It is still a challenging problem to the theoretical physicists to know the exact nature of the galactic dark matter which causes the galactic rotational velocity to be more or less a constant. We have proposed that the dark matter as an effect of f(T) gravity. Assuming the flat rotation curves as input we have shown that f(T) gravity can explain galactic dynamics. Here, we don' have to introduce dark matter. Spacetime metric inspired by f(T) gravity describes the region up to which the tangential velocity of the test particle is constant. This inherent property appears to be enough to produce stable circular orbits as well as attractive gravity.
In this paper we extend some previous results for a new proposal for gravity and place them into overall context. The basic fields of this proposal provide an off-shell realization of symmetry with respect to SO(3,C) gauge transformations and general coordinate transformations of 4-dimensional spacetime.
We propose a model for the quantum theory of gravity. the model has diffeomorphism invariance, a natural length scale, and (plausibly) propagating modes. in the new addendum, we alter the model in a way which makes the propagating modes much easier to approach.
In this paper we perform a full gauge-fixing of the phase space of four dimensional General Relativity (GR) of Lorentzian signature for the time symmetric case, using the CDJ variables. In particular, the Gauss' law constraint in the chosen gauge meets the conditions of the Cauchy-Kovalevskaya theorem for first order, quasilinear PDEs. This implies the existence of a unique analytic solution to the initial value constraints problem in some region of 3-space, featuring four free functions per spacetime point. This result constitutes a step toward addressal of the reduced phase space problem of …
Covariant models of loop quantum gravity generically imply dynamical signature change at high density. This article presents detailed derivations that show the fruitful interplay of this new kind of signature change with wave-function proposals of quantum cosmology, such as the no-boundary and tunneling proposals. In particular, instabilities of inhomogeneous perturbations found in a Lorentzian path-integral treatment are naturally cured. Importantly, dynamical signature change does not require Planckian densities when off-shell instantons are relevant.
A growing number of studies is being devoted to the identification of plausible quantum properties of spacetime which might give rise to observably large effects. The literature on this subject is now relatively large, including studies in string theory, loop quantum gravity and noncommutative geometry. It is useful to divide the various proposals into proposals involving a systematic quantum-gravity effect (an effect that would shift the main/average prediction for a given observable quantity) and proposals involving a non-systematic quantum-gravity effect (an effect that would introduce new …
In this paper, I investigate the possible quantization, in the context of LQG, of three dimensional gravity in the case of positive cosmological constant Λ and try to make contact with alternative quantization approaches already existing in the literature. Due to the appearance of an anomaly in the constraints algebra, previously studied as a first step of the analysis, alternative techniques developed for the quantization of systems with constraints algebras not associated with a structure Lie group need to be adopted. Therefore, I introduce an ansatz for a physical state which gives some tra…
The "problem of time" in canonical quantum gravity refers to the difficulties involved in defining a Hilbert space structure on states -- and local observables on this Hilbert space -- for a theory in which the spacetime metric is treated as a quantum field, so no classical metrical or causal structure is present on spacetime. We describe an approach -- much in the spirit of ideas proposed by Misner, Kuchar and others -- to defining states and local observables in quantum gravity which exploits the analogy between the Hamiltonian formulation of general relativity and that of a relativistic par…
We elaborate on a proposal made by Greensite and others to solve the problem of time in quantum gravity. The proposal states that a viable concept of time and a sensible inner product can be found from the demand for the Ehrenfest equations to hold in quantum gravity. We derive and discuss in detail exact consistency conditions from both Ehrenfest equations as well as from the semiclassical approximation. We also discuss consistency conditions arising from the full field theory. We find that only a very restricted class of solutions to the Wheeler-DeWitt equation fulfills all consistency condi…
