I address some problems encountered in the formulation of relativistic models encompassing the MOND phenomenology of radial acceleration. I explore scalar and vector theories with fractional kinetic terms and $f(R)$-type gravity, demanding that the energy density be bounded from below and that superluminal modes be absent, but also that some consistency constraints with observational results hold. I identify configurations whose energy is unbounded from below and formulate some no-go statements for vector field models and modified gravity theories. Finally, I discuss superfluid dark matter as a hybrid theory lying between CDM and modified gravity, highlighting some difficulties present also in this case, which appears preferable to the others.
A generally covariant version of Erik Verlinde's emergent gravity model is proposed. The Lagrangian constructed here allows an improved interpretation of the underlying mechanism. It suggests that de-Sitter space is filled with a vector-field that couples to baryonic matter and, by dragging on it, creates an effect similar to dark matter. We solve the covariant equation of motion in the background of a Schwarzschild space-time and obtain correction terms to the non-covariant expression. Furthermore, we demonstrate that the vector field can also mimic dark energy.
We derive the full set of field equations based on Hossenfelder's recent covariant formulation of the emergent gravity model, along with perturbative and exact solutions. The exact solution describes a static, spherically-symmetric spacetime with a non-trivial vector field which plays the role of dark matter under the emergent gravity paradigm. Equations of motion of relativistic test masses are derived and are shown to reduce to Modified Newtonian Dynamics with additional relativistic corrections. It is also shown that the presence of the vector field gives an additional positive contribution…
We study the Padmanabhan's emergent Universe in the context of Bousso's covariant entropy conjecture. We find that for a flat Universe, this conjecture can be applied for the system of Padmanabhan's emergent Universe. It turns out that the maximum "bulk entropy" of Padmanabhan's emergent Universe coincides with the upper bound of Bousso's covariant entropy on the null surface defined by Hubble horizon, provided that the Universe is just filled by the cosmological constant or radiation field which represent maximal entropy during inflation and subsequent radiation dominant era. This maximal ent…
We study perturbations of 4-dimensional fuzzy spheres as backgrounds in the IKKT or IIB matrix model. Gauge fields and metric fluctuations are identified among the excitation modes with lowest spin, supplemented by a tower of higher-spin fields. They arise from an internal structure which can be viewed as a twisted bundle over $S^4$, leading to a covariant noncommutative geometry. The linearized 4-dimensional Einstein equations are obtained from the classical matrix model action under certain conditions, modified by an IR cutoff. Some one-loop contributions to the effective action are computed…
Following recent Verlinde's heuristic construction or emergent gravity, Hossenfelder wrote down the Lagrangian capturing some aspects of this theory. We point out that there is an error in calculations whose consequence is that a cosmological de Sitter space solution is not recovered from this Lagrangian. We correct this error in order to obtain the desired solution. We also show that small perturbations around de Sitter space grow, which implies that this state is not stable. However, the presence of matter and radiation might in principle provide stability.
Emergent fracton strings from covariant bi-form gauge field theory
School of Theoretical Physics, Dublin Institute for Advanced Studies（都柏林高等研究院理论物理学院）；Centre for Mathematics and Theoretical Physics Research, Department of Physics, Astronomy and Mathematics, University of Hertfordshire（赫特福德大学物理、天文与数学系数学与理论物理研究中心）；CFisUC, Department of Physics, University of Coimbra（科英布拉大学物理学院）
Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as macroscopic constraints we consider statistical ensembles over the space of classical probability distributions or quantum wave-functions. The ensembles are covariantized using dual field theories with either complex or real scalar fields identified with complex wave-functions or square root of probabilities. We argue that a full space-time covariance on a field …
In this essay we review the central difficulty in formulating a viable quantum field theory in which gravity is emergent at low energies, rather than mediated by a fundamental gauge field. The Weinberg-Witten theorem forbids spin 2 massless modes from carrying Lorentz covariant stress-energy. In General Relativity the stress-energy is not covariant because it violates a gauge symmetry, but a gravitational theory without fundamental spin 2 gauge invariance must either lack a stress-energy operator or have a non-relativistic graviton. The latter option is incompatible with the principle of equiv…
Field theories that are generally covariant but nongravitational at tree level typically give rise to an emergent gravitational interaction whose strength depends on a physical regulator. We consider emergent gravity models in which scalar fields assume the role of clock and rulers, addressing the problem of time in quantum gravity. We discuss the possibility of nontrivial dynamics for clock and ruler fields, and describe some of the consequences of those dynamics for the emergent gravitational theory.
