We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime which causes a noncommutative spacetime at the Planck scale L_P. The symplectic structure of spacetime M leads to an isomorphism between symplectic geometry (M, ω) and Riemannian geometry (M, g) where the deformations of symplectic structure ωin terms of electromagnetic fields F=dA are transformed into those of Riemannian metric g. This approach for quantum gravity allows a background independent formulation where spacetime as well as matter fields is equally emergent from a universal vacuum of quantum gravity which is thus dubbed as the quantum equivalence principle.
We address issues on the origin of gravity and the cosmological constant problem based on a recent understanding about the correspondence between noncommutative field theory and gravity. We suggest that the cosmological constant problem can be resolved in a natural way if gravity emerges from a gauge theory in noncommutative spacetime. Especially, we elucidate why the emergent gravity implies that vacuum energy does not gravitate but only fluctuations around the vacuum generate gravity. That is, a flat spacetime emerges from uniform condensation of energy, previously identified with the cosmol…
We address issues on the origin of gravity and the dark energy (or the cosmological constant) from the perspectives of emergent gravity. We discuss how the emergent gravity reveals a noble, radically different picture about the origin of spacetime, which is crucial for a tenable solution of the cosmological constant problem. In particular, the emergent gravity naturally explains the dynamical origin of flat spacetime, which is absent in Einstein gravity.
We showed before that self-dual electromagnetism in noncommutative (NC) spacetime is equivalent to self-dual Einstein gravity. This result implies a striking picture about gravity: Gravity can emerge from electromagnetism in NC spacetime. Gravity is then a collective phenomenon emerging from gauge fields living in fuzzy spacetime. We elucidate in some detail why electromagnetism in NC spacetime should be a theory of gravity. In particular, we show that NC electromagnetism is realized through the Darboux theorem as a diffeomorphism symmetry G which is spontaneously broken to symplectomorphism H…
We investigate emergent gravity extending the paradigm of the AdS/CFT correspondence. The emergent graviton is associated to the (dynamical) expectation value of the energy-momentum tensor. We derive the general effective description of such dynamics, and apply it to the case where a hidden theory generates gravity that is coupled to the Standard Model. In the linearized description, generically, such gravity is massive with the presence of an extra scalar degree of freedom. The propagators of both the spin-two and spin-zero modes are positive and well defined. The associated emergent gravitat…
We point out that recent Verlinde's proposal of emergent gravity suffers from some internal inconsistencies. The main idea in this proposal is to preserve general relativity at short scales where numerous tests verified its validity, but modify it on large scales where we meet puzzles raised by observations (in particular dark matter), by using some entropic concepts. We first point out that gravity as a conservative force is very difficult (if possible at all) to portray as an entropic force. We then show that the derivation of the MOND relation using the elastic strain idea is not self-consi…
We revisit a non-perturbation theory of quantum gravity in $1.5$ order underlying an emergent gravitational pair of $(4{\bar 4})$-brane with a renewed interest. In particular the formulation is governed by a geometric torsion ${\cal H}_3$ in second order with an on-shell NS form in first order. Interestingly the gravitational pair is sourced by a Kalb-Ramond two form CFT on a $D_5$-brane in $d$$=$$10$ type IIB superstring theory. We show that a generic form theory containing a CFT sector in $d=6$ bulk may be described by a boundary ${\rm AdS}_5$ with a quintessence Q. Analysis reveals that the…
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.
Kaluza-Klein gravity is revisted, with renewed interest, in a type IIB string theory on $S^1\times K3$. The irreducible curvature tensors are worked out in the, T-dual, emergent gravity in 4D to yield a non-linear U(1) gauge theory. Interestingly, the T-duality may be seen to describe an open/closed string duality at a self-dual string coupling. The obtained deformation in $AdS_5$ black hole is analyzed to introduce the notion of temperature in the emergent gravity underlying the recent idea of entropic force.
We present an exposition on the geometrization of the electromagnetic force. We show that, in noncommutative (NC) spacetime, there always exists a coordinate transformation to locally eliminate the electromagnetic force, which is precisely the Darboux theorem in symplectic geometry. As a consequence, the electromagnetism can be realized as a geometrical property of spacetime like gravity. We show that the geometrization of the electromagnetic force in NC spacetime is the origin of gravity, dubbed as the emergent gravity. We discuss how the emergent gravity reveals a novel, radically different …
The idea of gravity as an "emergent" phenomenon has gained popularity in recent years. I discuss some of the obstacles that any such model must overcome in order to agree with the observational underpinnings of general relativity.