We consider the possibility of an alternative gravity theory explaining the dynamics of galactic systems without dark matter. From very general assumptions about the structure of a relativistic gravity theory we derive a general expression for the metric to order $(v/c)^2$. This allows us to compare the predictions of the theory with various experimental data: the Newtonian limit, light deflection and retardation, rotation of galaxies and gravitational lensing. Our general conclusion is that the possibility for any gravity theory to explain the behaviour of galaxies without dark matter is rath…
We describe a scheme for the exploration of quantum gravity phenomenology focussing on effects that could be thought as arising from a fundamental granularity of space-time. In contrast with the simplest assumptions, such granularity is assumed to respect Lorentz Invariance but is otherwise left unspecified. The proposal is fully observer covariant, it involves non-trivial couplings of curvature to matter fields and leads to a well defined phenomenology. We present the effective Hamiltonian which could be used to analyze concrete experimental situations, some of which are briefly described, an…
Two very similar proposals have been made recently for witnessing nonclassical features of gravity, by Bose et al. and by Marletto and Vedral. However, while these proposals are asserted to be very general, they are in fact based on a very strong claim: that quantum systems cannot become entangled via a classical intermediary. We point out that the support provided for this claim is only applicable to a very limited class of quantum-classical interaction models, corresponding to Koopman-type dynamics. We show that the claim is also valid for mean-field models, but that it is contradicted by ex…
It is known that the no-boundary proposal in the traditional Einstein gravity does not prefer inflation, that is, the probability of realizing a large number of e-folds is exponentially suppressed. This situation may be changed drastically in a class of nonlinear massive gravity theories recently proposed by deRham, Gabadadze and Tolley, called dRGT massive gravity. We show that the contribution from the massive gravity sector can enhance the probability of a large number of e-folds substantially for a sufficiently large mass parameter mg comparable to the Hubble parameter during inflation, sa…
Penrose suggested that issues with the origin of the second law of thermodynamics and the remarkable homogeneous and isotropic nature of the universe on large scales can be resolved with a concept of an entropy for gravitational fields captured by the Weyl curvature tensor. This has led to various proposals for an entropy density for gravity constructed from the Weyl tensor. Most work investigating such entropy densities have been restricted to general relativity and little work has been done to them in modified theories of gravity. To remedy this, we investigate the simplest proposal for an e…
We review a recent proposal for the construction of a quantum theory of the gravitational field. The proposal is based on approximating the continuum theory by a discrete theory that has several attractive properties, among them, the fact that in its canonical formulation it is free of constraints. This allows to bypass many of the hard conceptual problems of traditional canonical quantum gravity. In particular the resulting theory implies a fundamental mechanism for decoherence and bypasses the black hole information paradox.
We propose new version of massive $F(R)$ gravity which is natural generalization of convenient massive ghost-free gravity. Its Hamiltonian formulation in scalar-tensor frame is developed. We show that such $F(R)$ theory is ghost-free. The cosmological evolution of such theory is investigated. Despite the strong Bianchi identity constraint the possibility of cosmic acceleration (especially, in the presence of cold dark matter) is established. Ghost-free massive $F(R,T)$ gravity is also proposed.
The class of covariant gravity theories which have nice ultraviolet behavior and seem to be (super)-renormalizable is proposed. The apparent breaking of Lorentz invariance occurs due to the coupling with the effective fluid which is induced by Lagrange multiplier constrained scalar field. Spatially-flat FRW cosmology for such covariant field gravity may have accelerating solutions. Renormalizable versions of more complicated modified gravity which depends on Riemann and Ricci tensor squared may be constructed in the same way.
We study the thermodynamics of galactic clustering under the higher-order corrected Newtonian dynamics. The clustering of galaxies is considered as a gravitational phase transition. In order to study the effects of higher-order correction to the thermodynamics of gravitational system, we compute more exact equations of state. Moreover, we investigate the corrected probability distribution function for such gravitating system. A relation between order parameter and the critical temperature is also established.