A trajectory-based representation for the quantum theory of the gravitational field is formulated. This is achieved in terms of a covariant Generalized Lagrangian-Path (GLP) approach which relies on a suitable statistical representation of Bohmian Lagrangian trajectories, referred to here as GLP-representation. The result is established in the framework of the manifestly-covariant quantum gravity theory (CQG-theory) proposed recently and the related CQG-wave equation advancing in proper-time the quantum state associated with massive gravitons. Generally non-stationary analytical solutions for …
We consider a theory of scalars minimally coupled to an auxiliary background metric. The theory is generally covariant and subject to the constraint of vanishing energy-momentum tensor. Eliminating the auxiliary metric leads to a reparametrization invariant, non-polynomial, metric-independent action for the scalar fields. Working in the limit of a large number of physical scalars, a composite massless spin-2 state, the graviton, was identified in previous work, in a two-into-two scalar scattering process. Here, we further explore the possibility that dynamical emergent gravity is a natural fea…
The nonlinear affine Goldstone model of the emergent gravity, built on the nonlinearly realized/hidden affine symmetry, is concisely revisited. Beyond General Relativity, the explicit violation of general invariance/relativity, under preserving general covariance, is exposed. Dependent on a nondynamical affine connection, a generally covariant second-order effective Lagrangian for metric gravity is worked out, with the general relativity violation and the gravitational dark matter serving as the signatures of emergence.
Spin Foam Models (SFMs) are covariant formulations of Loop Quantum Gravity (LQG) in 4 dimensions. This work studies the perturbations of SFMs on a flat background. It demonstrates for the first time that smooth curved spacetime geometries satisfying Einstein equation can emerge from discrete SFMs under an appropriate low energy limit, which corresponds to a semiclassical continuum limit of SFMs. In particular, we show that the low energy excitations of SFMs on a flat background give all smooth solutions of linearized Einstein equations (spin-2 gravitons). This indicates that at the linearized …
The framework of emergent gravity arising from Yang-Mills matrix models is developed further, for general noncommutative branes embedded in R^D. The effective metric on the brane turns out to have a universal form reminiscent of the open string metric, depending on the dynamical Poisson structure and the embedding metric in R^D. A covariant form of the tree-level equations of motion is derived, and the Newtonian limit is discussed. This points to the necessity of branes in higher dimensions. The quantization is discussed qualitatively, which singles out the IKKT model as a prime candidate for …
In order to bypass the big bang singularity, we develop an emergent universe scenario within a covariant extension of General Relativity known as \emph{"Energy-Momentum Squared Gravity"}. The extra terms of the model emerge in the high energy regime. Considering dynamics in a Friedmann-Lemaître-Robertson-Walker background, critical points, representing stable Einstein static states of the phase space, result as solutions. It then turns out that as the equation of state parameter $ω$ gradually declines from a constant value as $t\rightarrow-\infty$, eventually some of the static past eternal so…
We elaborate the description of the semi-classical gravity sector of Yang-Mills matrix models on a covariant quantum FLRW background. The basic geometric structure is a frame, which arises from the Poisson structure on an underlying $S^2$ bundle over space-time. The equations of motion for the associated Weitzenböck torsion obtained in arXiv:2002.02742 are rewritten in the form of Yang-Mills-type equations for the frame. An effective action is found which reproduces these equations of motion, which contains an Einstein-Hilbert term coupled to a dilaton, an axion and a Maxwell-type term for the…
The framework of the Covariant Canonical Gauge theory of Gravity (CCGG) is described in detail. CCGG emerges naturally in the Palatini formulation, where the vierbein and the spin connection are independent fields. Neither torsion nor non-metricity are excluded. The manifestly covariant gauge process is based on canonical transformations in the De Donder-Weyl Hamiltonian formalism, starting from a small number of basic postulates. Thereby, the original system of matter fields in flat spacetime, represented by non-degenerate Hamiltonian densities, is amended by spacetime fields. The coupling of…
We consider a non-standard model of gravity coupled to a neutral scalar "inflaton" as well as to SU(2)xU(1) iso-doublet scalar with positive mass squared and without self-interaction, and to SU(2)xU(1) gauge fields. The principal new ingredient is employing two alternative non-Riemannian space-time volume-forms (covariant integration measure densitities) independent of the metric. The latter have a remarkable impact - although not introducing any additional propagating degrees of freedom, their dynamics triggers a series of important features: appearance of infinitely large flat regions of the…
Based on the Padmanabhan's proposal, the accelerated expansion of the universe can be driven by the difference between the surface and bulk degrees of freedom in a region of space, described by the relation $dV/dt=N_{sur}-N_{bulk}$ where $N_{sur}$ and $N_{bulk}=-N_{em}+N_{de}$ are the degrees of freedom assigned to the surface area and the matter-energy content inside the bulk such that the indexes $"em"$ and $"de"$ represent energy-momentum and dark energy, respectively. In the present work, the dynamical effect of the Weyssenhoff perfect fluid with intrinsic spin and its corresponding spin d…
Emergent gravity from nonlinear perturbation of spherical accretion with variable adiabatic index
Visva-Bharati（维斯瓦-巴拉蒂大学）；University of North Bengal（北孟加拉大学）；Harish-Chandra Research Institute（哈里什-钱德拉研究所）；Homi Bhabha National Institute (HBNI)（霍米·巴巴国立研究所）
