration regime. We show how to restore the general covariance of the model by adding one gravitational degree of freedom in the form of the scalar Khronon field.

The canonical quantization of gravity in general relativity is greatly simplified by the artificial decomposition of space time into a 3 + 1 formalism. Such a simplification appears to come at the cost of general covariance. This quantization procedure requires tangential and perpendicular infinitesimal diffeomorphisms generated by the symmetry group under the Legendre transformation of the given action. This gauge generator, along with the fact that Weyl curvature scalars may act as “intrinsic coordinates” (or a dynamical reference frame) that depend only on the spatial metric (gab) and the conjugate momenta (pcd), allows for an alternative approach to canonical quantization of gravity. In this paper, we present the tensorial solution of the set of Weyl scalars in terms of canonical phase-space variables.

This work reveals a fundamental link between general covariance and Birkhoff's theorem. We extend Birkhoff's theorem from general relativity to a broad class of generally covariant gravity theories formulated in the Hamiltonian framework. Conversely, we show that each one-parameter family of static, spherically symmetric spacetimes determines a class of covariant theories, each of which has that family of spacetimes as its entire vacuum solution space. Our systematic and model-independent framework applies to a wide range of spacetimes, including observationally inferred, quantum-gravity-inspired, and regular black holes. It provides a universal tool for probing their dynamical origins and enables the reconstruction of the underlying covariant theories from observational data, including gravitational-wave and black-hole-shadow measurements.

Abstract We follow a new pathway to the definition of the Stochastic Quantization (SQ), first proposed by Parisi and Wu, of the action functional yielding the Einstein equations. Hinging on the functional similarities between the Ricci‐Flow equation and the SQ Langevin equations proposed by Rumpf, a novel approach is pushed forward, characterized by a multiplicative noise and a stochastic time that is found to converge to the proper time of a space‐like foliation in the equilibrium limit, where quantities are observed to have constant averages. The starting system of equations is expressed using the Arnowitt–Deser–Misner (ADM) variables and their conjugated Hamiltonian momenta. Such a choice is instrumental in understanding the newly derived equations in terms of the breakdown of the diffeomorphism invariance of the classical theory, which instead will hold on average at the steady state. The physical interpretation of the Ricci‐flow equations is commented upon, and it is argued that they can naturally provide, in a geometrical way, the renormalization group equation for gravity theories. In the general setting, the equation associated to the shift vector yields the Navier–Stokes equation with a stochastic source. Moreover, it is shown that the fluctuations of the metric tensor components around the equilibrium configurations, far away from the horizon of a Schwarzschild black hole, are forced by the Ricci‐flow to follow the Kardar–Parisi–Zhang equation, whose probabilistic distribution can yield an intermittent statistics. Finally, the possible applications of this novel scenario to the cosmological constant are commented upon, and it is argued that the Ricci‐flow may provide a solution to the Hubble tension, as a macroscopic effect of scale dependence of the quantum fluctuations of the metric tensor.

Abstract Diffeomorphism invariance breaking has been investigated in the literature in several contexts, including emergent General Relativity (GR). If GR emerges from an underlying theory without diffeomorphism invariance, there may be small violations of this symmetry at low energies. Since such small violations should not cause instabilities in cosmological evolution, it is a suitable framework for examining such symmetry-breaking effects. In this paper, the cosmological evolution with broken diffeomorphism invariance is investigated in the (modified) FLRW spacetime in the effective theory framework. The GR Lagrangian is augmented with all diffeomorphism-breaking but Lorentz-invariant terms in the leading order, namely, those involving two derivatives. The magnitudes of (minor) violations are kept general modulo the conditions arising in the linearized theory. The analytic solutions of the scale factor in the full non-linear theory for the single-component universes are attempted; the radiation and vacuum solutions are found analytically, whereas the matter solution is worked out numerically since an analytic solution does not exist in the required form. It is observed that the solutions smoothly connect to those of GR in the limit of vanishing symmetry-breaking. The more realistic, two-component, and three-component universes are numerically studied, and no signs of singular behavior are observed: minor diffeomorphism-violating modifications to GR at the level of two derivatives do not cause instabilities in the basic cosmological evolution.

Abstract Two models for Schwarzschild-like black holes with quantum corrections, derived from the Hamiltonian constraints approach to quantum gravity while preserving general covariance, have been developed in Zhang et al. (Phys. Rev. D 111, L081504, 2025, arXiv:2407.10168 [gr-qc]). In this work, we study the quasinormal modes of a massive scalar field and demonstrate that the spectrum includes arbitrarily long-lived modes, known as quasi-resonances. Precise calculations using the Leaver method show good agreement with WKB data and time-domain integration within the range where these methods are reliable, specifically for small field masses.