Explicit tests are presented of the conjectured entropic origin of the gravitational force. The gravitational force on a test particle in the vicinity of the horizon of a large Schwarzschild black hole in arbitrary spacetime dimensions is obtained as entropic force. The same conclusion can be reached for the cases of a large electrically charged black hole and a large slowly rotating Kerr black hole. The generalization along the same lines to a test mass in the field of an arbitrary spherical star is also studied and found not to be possible. Our results thus reinforce the argument that the en…
Weak field approximate solutions in the Lambda-->0 limit of a model of de Sitter gravity have been presented in the static and spherically symmetric case. Although the model looks different from general relativity, among those solutions, there still exist the weak Schwarzschild fields with the smooth connection to regular internal solutions obeying the Newtonian gravitational law. The existence of such solutions would determine the value of the coupling constant, which is different from that of the previous literature. Moreover, there also exist solutions that could deduce the galactic rotatio…
We present a geometric scalar theory of gravity. Our proposal will be described using the "background field method" introduced by Gupta, Feynman and others as a field theory formulation of general relativity. We analyze previous criticisms against scalar gravity and show how the present proposal avoids these difficulties. This concerns not only the theoretical complaints but also those related to observations. In particular, we show that the widespread belief of the conjecture that the source of scalar gravity must be the trace of the energy-momentum tensor - which is one of the main difficult…
We consider possible signatures for the so called {\it hybrid gravity} within the Galactic Central Parsec. This modified theory of gravity consists of a superposition of the metric Einstein-Hilbert Lagrangian with an $f(R)$ term constructed {\it à la Palatini} and can be easily reduced to an equivalent scalar-tensor theory. Such an approach is introduced in order to cure the shortcomings related to $f(R)$ gravity, in general formulated either in metric or in metric-affine frameworks. Hybrid gravity allows to disentangle the further gravitational degrees of freedom with respect to those of stan…
We propose a new method of searching for the composition-dependent dilatonic waves, predicted by unified theories of strings. In this method, Earth's surface-gravity changes due to translational motions of its inner core, excited by dilatonic waves, are searched for by using superconducting gravimeters. This method has its best sensitivity at the frequency of $\sim$ 7 $\times$ 10$^{-5}$ Hz, which is lower than the sensitive frequencies of previous proposals using gravitational-wave detectors: $\sim$ 10 to 1000 Hz. Using available results of surface-gravity measurements with superconducting gra…
Various approaches to quantum gravity such as string theory, loop quantum gravity and Horava-Lifshitz gravity predict modifications of the energy-momentum dispersion relation. Magueijo and Smolin incorporated the modified dispersion relation (MDR) with the general theory of relativity to yield a theory of gravity's rainbow. In this paper, we investigate the Schwarzschild metric in the context of gravity's rainbow. We investigate rainbow functions from three known modified dispersion relations that were introduced by Amelino-Camelia, et el. in [arXiv:hep-th/9605211, arXiv:0806.0339v2, arXiv:ast…
In the first paper of this series, we have introduced the concept of an atom of space-time-matter [STM], which is described by the spectral action of non-commutative geometry, corresponding to a classical theory of gravity. In the present work, we use the Connes time parameter along with the spectral action, to incorporate gravity into trace dynamics. We then derive the spectral equation of motion for the STM atom, which turns out to be the Dirac equation on a non-commutative space.
