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 spacetimes, and for non-AdS geometries we interpret them in terms of the long string degrees of freedom of symmetric product conformal field theories.
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 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.
In holographic duality, dynamics along the emergent extra-dimensional space describes a renormalization group (RG) flow of the corresponding quantum field theory (QFT). Following this idea, we develop an emergent holographic description of a QFT, where not only the information of the RG flow is introduced into an IR holographic dual effective field theory (HDEFT), but also the UV information of the QFT is encoded in the HDEFT through the IR boundary condition. In particular, we argue that this dual holographic construction is self-consistent within the assumption of bulk locality, showing the …
We revisit the theory of strongly correlated quantum matter perturbed by Harris-marginal random-field disorder, using the simplest holographic model. We argue that for weak disorder, the ground state of the theory is not Lifshitz invariant with a non-trivial disorder-dependent dynamical exponent, as previously found. Instead, below a non-perturbatively small energy scale, we predict infrared physics becomes independent of the disorder strength.
Motivated by Granda and Oliveros (GO) model, we generalize their work to the non-flat case. We obtain the evolution of the dark energy density, the deceleration and the equation of state parameters for the holographic dark energy model in a non-flat universe with GO cut-off. In the limiting case of a flat universe, i.e. $k = 0$, all results given in GO model are obtained.
I propose a random network model governed by a Gaussian weight corresponding to Ising link antiferromagnetism as a model for emergent quantum space-time. In this model, discrete space is fundamental, not a regularization, its spectral dimension $d_s$ is not a model input but is, rather, completely determined by the antiferromagnetic coupling constant. Perturbative terms suppressing triangles and favouring squares lead to locally Euclidean ground states that are Ricci flat "large worlds" with power-law extension. I then consider the quenched graphs of lowest energy for $d_s=2$ and $d_s=3$ and I…
To clarify the mathematical structure of the RG-derived holographic dual field theory, we rewrite the string-theory based conventionally utilized dual holographic effective field theory based on the ADM decomposition of the metric tensor. This comparison leads us to claim that the RG-derived emergent holographic dual field theory takes into account higher-derivative curvature terms with gauge fixing in the string-theory based conventionally utilized Einstein-Klein-Gordon theory, giving rise to the RG flow of the metric tensor beyond the AdS (anti-de Sitter space) geometry. Furthermore, we comp…
We explore the phenomenon of emergent Lorentz invariance in strongly coupled theories. The strong dynamics is handled using the gauge/gravity correspondence. We analyze how the renormalization group flow towards Lorentz invariance is reflected in the two-point functions of local operators and in the dispersion relations of the bound states. The deviations of these observables from the relativistic form at low energies are found to be power-law suppressed by the ratio of the infrared and ultraviolet scales. We show that in a certain subclass of models the velocities of the light bound states st…
We discuss a scenario that the dark matter in late time universe emerges as part of the holographic stress-energy tensor on the hypersurface in higher dimensional flat spacetime. Firstly we construct a toy model with a de Sitter hypersurface as the holographic screen in the flat bulk. After adding the baryonic matter on the screen, we assume that both of the dark matter and dark energy can be described by the Brown-York stress-energy tensor. From the Hamiltonian constraint equation in the flat bulk, we find an interesting relation between the dark matter and baryonic matter's energy density pa…
We study self-consistent static solutions for an Einstein universe in a graph-based induced gravity. The one-loop quantum action is computed at finite temperature. In particular, we demonstrate specific results for the models based on cycle graphs.
The possibility of an emergent universe solution to Einstein's field equations allowing for an irreversible creation of matter at the expense of the gravitational field is shown. With the universe being chosen as spatially flat FRW spacetime together with equation of state proposed in [17], the solution exists when the ratio of the phenomenological matter creation rate to the number density times the Hubble parameter is a number $β$ of the order of unity and independent of time. The thermodynamic behaviour is also determined for this solution. Interestingly, we also find that an emergent unive…
Quantum fluctuations endow spacetime with a foamy texture. The degree of foaminess is dictated by blackhole physics to be of the holographic type. Applied to cosmology, the holographic foam model predicts the existence of dark energy with critical energy density in the current (late) universe, the quanta of which obey infinite statistics. Furthermore we use the deep similarities between turbulence and the spacetime foam phase of strong quantum gravity to argue that the early universe was in a turbulent regime when it underwent a brief cosmic inflation with a "graceful" transition to a laminar …
We propose a new entropy construct that generalizes the Tsallis, Rényi, Sharma-Mittal, Barrow, Kaniadakis, and Loop Quantum Gravity entropies and reduces to the Bekenstein-Hawking entropy in a certain limit. This proposal is applied to the Schwarzschild black hole and to spatially homogeneous and isotropic cosmology, where it is shown that it can potentially describe inflation and/or holographic dark energy.