We investigate an emergent gravity in $(4+1)$ dimensions underlying a geometric torsion ${\cal H}_3$ in $1.5$ order formulation. We show that an emergent pair-symmetric $4$th order curvature tensor underlying a NS field theory governs a torsion free geometry and is identified as the Riemann type tensor. Interestingly a pair anti-symmetric $4$th order tensor is shown to incorporate a dynamical correction underlying a ${\cal H}_3$ gauge potential and is identified with a non-perturbative correction. The non-perturbative term in the emergent action is shown to be described by a $U(1)$ gauge invar…
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.
In this paper, we study the collapsing scenario for the k-essence emergent Vaidya spacetime in the context of massive gravity's rainbow. For this study, we consider that the background metric is Vaidya spacetime in massive gravity's rainbow. We show that the k-essence emergent gravity metric resembles closely to the new type of generalized Vaidya massive gravity metric with the rainbow deformations for null fluid collapse where we consider the k-essence scalar field as a function solely of the advanced or the retarded time. The k-essence emergent Vaidya massive gravity rainbow mass function is…
I review recent work toward constructing, via five-dimensional holographic duals, four-dimensional theories in which spin-2 states (gravitons) are emergent. The basic idea is to extend to gravity model-building the applications of holographic duality to phenomenology construction.
A constraint of vanishing energy-momentum tensor is motivated by a variety of perspectives on quantum gravity. We demonstrate in a concrete example how this constraint leads to a metric-independent theory in which quantum gravity emerges as a nonperturbative artifact of regularization-scale physics. We analyze a scalar theory similar to the Dirac-Born-Infeld (DBI) theory with vanishing gauge fields, with the DBI Lagrangian modulated by a scalar potential. In the limit of a large number of scalars, we explicitly demonstrate the existence of a composite massless spin-2 graviton in the spectrum t…
We show that if one starts with a Universe with some matter and a cosmological constant, then quantum mechanics naturally induces an attractive gravitational potential and an effective Newton's coupling. Thus gravity is an emergent phenomenon and what should be quantized are the fundamental degrees of freedom from which it emerges.
We consider a deformation of five-dimensional warped gravity with bulk and boundary mass terms to quadratic order in the action. We show that massless zero modes occur for special choices of the masses. The tensor zero mode is a smooth deformation of the Randall-Sundrum graviton wavefunction and can be localized anywhere in the bulk. There is also a vector zero mode with similar localization properties, which is decoupled from conserved sources at tree level. Interestingly, there are no scalar modes, and the model is ghost-free at the linearized level. When the tensor zero mode is localized ne…
We give a critical overview of various attempts to describe gravity as an emergent phenomenon, starting from examples of condensed matter physics, to arrive to more sophisticated pregeometric models. The common line of thought is to view the graviton as a composite particle/collective mode. However, we will describe many different ways in which this idea is realized in practice.
We discuss the relevance of quantum gravity to the frontier questions in high energy phenomenology: the problems of dark matter, dark energy, and vacuum selection as well as the problems of emergent spacetime and wormholes. Dark matter and dark energy phenomenology, and the problem of vacuum selection are discussed within the context of string theory as a model of quantum gravity. Emergent spacetime and wormholes are discussed in a more general context of effective theories of quantum gravity.
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…
We explore emergent geometry of the spacetime at the microscopic scale by adiabatic transport of a quasi-coherent state of a fermionic string, with quantum spacetime described by the matrix theory (BFSS matrix model). We show that the generator of the Berry phase is the shift vector of the spacetime foliation by spacelike surfaces associated with the quasi-coherent state. The operator-valued generator of the geometric phase of weak adiabatic transport is the Lorentz connection of the emergent geometry which is not torsion free at the microscopic scale. The effects of the torsion seem consisten…
A direct and non-trivial link between Padmanabhan's entropy used in emergent gravity and standard GR action is established. To do that, Augmented Variational Principles (AVP) will be used. We shall discuss how this link accounts for the details of the variation of Padmanabhan's action based on gravitational entropy. It will also clarify the role of the background metric and its non-dynamical role.
General theory of relativity (or Lovelock extensions) is a dynamical theory; given an initial configuration on a space-like hypersurface, it makes a definite prediction of the final configuration. Recent developments suggest that gravity may be described in terms of macroscopic parameters. It finds a concrete manifestation in the fluid-gravity correspondence. Most of the efforts till date has been to relate equilibrium configurations in gravity with fluid variables. In order for the emergent paradigm to be truly successful, it has to provide a statistical mechanical derivation of how a given i…
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…
We consider alternative inflationary cosmologies in massive gravity with degenerate reference metrics and study the feasibilities of the emergent universe scenario, bouncing and cyclic universes. We focus on the construction of the Einstein static universe, classes of exact solutions of bouncing and cyclic universes in degenerate massive gravity. We further study the stabilities of the Einstein static universe against both homogeneous and inhomogeneous scalar perturbations and give the parameters region for a stable Einstein static universe.
