Emergent Gravity Research Articles

A test of MOND and emergent gravity with SMACS J0723.3-7327 using eROSITA observations

We implement a test of MOND and Verlinde's Emergent Gravity using the galaxy cluster SMACS J0723-7327, which has been recently imaged using the eROSITA X-ray telescope as well as with JWST. We test MOND using two independent methods. The first method involves comparing the dynamical MOND mass and baryonic mass, while the second method entails a comparison of the MOND-estimated temperature with the observed temperature. We then compare the unseen mass predicted by Emergent Gravity with the estimated dark matter mass. We find that MOND shows a mass discrepancy in the central regions at high significance levels. The observed temperature profile is in marginal disagreement with that in the MOND paradigm. However, the Emergent Gravity Theory agrees in accurately accounting for the dynamical mass in the inner regions within 1σ. Our results are qualitatively consistent with the earlier tests on other clusters.

Interactions in the IKKT matrix model on covariant quantum spacetime

We study the interactions of the higher-spin gauge theory arising from the IKKT matrix model on a covariant quantum FLRW quantum space-time MJ1,3, denoted as HS-IKKT. In particular, we elaborate some of the vertices and observe that they are not manifestly Lorentz invariant in the unitary formulation. We argue that Lorentz invariance of HS-IKKT can be recovered since Lorentz transformations are part of the gauge invariance in the covariant formulation. This statement is verified for some vertices with lowest number of derivatives. The lowest-derivative sector of this theory is expected to be governed by an “almost”-Lorentz-invariant Yang-Mills theory coupled to emergent gravity.

Quantum Liquids: Emergent Higher-Rank Gauge Theory and Fractons

Fractons emerge from many-body systems, featuring subdimensional particles with restricted mobility. These particles have attracted interest for their roles across disciplines, including topological quantum codes, quantum field theory, emergent gravity, and quantum information. They display unique nonequilibrium behaviors such as nonergodicity and glassy dynamics. This review offers a structured overview of fracton phenomena, especially those of gapless fracton liquids, which enable collective modes similar to gauge fluctuations in Maxwell's electromagnetic framework, yet their phenomena are distinguished by a unique conservation law that restricts the mobility of individual charges and monopoles. We delve into the theoretical basis of three-dimensional (3D) fracton liquids, exploring emergent symmetric tensor gauge theories and their properties. We also discuss the material realization of fracton liquids in Yb-based pyrochlore lattices and other synthetic quantum matter platforms.

A path integral formula of quantum gravity emergent from entangled local structures

We couple to group field theory (GFT) a scalar field that encodes the entanglement between manifold sites. The scalar field provides a relational clock that enables the derivation of the Hamiltonian of the system from the GFT action. Inspecting the Hamiltonian, we show that a theory of emergent gravity arises, and that this can be recast according to the Ashtekar’s formulation of general relativity. The evolution of the GFT observables is regulated by the Shrödinger equation generated by the Hamiltonian. This is achieved by imposing a renormalization group (RG) flow that corresponds to a simplified Ricci flow. As a consequence of the quantization procedure, the Hamiltonian is recovered to be non-Hermitian, and can be related to the complex action formalism, in which the initial conditions and the related future evolution of the systems are dictated by the imaginary part of the action.

On the emergence of gravity in a framework of emergent quantum mechanics

In this work, we consider the emergent origin of gravity in the framework of Hamilton–Randers theory, a theoretical framework for emergent quantum mechanics. After presenting the essential ingredients of the theory, a derivation of the weak equivalence principle from the first principles of the theory follows. Then it is shown that the Newtonian model of gravity and certain modified gravity models are consistent with Hamilton–Randers theory. One of these models has strong formal resemblance with MOND, providing further ground to think that Hamilton–Randers theory could be a natural theoretical frame for realistic modified gravity models.