An attempt has been made to explore the galactic dynamics via the rotational velocity beyond the Einstein's geometric theory of gravity. It is inspired from the geometric relation obtained in the power law $f(R)$ gravity model in vacuum. We analyse the action with a small positive deviation from the Einstein-Hilbert action (taking $R$ as $f(R)\propto R^{1+δ}$) at the galactic scales for the explanation of cosmological dark matter problem and obtain the contribution of dynamical $f(R)$ background geometry in accelerating the test mass. In the weak field limits, we obtain the effective accelerat…
The GRAVITY Collaboration achieved the remarkable detection of the orbital precession of the S2 star around the Galactic centre supermassive black hole, providing yet another proof of the validity of the General Relativity. The departure from the Schwarzschild precession is encoded in the parameter $f_{\rm SP}$ which multiplies the predicted general relativistic precession. Such a parameter results to be $f_{\rm SP}=1.10\pm0.19$, which is consistent with General Relativity ($f_{\rm SP}=1$) at 1$σ$ level. Nevertheless, this parameter may also hide an effect of modified theories of gravity. Thus…
This note includes five sections. In section 2 a number of aesthetically motivated f(R) Lagrangians is proposed and frivolously explored in the metric formalism with variable Newton constant G(x). In section 3 the idea of deforming the terms in a given f(R) gravity-matter action S, and prior to extremizing it, is promoted with the aim of reducing S via an algebraic mixing between few selected gravity and matter terms without invoking new fields. The result of this is a number of constraint equations among the fields and often eccentric looking field equations derived from the reduced action. S…
The observations of photons from the BL Lac object Mk501 with energies above 10 TeV and of cosmic rays with energies above the GZK threshold appear to be inconsistent with conventional theories. Remarkably, among the recent new-physics proposals of solutions of these threshold paradoxes a prominent role has been played by proposals based on quantum properties of space-time. While the experimental evidence (and theory work attempting to interpret it) is much too preliminary to justify any serious hopes that we might have stumbled upon the first manifestation of a "quantum gravity", the fact tha…
In this work we derive a generalized Newtonian gravitational force and show that it can account for the anomalous galactic rotation curves. We derive the entropy-area relationship applying the Feynman-Hibbs procedure to the supersymmetric Wheeler-DeWitt equation of the Schwarzschild black hole. We obtain the modifications to the Newtonian gravitational force from the entropic formulation of gravity.
We present a new, falsifiable, quantum theory of gravity, which we name Non-commutative Matter-Gravity. The commutative limit of the theory is classical general relativity. In the first two papers of this series, we have introduced the concept of an atom of space-time-matter [STM], which is described by the spectral action in non-commutative geometry, corresponding to a classical theory of gravity. We used the Connes time parameter, along with the spectral action, to incorporate gravity into trace dynamics. We then derived the spectral equation of motion for the gravity part of the STM atom, w…
The sparsity parameter for clusters of galaxies is obtained in the context of $Λ$-gravity. It is shown that, the theoretical estimated values are within the reported error limits of the measured data. Thus, in the future the sparsity parameter can serve as an informative new test to detect the discrepancy between General Relativity and $Λ$-gravity.
The accelerated expansion of the universe is the most debatable cosmological scenario in the last two decades. Looking for the proper explanation of this scenario, researchers have presented a lot of proposals to discuss it. However, somehow, most of the proposal seems incomplete and needs to improve for a better representation of the universe. Therefore, this thesis aims to investigate some problems searching for an accurate explanation of the accelerated scenario of the universe...
In this series of papers, we propose a new rendition of 3d and 4d state sum models based upon the group field theory (GFT) approach to non-perturbative quantum gravity. We will see that the group field theories investigated in the literature to date are, when judged from the position of quantum field theory, an unusual manifestation of quantum dynamics. They are one in which the Hadamard function for the field theory propagates a-causally the physical degrees of freedom of quantum gravity. This is fine if we wish to define a scalar product on the physical state space, but it is not what we gen…
"Wave gravity" refers to a quantum-mechanical gravity theory introduced in two previous papers [1,2]. Although based on the optics of de Broglie waves instead of curved space-time, it agrees with the standard tests of general relativity. As in that theory, galactic nuclei are dark objects where gravity prevents the escape of most radiation. In this case, collapse is counteracted by rising internal pressure and black hole singularities don't occur. Unlike black holes, these nuclei can have internal magnetic fields, and high-energy plasma can escape along magnetic field lines closely aligned wit…
This is my Thèse d'Habilitation (HDR) on the topic of spinfoam models for quantum gravity, which I presented in l'Ecole Normale Supérieure de Lyon on december 16 2010. The spinfoam framework is a proposal for a regularized path integral for quantum gravity, inspired from Topological Quantum Field Theory (TQFT) and state-sum models. It can also be seen as defining transition amplitudes for the quantum states of geometry for Loop Quantum Gravity (LQG).