We examine the picture of emergent geometry arising from a mass-deformed matrix model. Because of the mass-deformation, a vacuum geometry turns out to be a constant curvature spacetime such as d-dimensional sphere and (anti-)de Sitter spaces. We show that the mass-deformed matrix model giving rise to the constant curvature spacetime can be derived from the d-dimensional Snyder algebra. The emergent geometry beautifully confirms all the rationale inferred from the algebraic point of view that the d-dimensional Snyder algebra is equivalent to the Lorentz algebra in (d+1)-dimensional {\it flat} s…
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 introduce a novel model of affine gravity, which implements the no-scale scenario. Namely, Planck mass and Hubble constant emerge dynamically, through the mechanism of spontaneous breaking of scale-invariance. Moreover, in our model the time direction and non--degenerate metric emerge dynamically as well. This naturally gives rise to the inflation and may server as a starting point for the "birth" of the Universe. We show that our model is phenomenologically viable, both from the perspective of the direct tests of gravity and cosmological evolution.
We discuss how inflation can emerge from a four-fermion interaction induced by torsion. Inflation can arise from coupling torsion to Standard Model fermions, without any need of introducing new scalar particles beyond the Standard Model. Within this picture, the inflaton field can be a composite field of the SM-particles and arises from a Nambu-Jona-Lasinio mechanism in curved space-time, non-minimally coupled with the Ricci scalar. The model we specify predicts small value of the r-parameter, namely $r\sim 10^{-4} ÷10^{-2}$, which nonetheless would be detectable by the next generation of expe…
We present some general approach to emergent gauge theories and consider in significant detail the emergent tensor field gravity case. In essence, an arbitrary local theory of a symmetric two-tensor field $H_{μν}$ in Minkowski spacetime is considered, in which the equations of motion are required to be compatible with a nonlinear $σ$ model type length-fixing constraint $H_{μν}^{2}=\pm M^{2}$ leading to spontaneous Lorentz invariance violation, SLIV ($M$ is the proposed scale for SLIV). Allowing the parameters in the Lagrangian to be adjusted so as to be consistent with this constraint, the the…
We verify explicitly that UV/IR mixing for noncommutative gauge theory can be understood in terms of an induced gravity action, as predicted by the identification [1] of gravity within matrix models of NC gauge theory. More precisely, we obtain the Einstein-Hilbert action by integrating out a scalar field in the adjoint. It arises from the well-known UV/IR mixing of NC gauge theory, which is carefully re-analyzed and interpreted in terms of gravity. The matrix model therefore contains gravity as an IR effect, due to UV/IR mixing.
In this paper we examine a small but detailed test of the emergent gravity picture with explicit solutions in gravity and gauge theory. We first derive symplectic U(1) gauge fields starting from the Eguchi-Hanson metric in four-dimensional Euclidean gravity. The result precisely reproduces the U(1) gauge fields of the Nekrasov-Schwarz instanton previously derived from the top-down approach. In order to clarify the role of noncommutative spacetime, we take the Braden-Nekrasov U(1) instanton defined in ordinary commutative spacetime and derive a corresponding gravitational metric. We show that t…
While the idea of gravity as an emergent phenomenon is an intriguing one, little is known about concrete implementations that could lead to viable phenomenology, most of the obstructions being related to the intrinsic difficulties of formulating genuinely pregeometric theories. In this paper we present a preliminary discussion of the impact of critical behavior of certain microscopic models for gravity, based on group field theories, on the dynamics of the macroscopic regime. The continuum limit is examined in light of some scaling assumption, and the relevant consequences for low energy effec…
Fermions coupled to Yang-Mills matrix models are studied from the point of view of emergent gravity. We show that the simple matrix model action provides an appropriate coupling for fermions to gravity, albeit with a non-standard spin connection. Integrating out the fermions in a nontrivial geometrical background induces indeed the Einstein-Hilbert action and a dilaton-like term, at least for on-shell geometries. This explains and precisely reproduces the UV/IR mixing for fermions in noncommutative gauge theory, extending recent results for scalar fields. It also explains why some UV/IR mixing…
A natural geometric framework of noncommutative spacetime is symplectic geometry rather than Riemannian geometry. The Darboux theorem in symplectic geometry then admits a novel form of the equivalence principle such that the electromagnetism in noncommutative spacetime can be regarded as a theory of gravity. Remarkably the emergent gravity reveals a noble picture about the origin of spacetime, dubbed as emergent spacetime, which is radically different from any previous physical theory all of which describe what happens in a given spacetime. In particular, the emergent gravity naturally explain…