Testing Verlinde’s emergent gravity with the low acceleration gravitational anomaly observed in wide binary stars

Recent binary orbit analysis by Chae, and independently by Hernandez shows the breakdown of Newtonian gravity in the weak gravity regime. Unlike the galaxy rotation curves, this result cannot be explained by dark matter as the scale concerned is much smaller than the galactic scale, which makes the gravitational acceleration contribution of the dark matter completely negligible. We propose to explain this binary orbit anomaly by Verlinde’s emergent gravity by correcting a minor error in Verlinde’s emergent gravity. We theoretically derive g2=gB2+gD2, which replaces Verlinde’s g=gB+gD, where g is the total gravitational acceleration, gB is the usual Newtonian gravitational acceleration due to baryonic matter, and gD is what Verlinde calls gravitational acceleration due to “apparent dark matter.” This correction yields 1.29 for the Verlinde to Newton-predicted acceleration ratio, at the Newton-predicted acceleration gpred=10−10.00m/s2, for which Chae reported gobs/gpred=1.37−0.21+0.25 for the observed to Newton-predicted acceleration ratio at the same Newton-predicted acceleration. With our earlier successful fitting of galaxy rotation curves, our study provides the observational test of Verlinde’s emergent gravity.

Apparent and emergent dark matter around a Schwarzschild black hole

Inspired by the two different dark matter frameworks that were studied recently: one that arises from the non-local effects of entanglement entropy as emergent gravity (characterized by the parameter ξ(M), and zero-point scale length l), and one from dark energy viewed as a superconducting medium (characterized by η(M), and screening length parameter λG), two black hole solutions spherically surrounded with these dark matter models were derived. The effect of these two frameworks on SMBH was analyzed through the resulting deviations in the null regions and the black hole shadow. In addition, constraints to the parameters ξ and η (at 3σ level) were found using the available EHT data for Sgr. A* and M87*. These constraints allow one to deduce the effective mass M, which causes uncertainties in the measurement. On the other hand, if the effective mass is known, one can also deduce the constants associated with ξ, and η. The former framework also introduces an Appell function, a hypergeometric function of two variables that separately allows the analysis of macroscopic and (hypothetical) microscopic black holes. This first framework was found to decrease the radii of the null regions respective to the Schwarzschild counterpart. The shadow radius, however, behaves reversibly. The result of the numerical analysis for the latter framework revealed increased values for the photonsphere and shadow radii. Remarkably, the study also showed that for SMBHs, the amplifying effects of λG are stronger than the scale length l. Finally, results of constraints, as an example, for the upper bound in ξ for M87* indicated that the effective mass causing the deviation was around 2.4×1020M⊙ given that the observed Milgrom’s constant is 5.4×10−10m/s2.

Symplectic groupoids and Poisson electrodynamics

We develop a geometric approach to Poisson electrodynamics, that is, the semi-classical limit of noncommutative U(1) gauge theory. Our framework is based on an integrating symplectic groupoid for the underlying Poisson brackets, which we interpret as the classical phase space of a point particle on noncommutative spacetime. In this picture gauge fields arise as bisections of the symplectic groupoid while gauge transformations are parameterized by Lagrangian bisections. We provide a geometric construction of a gauge invariant action functional which minimally couples a dynamical charged particle to a background electromagnetic field. Our constructions are elucidated by several explicit examples, demonstrating the appearances of curved and even compact momentum spaces, the interplay between gauge transformations and spacetime diffeomorphisms, as well as emergent gravity phenomena.

Oxidation, reduction and semi-classical limit for quantum matrix geometries

Matrix configurations define noncommutative spaces endowed with extra structure including a generalized Laplace operator, and hence a metric structure. Made dynamical via matrix models, they describe rich physical systems including noncommutative gauge theory and emergent gravity. Refining the construction in [25], we construct a semi-classical limit through an immersed submanifold of complex projective space based on quasi-coherent states. We observe the phenomenon of oxidation, where the resulting semi-classical space acquires spurious extra dimensions. We propose to remove this artifact by passing to a leaf of a carefully chosen foliation, which allows to extract the geometrical content of the noncommutative spaces. This is demonstrated numerically via multiple examples.