For Rindler observers accelerating close to the horizon in local patches around a spacetime point, the matter-energy passing through the horizon increases the entropy and heat energy. Jacobson has showed that the Einstein equation can be derived from the consideration of this thermodynamic process. This, however, works only if the acceleration $a$ is much larger than the scale set by the curvature of the spacetime. It is explored here whether an extension is possible to the case with no lower bound on $a$. We show that this is possible if one assumes that in a locally accelerating frame, the m…
We describe a refined version of a previous proposal for the exploration of quantum gravity phenomenology. Unlike the original scheme, the one presented here is free from sign ambiguities while it shares with the previous one the essential features. It focuses on effects that could be thought as arising from a fundamental granularity of quantum space-time. The sort of schemes we consider are in sharp contrast with the simplest scenarios in that such granularity is assumed to respect Lorentz Invariance but it remains otherwise unspecified. The proposal is fully observer covariant, it involves n…
Holographic entanglement entropy provides a direct connection between classical geometry and quantum entanglement; however the usual prescription does not apply to theories of higher spin gravity, where standard notions of geometry are no longer gauge invariant. We present a proposal for the holographic computation of entanglement entropy in field theories dual to higher spin theories of gravity in AdS3. These theories have a Chern-Simons description, and our proposal involves a Wilson line in an infinite-dimensional representation of the bulk gauge group. In the case of spin-2 gravity such Wi…
We examine holographic complexity in the doubly holographic model introduced in [arXiv:2006.04851][arXiv:2010.00018] to study quantum extremal islands. We focus on the holographic complexity=volume (CV) proposal for boundary subregions in the island phase. Exploiting the Fefferman-Graham expansion of the metric and other geometric quantities near the brane, we derive the leading contributions to the complexity and interpret these in terms of the generalized volume of the island derived from the induced higher-curvature gravity action on the brane. Motivated by these results, we propose a gener…
We show quantitatively that an exact solution of Einstein's conformal gravity can explain very well the galactic rotation curves for a sample of 104 galaxies without need for dark matter or other exotic modification of gravity. The metric is an overall rescaling of the Schwarzschild-de Sitter spacetime as required by Weyl conformal invariance, which has to be spontaneously broken, and the velocity of the stars depends only on two universal parameters determined on the base of the observational data.
The black hole final state proposal implements manifest unitarity in the process of black hole formation and evaporation in quantum gravity, by postulating a unique final state boundary condition at the singularity. We argue that this proposal can be embedded in the gauge/gravity context by invoking a path integral formalism inspired by the Schwinger-Keldysh like thermo-field double construction in the dual field theory. This allows us to realize the gravitational quantum channels for information retrieval to specific deformations of the field theory path integrals and opens up new connections…
Bose-Einstein condensate dark matter model and Randall-Sundrum type 2 brane-world theory are tested with galactic rotation curves. Analytical expressions are derived for the rotational velocities of test particles around the galactic center in both cases. The velocity profiles are fitted to the observed rotation curve data of high surface brightness and low surface brightness galaxies. The brane-world model fits better the rotation curves with asymptotically flat behaviour.