A homogeneous part of the Seiberg-Witten gauge equivalence relation for gauge fields can lead to solutions that involve matter fields in such a way that the gauge equivalence and the dimensional and index structures are preserved. In particular, we consider scalar fields coupled to U(1) gauge fields. The matter fields appear non-linearly in the map. As an application, we analyze the implication of this ambiguity to emergent gravity at the first order in noncommutative parameter and show that the new ambiguity restores the possibility of conformal coupling of real scalar density field that is c…
We argue that a field theory defined on noncommutative (NC) spacetime should be regarded as a theory of gravity, which we refer to as the emergent gravity. A whole point of the emergent gravity is essentially originated from the basic property: A NC spacetime is a (NC) phase space. This fact leads to two important consequences: (I) A NC field theory can basically be identified with a matrix model or a large N field theory where NC fields can be regarded as master fields of large N matrices. (II) NC fields essentially define vector (tetrad) fields. So they define a gravitational metric of some …
Many inequivalent approaches to study black holes yield identical results. Any meaningful theory of gravity should explain the origin of this property. Here we show that the basic holomorphic modes characterising the underlying two dimensional conformal symmetry near the horizon bring about this universality. Moreover these modes lead to a law of equipartition of energy for black holes which suggests a statistical origin of gravity. This emergent nature of gravity is further bolstered by showing the equivalence of entropy with the action $\left(S=-\frac{i}{\hbar}\,I\right)$ and expressing the …
We show that the matrix-model action for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. This is elaborated in the 4-dimensional case. The SU(n) gauge fields as well as additional scalar fields couple to an effective metric G_{ab}, which is determined by a dynamical Poisson structure. The emergent gravity is intimately related to noncommutativity, encoding those degrees of freedom which are usually interpreted as U(1) gauge fields. This leads to a class of metrics which contains the physical degrees of freedom of gravitational waves, and allows to rec…
Off-shell processes do not preserve the Energy Momentum Tensor (EMT) in QFT. Fixing the EMT throughout off-shell processes, implies a graviton-like quantum field to emerge without dynamics. Its dynamics are generated through quantum corrections. This Fixed Off-Shell Energy Condition (FOSEC) implies the existence of a linear gravity-like theory, and in special cases the full Poincarè gauge theory. In this work it is shown that imposing the FOSEC in QFT implies the emergence of a viable quantum theory of gravity.
Near the event horizon of a black hole, the effective theory is two dimensional conformal theory. Here we show that the holographic modes characterising this underlying conformal symmetry and the basic definition of entropy $S$ in statistical mechanics lead the equipartition law of energy. We also show that $S$ is proportional to the gravity action which suggests the emergent nature of gravity. This is further bolstered by expressing the generalised Smarr formula as a thermodynamic relation, $S = E/ 2T$, where $T$ is the Hawking temperature and $E$ is shown to be the Komar energy.
First of all, we reconsider the tight - binding model of monolayer graphene, in which the variations of the hopping parameters are allowed. We demonstrate that the emergent 2D Weitzenbock geometry as well as the emergent U(1) gauge field appear. The emergent gauge field is equal to the linear combination of the components of the zweibein. Therefore, we actually deal with the gauge fixed version of the emergent 2+1 D teleparallel gravity. In particular, we work out the case, when the variations of the hopping parameters are due to the elastic deformations, and relate the elastic deformations wi…
Gravity stands out among the fundamental interactions because of its apparent incompatibility with having a quantum description. Moreover, thermodynamic aspects of gravitation theory appears as puzzling features of some classical solutions such as black holes. These and other aspects of gravitational theories have recently lead to the proposal that gravity might not be a fundamental interaction but rather an emergent phenomenon, a sort of hydrodynamic limit of some more fundamental theory. In order to further explore this possibility we shall here discuss two systems where such emergence of a …
Matrix models of Yang-Mills type lead to an emergent gravity theory, which may not require fine-tuning of a cosmological constant. We find cosmological solutions of Friedmann-Robertson-Walker type. They generically have a big bounce, and an early inflation-like phase with graceful exit. The mechanism is purely geometrical, no ad-hoc scalar fields are introduced. The solutions are stabilized through vacuum fluctuations and are thus compatible with quantum mechanics. This leads to a Milne-like universe after inflation, which appears to be in remarkably good agreement with observation and may pro…
I describe several broad features of a programme to understand gravity as an emergent, long wavelength, phenomenon (like elasticity) and discuss one concrete framework for realizing this paradigm in the backdrop of several recent results.