Cosmological effects on f(R̄,T̄) gravity through a non-standard theory

This study aims to investigate the impact of dark energy in cosmological scenarios by exploiting [Formula: see text] gravity within the framework of a nonstandard theory, called K-essence theory, where [Formula: see text] represents the Ricci scalar and [Formula: see text] denotes the trace of the energy–momentum tensor associated with the K-essence geometry. The Dirac–Born–Infeld (DBI) nonstandard Lagrangian has been employed to generate the emergent gravity metric [Formula: see text] associated with the K-essence. This metric is distinct from the usual gravitational metric [Formula: see text]. It has been shown that under a flat Friedmann–Lemaître–Robertson–Walker (FLRW) background gravitational metric, the modified field equations and the Friedmann equations of the [Formula: see text] gravity are distinct from the usual ones. In order to get the equation of state (EoS) parameter [Formula: see text], we have solved the Friedmann equations by taking into account the function [Formula: see text], where [Formula: see text] represents a parameter within the model. We have found a relationship between [Formula: see text] and time for different kinds of [Formula: see text] by treating the kinetic energy of the K-essence scalar field ([Formula: see text]) as the dark energy density which fluctuates with time. Surprisingly, this result meets the condition of the restriction on [Formula: see text]. By presenting graphical representations of the EoS parameter with time, we show that our model is consistent with the data of SNIa[Formula: see text][Formula: see text][Formula: see text]BAO[Formula: see text][Formula: see text][Formula: see text][Formula: see text] within a certain temporal interval.

Asymptotically‐Flat Black Hole Solutions in Symmergent Gravity

AbstractSymmergent gravity is an emergent gravity model with an curvature sector and an extended particle sector having new particles beyond the known ones. With constant scalar curvature, asymptotically flat black hole solutions are known to have no sensitivity to the quadratic curvature term (coefficient of ). With variable scalar curvature, however, asymptotically‐flat symmergent black hole solutions turn out to explicitly depend on the quadratic curvature term. In the present work, asymptotically‐flat symmergent black holes with variable scalar curvature are constructed and used its evaporation, shadow, and deflection angle to constrain the symmergent gravity parameters. Concerning their evaporation, new particles predicted by symmergent gravity are found, even if they do not interact with the known particles, can enhance the black hole evaporation rate. Concerning their shadow, statistically significant symmergent effects are reached at the level for the observational data of the Event Horizon Telescope (EHT) on the Sagittarius A* supermassive black hole are shown. Concerning their weak deflection angle, discernible features for the boson‐fermion number differences are revealed, particularly at large impact parameters. These findings hold the potential to serve as theoretical predictions for future observations and investigations on black hole properties.

Life as the Explanation of the Measurement Problem

This study argues that a biological cell, a dissipative structure, is the smallest agent capable of processing quantum information through its triangulated, holographic sphere of perception, where this mechanism has been extended by natural evolution to endo and exosemiosis in multicellular organisms and further to the language of Homo sapiens. Thus, life explains the measurement problem of quantum theory within the framework of the holographic principle, emergent gravity, and emergent dimensionality. Each Planck triangle on a black hole surface corresponds to a qubit in an equal superposition, attaining known bounds on the products of its energies and orthogonalization interval. Black holes generate entropy variation shells through the solid-angle correspondence. The entropic work introduces the bounds on the number of active Planck triangles dependent on the information capacity of the black hole generator. The velocity and dissipativity bounds and the bounds on the theoretical probabilities for active, energy-carrying Planck triangles were derived. In particular, this study shows that black holes, Turing machines, and viruses cannot assume the role of an observer. The entropy variation shells and black-body objects may hint at solutions to ball lightning and sonoluminescence unexplained physical spherical phenomena.“It is also possible that we learned that the principal problem is no longer the fight with the adversities of nature but the difficulty of understanding ourselves if we want to survive” [1].