The Schwarzschild singularity is known to be classically unstable. We demonstrate a simple holographic consequence of this fact, focusing on a perturbation that is uniform in boundary space and time. Deformation of the thermal state of the dual CFT by a relevant operator triggers a nonzero temperature holographic renormalization group flow in the bulk. This flow continues smoothly through the horizon and, at late interior time, deforms the Schwarzschild singularity into a more general Kasner universe. We show that the deformed near-singularity, trans-horizon Kasner exponents determine specific…
Considering a thermal state of the dual CFT with a uniform deformation by a scalar operator, we study a holographic renormalization group flow at nonzero temperature in the bulk described by the Einstein-scalar field theory with the self-interaction term $λϕ^4$ in asymptotic anti-de Sitter spacetime. We show that the holographic flow with the self-interaction term could run smoothly through the event horizon of a black hole and deform the Schwarzschild singularity to a Kasner universe at late times. Furthermore, we also study the effect of the scalar self-interaction on the deformed near-singu…
Holographic superconductors have been studied so far in the absence of dynamical electromagnetic fields, namely in the limit in which they coincide with holographic superfluids. It is possible, however, to introduce dynamical gauge fields if a Neumann-type boundary condition is imposed on the AdS-boundary. In 3+1 dimensions, the dual theory is a 2+1 dimensional CFT whose spectrum contains a massless gauge field, signaling the emergence of a gauge symmetry. We study the impact of a dynamical gauge field in vortex configurations where it is known to significantly affect the energetics and phase …
We investigate the infinite-distance properties of families of unstable flux vacua in string theory with broken supersymmetry. To this end, we employ a generalized notion of distance in the moduli space and we build a holographic description for the non-perturbative regime of the tunneling cascade in terms of a renormalization group flow. In one limit we recover an exponentially light tower of Kaluza-Klein states, while in the opposite limit we find a tower of higher-spin excitations of D1-branes, realizing the emergent string proposal. In particular, the holographic description includes a fre…
We derive an effective dual holographic Einstein-Maxwell theory, applying renormalization group transformations to interacting Dirac fermions in a recursive way. In particular, we show how both background metric tensor and U(1) gauge fields become dynamical to describe the renormalization group flows of coupling functions and order parameter fields of the corresponding quantum field theory through natural emergence of an extra-dimensional space, respectively. Finally, we propose a prescription on how to calculate correlation functions in a non-perturbative way, where quantum fluctuations of bo…
In this work we propose an alternative scheme for an Emergent Universe scenario where the universe is initially in a static state supported by a scalar field located in a false vacuum. The universe begins to evolve when, by quantum tunneling, the scalar field decays into a state of true vacuum. The Emergent Universe models are interesting since they provide specific examples of nonsingular inflationary universes.
In this paper, we propose an {\it exact holographic mapping} which is a unitary mapping from the Hilbert space of a lattice system in flat space (boundary) to that of another lattice system in one higher dimension (bulk). By defining the distance in the bulk system from two-point correlation functions, we obtain an emergent bulk space-time geometry that is determined by the boundary state and the mapping. As a specific example, we study the exact holographic mapping for $(1+1)$-dimensional lattice Dirac fermions and explore the emergent bulk geometry corresponding to different boundary states …
We investigate the stability of the holographic description of the universe. By treating the perturbation globally, we discover that this description is stable, which is support for the holographic description of the universe.
We investigate the holographic complexity growth rate of a conformal field theory in a FLRW universe. We consider two ways to realize a FLRW spacetime from an Anti-de Sitter Schwarzschild geometry. The first one is obtained by introducing a new foliation of the Schwarzschild geometry such that the conformal boundary takes the FLRW form. The other one is to consider a brane universe moving in the Schwarzschild background. For each case, we compute the complexity growth rate in a closed universe and a flat universe by using both the complexity-volume and complexity-action dualities. We find that…
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.