On a given Riemann surface, we construct a path integral based on the Liouville action functional with imaginary parameters. The construction relies on the compactified Gaussian Free Field (GFF), which we perturb with a curvature term and an exponential potential. In physics this path integral is conjectured to describe the scaling limit of critical loop models such as Potts and O(n) models. The potential term is defined by means of imaginary Gaussian Multiplicative Chaos theory. The curvature term involves integrated 1-forms, which are multivalued on the manifold, and requires a delicate regularisation in order to preserve diffeomorphism invariance. We prove that the probabilistic path integral satisfies the axioms of Conformal Field Theory (CFT) including Segal’s gluing axioms and we construct the correlation functions for this CFT, involving electro-magnetic operators. This CFT has several conjectural exotic features: most importantly, it should be non-unitary with the structure of a logarithmic CFT. Our motivation is thus to provide a concrete setup for the mathematical study of logarithmic CFTs.

A recent covariant formulation, that includes nonperturbative effects from loop quantum gravity (LQG) as self-consistent effective models, has revealed the possibility of nonsingular black hole solutions. The new framework makes it possible to couple scalar matter to such LQG black holes and derive Hawking radiation in the presence of quantum spacetime effects while respecting general covariance. Standard methods to derive particle production both within the geometric optics approximation and the Parikh-Wilczek tunnelling approach are therefore available and confirm the thermal nature of Hawking radiation. The covariant description of scale-dependent decreasing holonomy corrections maintains Hawking temperature as well as universality of the low-energy transmission coefficients, stating that the absorption rates are proportional to the horizon area at leading order. Quantum-geometry effects enter the thermal distribution only through subleading corrections in the graybody factors. Nevertheless, they do impact energy emission of the black hole and its final state in a crucial way regarding one of the main questions of black-hole evaporation: whether a black-to-white-hole transition, or a stable remnant, is preferred. For the first time, a first-principles derivation, based on a discussion of backreaction, finds evidence that points to the former outcome.

Abstract We perform the manifestly covariant quantization of f(R) gravity in the de Donder gauge condition (or harmonic gauge condition) for general coordinate invariance. We explicitly calculate various equal-time commutation relations (ETCRs), in particular the ETCR between the metric and its time derivative, and show that it has a nonvanishing and nontrivial expression, whose situation should be contrasted to the previous result in higher-derivative or quadratic gravity where the ETCR was found to be identically vanishing. We also clarify global symmetries, the physical content of f(R) gravity, and clearly show that this theory is manifestly unitary and has a massive scalar and massless graviton as physical modes.

There is a long history in both general relativity and quantum mechanics of removing fixed background structures, thereby making observed objects and measurement processes dynamical. We continue this evolution by combining central insights from both theories to argue that physical limits on information collection resulting from quantum gravity coupled with general covariance preclude the fixed information geometry still assumed in both information theory and quantum mechanics. As a consequence there must be a gravitized, generally covariant extension of both theories. We also propose a novel experimental test involving intrinsic triple and higher-order quantum interferences that would provide evidence for dynamical information metrics and a dynamical Born rule.

Abstract In earlier papers a method was given for constructing from first principles a holographic bulk dual action in Euclidean AdS space for a Euclidean CFT on the boundary. The starting point was an Exact RG for the boundary theory. The bulk action is obtained from the evolution operator for this ERG followed by a field redefinition. This procedure guarantees that the boundary correlators are all recovered correctly. In this paper we use the same method in an attempt to construct a holographic dual action for the free O(N) model where the bulk is flat Euclidean space with a plane boundary wall. The scalar cubic interaction is found to be local (in D = 3) but depends on the distance from the boundary — which can be interpreted as a non constant background dilaton field. The spin 2-scalar-scalar interaction is found to be non local — in contrast to the AdS case. A field redefinition that makes the kinetic term quartic in derivatives can be done to eliminate this non locality. It is shown that the action can be obtained by gauge fixing an action that has the linearized gauge invariance associated with general coordinate invariance. Boundary correlators (two point and three point) are shown to be reproduced by bulk calculations — as expected in this approach to holography.

In this paper, we introduce Kluitenberg’s formulation of non-equilibrium thermodynamics with internal variables in the context of a Riemannian space, as required by Einstein’s general relativity. Using the formulation of the second law of thermodynamics in general coordinates with a pseudo-Euclidean metric, we derive a Levi-Civita-like energy tensor and propose a generalization of the second law within a Riemannian space, in agreement with Tolman’s approach. In addition, we determine the expression for the entropy density in a general Riemannian space and identify the new variables upon which it depends. This allows us to deduce, within this framework, the equilibrium inelastic and viscous stress tensors as well as the entropy production. These expressions are consistent with the principle of general covariance and Einstein’s equivalence principle.

We investigate on the diffeomorphism invariance of the effective gravitational action, focusing in particular on the path integral measure. In the literature, two different measures are mainly considered, the Fradkin-Vilkovisky and the Fujikawa one. With the help of detailed calculations, we show that, despite claims to the contrary, the Fradkin-Vilkovisky measure is diffeomorphism invariant, while the Fujikawa measure is not. In particular, we see that, contrary to naïve expectations, the presence of g00 factors in the Fradkin-Vilkovisky measure is necessary to ensure the invariance of the effective gravitational action. We also comment on results recently appeared in the literature, and show that formal calculations can easily miss delicate points.