Null geodesic structure for the Barriola–Vilenkin spacetime via k-essence

Based on the work of Chandrasekhar [The Mathematical Theory of Black Holes, Chap. 3, Sec. 20 (Oxford University Press, 1992)], we investigate the null geodesic structure of the emergent Barriola–Vilenkin (BV) spacetime in the context of k-essence theory. For k-essence, the emergent gravity metric is a one-to-one correspondence with the BV metric connected to the Schwarzschild background, where the global monopole charge is replaced by the dark energy density. This equivalence holds specifically for a certain class of k-essence scalar fields that have been constructed by Gangopadhyay and Manna [Eur. Phys. Lett. 100, 49001 (2012)]. We have traced out different trajectories for null geodesic in the presence of dark energy for the k-essence emergent BV spacetime. It is demonstrated that the outcomes deviate from the typical Schwarzschild spacetime owing to the fundamental configuration with a constant dark energy density.

Implications of a Simpson–Visser solution in Verlinde’s framework

This study focuses on investigating a regular black hole within the framework of Verlinde’s emergent gravity. In particular, we explore the main aspects of the modified Simpson–Visser solution. Our analysis reveals the presence of a unique physical event horizon under certain conditions. Moreover, we study the thermodynamic properties, including the Hawking temperature, the entropy, and the heat capacity. Based on these quantities, our results indicate several phase transitions. Geodesic trajectories for photon-like particles, encompassing photon spheres and the formation of black hole shadows, are also calculated to comprehend the behavior of light in the vicinity of the black hole. Additionally, we also provide the calculation of the time delay and the deflection angle. Corroborating our results, we include an additional application in the context of high-energy astrophysical phenomena: neutrino energy deposition. Finally, we investigate the quasinormal modes using third-order WKB approximation.

Thermal properties of Simpson–Visser Minkowski core regular black holes solution in Verlinde’s emergent gravity

In this study, we investigate the thermodynamic characteristics of the Simpson–Visser Minkowski core black hole solution within Verlinde’s emergent gravity framework. Our analysis encompasses the examination of energy emission, Gibbs free energy, and thermal fluctuations. We calculate various quantities such as the Hawking temperature, geometric mass, and heat capacity to assess the local and global thermodynamic stability. The temperature of the black hole is determined using the first law of thermodynamics, while the energy emission rate is evaluated as well. By computing the Gibbs free energy, we explore the phase transition behavior exhibited by Verlinde’s emergent gravity black holes, specifically examining the swallowing tails. Moreover, we derive the corrected entropy to investigate the influence of thermal fluctuations on small and large black holes. Notably, we compare the impact of correction terms on the thermodynamic system by comparing the results obtained for large black holes and small black holes.

Analysis of a regular black hole in Verlinde’s gravity

This work focuses on the examination of a regular black hole within Verlinde’s emergent gravity, specifically investigating the Hayward-like (modified) solution. The study reveals the existence of three horizons under certain conditions, i.e. an event horizon and two Cauchy horizons. Our results indicate regions which phase transitions occur based on the analysis of heat capacity and Hawking temperature. To compute the latter quantity, we utilize three distinct methods: the surface gravity approach, Hawking radiation, and the application of the first law of thermodynamics. In the case of the latter approach, it is imperative to introduce a correction to ensure the preservation of the Bekenstein–Hawking area law. Geodesic trajectories and critical orbits (photon spheres) are calculated, highlighting the presence of three light rings. Additionally, we investigate the black hole shadows. Furthermore, the quasinormal modes are explored using third- and sixth-order Wentzel–Kramers–Brillouin approximations. In particular, we observe stable and unstable oscillations for certain frequencies. Finally, in order to comprehend the phenomena of time-dependent scattering in this scenario, we provide an investigation of the time-domain solution.

Limits of a non-local quantum spacetime

A generic implication of incorporating gravitational effects in the analysis of quantum measurements is the existence of a zero-point length of spacetime. This requires an inherently non-local description of spacetime, beyond the usual one based on metric [Formula: see text] etc. The quantum spacetime should instead be reconstructed from non-local bi-tensors of the form [Formula: see text]. A deeper look then reveals a subtle interplay between non-locality and the limit [Formula: see text]. In particular, the so-called emergent gravity paradigm — in which gravitational dynamics/action/spacetime are emergent and characterized by an entropy functional — arises as the Cheshire grin of a fundamentally non-local quantum spacetime. This paper describes the flow of metric with respect to Planck length, and proposes a novel action for the same.