We investigate galactic rotation curves in $f(T)$ gravity, where $T$ represents a torsional quantity. Our study centers on the particular Lagrangian $f(T)=T+α{T^n}$, where $|n|\neq 1$ and $α$ is a small unknown constant. To do this we treat galactic rotation curves as being composed from two distinct features of galaxies, namely the disk and the bulge. This process is carried out for several values of the index $n$. The resulting curve is then compared with Milky Way profile data to constrain the value of the index $n$ while fitting for the parameter $α$. These values are then further tested o…
As an attempt to realize Wheeler's "it-from-bit proposal" that physics should be reduced to simple yes-no questions we consider a model of loop quantum gravity, where the only allowed values of the quantum numbers $j_p$ at the punctures of the spin network on the spacelike two-surfaces of spacetime are $0$ and $\frac{1}{2}$. When $j_p=0$, the puncture is in the vacuum, and it does not contribute to the area of the two-surface, whereas when $j_p=\frac{1}{2}$, the puncture is in an excited state, and the allowed values of the associated quantum number $m_p$ are $-\frac{1}{2}$ and $+\frac{1}{2}$.…
We examine the viability of Weyl conformal gravity as an alternative to the general theory of relativity. By using the extended rotation curve of the Milky Way and velocity dispersions of four globular clusters, we show that Weyl gravity predictions without resorting to dark matter comply with observations at the galactic scale. For the Milky Way, we demonstrate that the uncertainty in baryonic modelling results a bracket of possible rotational velocities which well encompasses the diversity in rotation curve construction. Such diversity generally arises from differences in measurements of vel…
We elaborate on our proposal regarding a connection between global physics and local galactic dynamics via quantum gravity. This proposal calls for the concept of MONDian dark matter which behaves like cold dark matter at cluster and cosmological scales but emulates modified Newtonian dynamics (MOND) at the galactic scale. In the present paper, we first point out a surprising connection between the MONDian dark matter and an effective gravitational Born-Infeld theory. We then argue that these unconventional quanta of MONDian dark matter must obey infinite statistics, and the theory must be fun…
In this thesis, we study the implications of Quantum Gravity models for the dynamics of spacetime and the ensuing departures from classical General Relativity. The main focus is on cosmological applications, particularly the impact of quantum gravitational effects on the dynamics of a homogenous and isotropic cosmological background. Our interest lies in the consequences for the evolution of the early universe and singularity resolution, as well as in the possibility of providing an alternative explanation for dark matter and dark energy in the late universe. The thesis is divided into two mai…
We analyze the classical limit of kinematic loop quantum gravity in which the diffeomorphism and hamiltonian constraints are ignored. We show that there are no quantum states in which the primary variables of the loop approach, namely the SU(2) holonomies along {\em all} possible loops, approximate their classical counterparts. At most a countable number of loops must be specified. To preserve spatial covariance, we choose this set of loops to be based on physical lattices specified by the quasi-classical states themselves. We construct ``macroscopic'' operators based on such lattices and prop…
The nonperturbative renormalization group flow of Quantum Einstein Gravity (QEG) is reviewed. It is argued that there could be strong renormalization effects at large distances, in particular a scale dependent Newton constant, which mimic the presence of dark matter at galactic and cosmological scales.
Over the last few years the study of possible Planck-scale departures from classical Lorentz symmetry has been one of the most active areas of quantum-gravity research. We now have a satisfactory description of the fate of Lorentz symmetry in the most popular noncommutative spacetimes and several studies have been devoted to the fate of Lorentz symmetry in loop quantum gravity. Remarkably there are planned experiments with enough sensitivity to reveal these quantum-spacetime effects, if their magnitude is only linearly suppressed by the Planck length. Unfortunately, in some quantum-gravity sce…
We show that a recent proposal for the quantization of gravity based on discrete space-time implies a modification of standard quantum mechanics that naturally leads to a loss of coherence in quantum states of the type discussed by Milburn. The proposal overcomes the energy conservation problem of previously proposed decoherence mechanisms stemming from quantum gravity. Mesoscopic quantum systems (as Bose--Einstein condensates) appear as the most promising testing grounds for an experimental verification of the mechanism.
We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction is the inclusion of new proposals for coupling matter to gravity that can be used to deparametrize the theory, thus making its dynamics more tractable. The classical and quantum aspects of these new proposals are explained alongside the standard quantization of vacuum general relativity in loop quantum gravity.