We clarify the problem in which occasions can gravitational force be regarded emergent from thermodynamics, by proposing an entropic mechanism that can extract the entropic gradient existing in spacetime, due to the variation of the Casini-Bekenstein bound in specific quasi-static processes with the heat flux $δQ$ into the whole casual wedge. We explicitly formulate the derivation of inertial force as the emergent gravitational attraction from the Entanglement First Law. We find the saturation of the bound along with the vanishing relative entropy corresponds to the variation of minimal surfac…
Quantum-Deformed Phase-Space Geometry and Emergent Inflation in Effective Four-Dimensional Spacetime
BMS College of Engineering（BMS工程学院）；Islamic University of Madinah（麦地那伊斯兰大学）；University of Hafr Al Batin（哈夫阿尔巴廷大学）；Benha University（本哈大学）；Ahram Canadian University（埃及加拿大大学）
A new class of gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold are studied in some detail. These models involve an additional $R^2$ (square of the scalar curvature) term as well as scalar matter field potentials of appropriate form so that the pertinent action is invariant under global Weyl-scale symmetry. Scale invariance is spontaneously broken upon integration of the equations of motion for the auxiliary volume-form degrees of freedom. After performing transition …
The Poincaré gauge gravity (PGG) with the underlying vector fields of tetrads and spin-connections is perhaps the best theory candidate for gravitation to be unified with the other three elementary forces of nature. There is a clear analogy between local frame in PGG and local internal symmetry space in the Standard Model. As a result, the spin-connection fields, gauging the local frame Lorentz symmetry group SO(1,3)_{LF}, appear in PGG much as photons and gluons appear in SM. We propose that such an analogy may follow from their common emergent nature allowing to derive PGG in the same way as…
Modified Newtonian Dynamics has one free parameter and requires an interpolation function to recover the normal Newtonian limit. We here show that this interpolation function is unnecessary in a recently proposed covariant completion of Erik Verlinde's emergent gravity, and that Verlinde's approach moreover fixes the function's one free parameter. The so-derived correlation between the observed acceleration (inferred from rotation curves) and the gravitational acceleration due to merely the baryonic matter fits well with data. We then argue that the redshift-dependence of galactic rotation cur…
Motivated by the ideas of Jacob Bekenstein concerning gravity-assisted symmetry breaking, we consider a non-canonical model of f(R)=R+R^2 extended gravity coupled to neutral scalar "inflaton", as well as to SU(2)xU(1) multiplet of fields matching the content of the bosonic sector of the electroweak particle model, however with the following significant difference - the SU(2)xU(1) iso-doublet Higgs-like scalar enters here with a standard positive mass squared and without quartic selfinteraction. Strong interaction dynamics and, in particular, QCD-like confinement effects are also considered by …
We consider FRW cosmology in $f(R)= R+ γR^2+δR^3$ modified framework. The Palatini approach reduces its dynamics to the simple generalization of Friedmann equation. Thus we study the dynamics in two-dimensional phase space with some details. After reformulation of the model in the Einstein frame, it reduces to the FRW cosmological model with a homogeneous scalar field and vanishing kinetic energy term. This potential determines the running cosmological constant term as a function of the Ricci scalar. As a result we obtain the emergent dark energy parametrization from the covariant theory. We s…
We study FLRW cosmology, taking into account quantum gravitational corrections in the formalism of the exact renormalization group flow of the effective action for gravity. We calculate the quantum corrected scale factor, energy density, and entropy production at late times, taking different cut-off functions. Our approach differs from previous ones in the way energy-momentum conservation is imposed -- we include the running Newton constant $G(k)$ in the definition of energy-momentum tensor, keeping in mind the covariant conservation identity of the Einstein tensor. The quantum corrections obt…
We present a concise description of the basic features of gravity-matter models based on the formalism of non-canonical spacetime volume-forms in its two versions: the method of non-Riemannian volume-forms (metric-independent covariant volume elements) and the dynamical spacetime formalism. Among the principal outcomes we briefly discuss: (i) quintessential universe evolution with a gravity-"inflaton"-assisted suppression in the "early" universe and, respectively, dynamical generation in the "late" universe of Higgs spontaneous electroweak gauge symmetry breaking; (ii) unified description of d…
The cosmological constant is the most economical candidate for dark energy. No other approach really alleviates the difficulties faced by the cosmological constant because, in all other attempts to model the dark energy, one still has to explain why the bulk cosmological constant (treated as a low-energy parameter in the action principle) is zero. I argue that until the theory is made invariant under the shifting of the Lagrangian by a constant, one cannot obtain a satisfactory solution to the cosmological constant problem. This is impossible in any generally covariant theory with the conventi…
We study a new class of vector dark energy models where multi-Proca fields $A_μ^a$ are coupled to cold dark matter by the term $f(X)\tilde{\mathcal{L}}_{m}$ where $f(X)$ is a general function of $X\equiv -\frac{1}{2}A^μ_ a A^a_μ$ and $\tilde{\mathcal{L}}_{m}$ is the cold dark matter Lagrangian. From here, we derive the general covariant form of the novel interaction term sourcing the field equations. This result is quite general in the sense that encompasses Abelian and non-Abelian vector fields. In particular, we investigate the effects of this type of coupling in a simple dark energy model b…