Derivation of MOND from Hossenfelder–Verlinde gravity

Verlinde proposed emergent gravity, which naturally explains the Tully–Fisher relation, an empirical relation in galaxy rotation curves. Inspired by this theory, Hossenfelder constructed a covariant formulation of Verlinde’s emergent gravity. In this work, we show that the equation of motion gains an extra acceleration in addition to the usual geodesic equation, according to Hossenfelder’s theory. Moreover, we show that the extra acceleration is precisely the square root of the Newtonian gravitational acceleration if the mass of the imposter field is negligible, thus completing the proof that Hossenfelder’s theory reduces to modified Newtonian dynamics (MOND) and determining which version of MOND it reduces to. We also obtain the value of L in Hossenfelder–Verlinde gravity theory, which is a constant, contrary to what Hossenfelder claimed. Finally, we suggest how the Newtonian limit that suitably describes our observations in Solar System is recovered in Hossenfelder’s theory, by considering the mass of the imposter field.

Dark Universe phenomenology from Yukawa potential?

We argue that the effect of cold dark matter in the cosmological setup can be explained by the coupling between the baryonic matter particles in terms of the long-range force having a graviton mass mg via the Yukawa gravitational potential. Such a quantum-corrected Yukawa-like gravitational potential is characterized by the coupling parameter α, the wavelength parameter λ, which is related to the graviton mass via mg=ħ/(λc), that determines the range of the force and, finally, a Planck length quantity l0 that makes the potential regular at the centre. The modified Friedmann equations are obtained using Verlinde’s entropic force interpretation of gravity based on the holographic scenario and the equipartition law of energy. The parameter α modifies the Newton’s constant as Geff=G(1+α). Interestingly, we find an equation that relates the dark matter density, dark energy density, and baryonic matter density. It is given by ΩD=2ΩBΩΛ(1+z)3. We argue that dark matter is an apparent effect as no dark matter particle exists in this picture. Furthermore, the dark energy is also related to graviton mass and α; in particular, we point out that the cosmological constant can be viewed as a self-interaction effect between gravitons. We further show a precise correspondence with Verlinde’s emergent gravity theory, and due to the long-range force, the theory can be viewed as a non-local gravity theory. To this end, we performed the phase space analyses and estimated λ≃103 [Mpc] and α≃0.04, respectively. Finally, from these values, for the graviton mass, we get mg≃10−68 kg, and cosmological constant Λ≃10−52m−2. Further, we argue how this theory reproduces the MOND phenomenology on galactic scales via the acceleration of Milgrom a0≃10−10m/s2.

Quasinormal modes and greybody factors of symmergent black hole

Symmergent gravity is an emergent gravity framework in which gravity emerges guided by gauge invariance, accompanied by new particles, and reconciled with quantum fields. In this paper, we perform a detailed study of the quasinormal modes and greybody factors of the black holes in symmergent gravity. Its relevant parameters are the quadratic curvature term cO and the vacuum energy parameter α. In our analyses, effects of the both parameters are investigated. Our findings suggest that, in both positive and negative direction, large |cO| values of the parameter on the quasinormal modes parallel the Schwarzschild black hole. Moreover, the quasinormal model spectrum is found to be sensitive to the symmergent parameter α. We contrast the asymptotic iteration and WKB methods in regard to their predictions for the quasinormal frequencies, and find that they differ (agree) slightly at small (large) multipole moments. We analyze time-domain profiles of the perturbations, and determine the greybody factor of the symmergent black hole in the WKB regime. The symmergent parameter α and the quadratic curvature term cO are shown to impact the greybody factors significantly. We provide also rigorous limits on greybody factors for scalar perturbations, and reaffirm the impact of model parameters.