This dissertation investigates thermodynamic, emergent and holographic aspects of gravity in the context of causal diamonds. We obtain a gravitational first law for causal diamonds in maximally symmetric spacetimes and argue that these diamonds are in thermodynamic equilibrium at negative temperature. Further, gravitational field equations, including higher curvature corrections, are derived from an equilibrium condition on the generalized entropy of small maximally symmetric diamonds. Finally, we assign three holographic microscopic quantities to causal diamonds in spherically symmetric space…
In this work, a clear connection is made between E. Verlinde's recent theory of emergent gravity in de Sitter space and the earlier work that described emergent gravity using holographic screens. A modified (non)holographic screen scenario is presented, wherein the screen fails to encode an emergent mass in the bulk "unemerged" part of space for sufficiently large length-scales, where the volume-law of the non-holographic bulk degrees of freedom overtakes the area-law scaling of the entropy of the screen. Within this framework, we can describe both an emergent dark gravitational force, which s…
We modify the construction of the spectral triple over an algebra of holonomy loops by introducing additional parameters in form of families of matrices. These matrices generalize the already constructed Euler-Dirac type operator over a space of connections. We show that these families of matrices can naturally be interpreted as parameterizing foliations of 4-manifolds. The corresponding Euler-Dirac type operators then induce Dirac Hamiltonians associated to the corresponding foliation, in the previously constructed semi-classical states.
There are many examples where geometry and gravity are concepts that emerge from a theory of quantum mechanics without gravity. This suggests thinking of gravity as an exotic phase of matter. Quantifying this phase in the Landau paradigm requires some sort of symmetry principle or order parameter that captures its appearance. In this essay we propose higher-form symmetries as a symmetry principle underlying emergent spacetime. We explore higher-form symmetries in gauge-gravity duality and explain how their breaking describes features of a gravitational theory. Such symmetries imply the existen…
We construct exact solutions to noncommutative gravity following the formulation of Chamseddine and show that they are in general accompanied by Abelian gauge fields which are first order in the noncommutative scale. This provides a mechanism for generating cosmological electromagnetic fields in an expanding space-time background, and also leads to multipole-like fields surrounding black holes. Exact solutions to noncommutative Einstein-Maxwell theory can give rise to first order corrections to the metric tensor, as well as to the electromagnetic fields. This leads to first order shifts in the…
It has been known for a long time that Einstein's field equations when projected onto a black hole horizon looks very similar to a Navier-Stokes equation in suitable variables. More recently, it was shown that the projection of Einstein's equation on to any null surface in any spacetime reduces exactly to the Navier-Stokes form when viewed in the freely falling frame. We develop an action principle, the extremization of which leads to the above result, in an arbitrary spacetime. The degrees of freedom varied in the action principle are the null vectors in the spacetime and not the metric tenso…
The theta expansion of the Seiberg-Witten map has ambiguities which can be removed by a gauge transformation and/or a field redefinition. In the context of emergent gravity such a field redefinition changes the emerging metric and requires the presence of non-minimal gravitational couplings. It also requires that a real scalar field becomes a scalar density and allows the introduction of a potential. We also find that the potential can have only one term and that a quartic interaction is not allowed. Even though the metric depends on the ambiguity we show that the dispersion relation does not …
We propose a model with quantum bosons on the fcc lattice, which has a stable algebraic Bose liquid phase at low energy. We show that this phase is described by emergent quantum gravity at the Gaussian z = 3 Lifshitz fixed point in 3+1 dimensions. The stability of this algebraic Bose liquid phase is guaranteed by the gauge symmetry of gravitons and self-duality of the low energy field theory. By tuning one parameter in the lattice boson model we can drive a phase transition between the z = 3 Lifshitz gravity and another algebraic Bose liquid phase, described by gravity at the z = 2 Lifshitz po…
I describe several conceptual aspects of a particular paradigm which treats the field equations of gravity as emergent. These aspects are related to the features of classical gravitational theories which defy explanation within the conventional perspective. The alternative interpretation throws light on these features and could provide better insights into possible description of quantum structure of spacetime. This review complements the discussion in arXiv:1207.0505, which describes space itself as emergent in the cosmological context.