Applying recursive renormalization group transformations to a scalar field theory, we obtain an effective quantum gravity theory with an emergent extra dimension, described by a dual holographic Einstein-Klein-Gordon type action. Here, the dynamics of both the dual order-parameter field and the metric tensor field originate from density-density and energy-momentum tensor-tensor effective interactions, respectively, in the recursive renormalization group transformation, performed approximately in the Gaussian level. This linear approximation in the recursive renormalization group transformation…
We proposed the generalized holographic dark energy model where infrared cutoff is identified with the combination of the FRW universe parameters: the Hubble rate, particle and future horizons, cosmological constant, the universe life-time (if finite) and their derivatives. It is demonstrated that with the corresponding choice of the cutoff one can map such holographic dark energy to modified gravity or gravity with general fluid. Explicitly, F(R) gravity and general perfect fluid are worked out in detail and corresponding infrared cutoff is found. Using this correspondence, we get realistic i…
We discuss universal properties of conformal field theories with holographic duals. A central feature of these theories is the existence of a low-lying sector of operators whose correlators factorize. We demonstrate that factorization can only hold in the large central charge limit. Using conformal invariance and factorization we argue that these operators are naturally represented as fields in AdS as this makes the underlying linearity of the system manifest. In this class of CFTs the solution of the conformal bootstrap conditions can be naturally organized in structures which coincide with W…
Based on an earlier introduced new class of generalized gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold, we derive an effective "Einstein-frame" theory featuring the following remarkable properties: (i) We obtain effective potential for the cosmological scalar field possessing two infinitely large flat regions which allows for a unified description of both early universe inflation as well as of present dark energy epoch; (ii) For a specific parameter range the model …
First, we reformulate RG transformations in a recursive way with introduction of an order-parameter field. As a result, we manifest the RG flow of an effective field theory through the emergence of an extra dimensional space, where both RG $β-$functions of coupling functions and RG flow equation of the order-parameter field appear in the resulting effective action explicitly through the extra dimensional space. Second, we consider an effective dual holographic description derived recently, where the classical gravity theory of the large $N$ limit takes into account quantum corrections in the a…
We employ the holographic model of interacting dark energy to obtain the equation of state for the holographic energy density in non-flat (closed) universe enclosed by the event horizon measured from the sphere of horizon named $L$.
We study the model for holographic dark energy in a spatially closed universe, generalizing the proposal in hep-th/0403127 for a flat universe. We provide independent arguments for the choice of the parameter $c=1$ in the holographic dark energy model. On the one hand, $c$ can not be less than 1, to avoid violating the second law of thermodynamics. On the other hand, observation suggests $c$ be very close to 1, it is hard to justify a small deviation of $c$ from 1, if $c>1$.
A closed universe containing pressureless dust, more generally perfect fluid matter with pressure-to-density ratio w in the range (1/3, - 1/3), violates holographic principle applied according to the Fischler-Susskind proposal. We show, first for a class of two-fluid solutions and then for the general multifluid case, that the closed universe will obey the holographic principle if it also contains matter with w < - 1/3, and if the present value of its total density is sufficiently close to the critical density. It is possible that such matter can be realised by some form of `quintessence', muc…
Summary of three talks on the Holographic Space Time models of early universe cosmology, particle physics, and the asymptotically de Sitter final state of our universe.
In this work we study superinflation in the context of the emergent universe (EU) scenario. The existence of a superinflating phase before the onset of slow-roll inflation arises in any emergent universe model. We found that the superinflationary period in the EU scenario produces a suppression of the CMB anisotropies at large scale which could be responsible for the observed lack of power at large angular scales of the CMB.
We present a holographic description of four-dimensional single-scalar inflationary universes in terms of a three-dimensional quantum field theory. The holographic description correctly reproduces standard inflationary predictions in their regime of applicability. In the opposite case, wherein gravity is strongly coupled at early times, we propose a holographic description in terms of perturbative QFT and present models capable of satisfying the current observational constraints while exhibiting a phenomenology distinct from standard inflation. This provides a qualitatively new method for gene…
We study the semi-holographic idea in context of decaying dark components. The energy flow between dark energy and the compensating dark matter is thermodynamically generalized to involve a particle number variable dark component with non-zero chemical potential. It's found that, unlike the original semi-holographic model, no cosmological constant is needed for a dynamical evolution of the universe. A transient phantom phase appears while a non-trivial dark energy-dark matter scaling solution keeps at late time, which evades the big-rip and helps to resolve the coincidence problem. For reasona…
Implementing the Wilsonian renormalization group (RG) transformation in a nonperturbative way, we construct an effective holographic dual description with an emergent extradimension identified with an RG scale. Taking the large$-N$ limit, we obtain an equation of motion of an order-parameter field, here the chiral condensate for our explicit demonstration. In particular, an intertwined structure manifests between the first-order RG flow equations of renormalized coupling functions and the second-order differential equation of the order-parameter field, thus referred to as a nonperturbative RG-…
Quantum mechanics emerges a la Verlinde from a foliation of space by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantised in units of Boltzmann's constant k. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of t…
In this paper we study emergent universe model in the context of a self interacting Jordan-Brans-Dicke theory. The model presents a stable past eternal static solution which eventually enters a phase where the stability of this solution is broken leading to an inflationary period. We also establish constraints for the different parameters appearing in our model.
We introduce the relation between the holographic entropy bounds and the inflationary universe. First the holographic entropy bounds for radiation-dominated universe, radiation-dominated universe with a positive cosmological constant are introduced. For an exact de Sitter phase, we use the maximal entropy bound. We classify the inflation based on the quasi-de Sitter spacetime into three steps: slow-roll period of inflation, epoch of reheating, and radiation-dominated era. Then we study how to apply three entropy bounds to the three steps of the inflation. Finally we discuss our results.
In this paper we study the cosmological evolution of the holographic dark energy in a cyclic universe, generalizing the model of holographic dark energy proposed by Li. The holographic dark energy with $c<1$ can realize a quintom behavior; namely, it evolves from a quintessence-like component to a phantom-like one. The holographic phantom energy density grows rapidly and dominates the late-time expanding phase, helping realize a cyclic universe scenario in which the high energy regime is modified by the effects of quantum gravity, causing a turnaround (and a bounce) of the universe. The dynami…
We investigate the realization of the emergent universe scenario in theories with natural UV cutoffs, namely a minimum length and a maximum momentum, quantified by a new deformation parameter in the generalized uncertainty principle. We extract the Einstein static universe solutions and we examine their stability through a phase-space analysis. As we show, the role of the new deformation parameter is crucial in a twofold way: Firstly, it leads to the appearance of new Einstein static universe critical points, that are absent in standard cosmology. Secondly, it provides a way for a graceful exi…
The emergent universe scenario provides a possible alternative to bouncing cosmology to avoid the Big Bang singularity problem. In this paper we study the realization of the emergent universe scenario by making use of Quintom matter with an equation of state across the cosmological constant boundary. We will show explicitly the analytic and numerical solutions of emergent universe in two Quintom models, which are a phenomenological fluid and a nonconventional spinor field, respectively.
We investigate the Einstein static universe (ESU) and the emergent universe scenario in the framework of Hořava-Lifshitz-like $F(R)$ gravity. We first perform a dynamical analysis in the phase space, and amongst others we show that a spatially open universe filled with matter satisfying the strong energy condition can exhibit a stable static phase. Additionally, we examine the behavior of the scenario under scalar perturbations and extract the conditions under which it is free of perturbative instabilities, showing that the obtained background ESU solutions are free of such instabilities. Howe…
Assuming gauge/gravity correspondence we study reheating of the Universe using its holographic dual. Inflaton decay and thermalisation of the decay products correspond to collapse of a spherical shell and formation of a blackhole in the dual anti-de Sitter (AdS) spacetime. The reheating temperature is computed as the Hawking temperature of the developed blackhole probed by a dynamical boundary, and is determined by the inflaton energy density and the AdS radius, with corrections from the dynamics of the shell collapse. For given initial energy density of the inflaton field the holographic mode…
Holographic duality conjecture has been proposed to be a novel non-perturbative theoretical framework for the description of strongly correlated electrons. However, the duality transformation is not specified to cause ambiguity in the application of this theoretical machinery to condensed matter physics. In this study, we propose a prescription for the holographic duality transformation. Based on recursive renormalization group (RG) transformations, we obtain an effective field theory, which manifests the RG flow of an effective action through the introduction of an extra dimension. Resorting …
Using the holographic entropy proposal for a closed universe by Verlinde, a bound on equations of state for different stages of the universe is obtained. Further exploring this bound, we find that an inflationary universe naturally emerges in the early universe and today's dark energy is also needed in the quantum cosmological scenario.
We propose a way to discover, in tabletop experiments, spacetime-emergent materials, that is, materials holographically dual to higher-dimensional quantum gravity systems under the AdS/CFT correspondence. The emergence of the holographic spacetime is verified by a mathematical imaging transform of the response function on the material. We consider theories on a 1-dimensional ring-shaped material, and compute the response to a scalar source locally put at a point on the ring. When the theory on the material has a gravity dual, the imaging in the low temperature phase exhibits a distinct differe…
In this work we study an alternative scheme for an Emergent Universe scenario in the context of a Jordan-Brans-Dicke theory, where the universe is initially in a truly static state supported by a scalar field located in a false vacuum. The model presents a classically stable past eternal static state which is broken when, by quantum tunneling, the scalar field decays into a state of true vacuum and the universe begins to evolve following the extended open inflationary scheme.
In this work, we reexamine the holographic dark energy concept proposed already for cosmological applications. By considering, more precisely, the bounds on the entropy arising from lattice field theory on one side and Bekenstein-Hawking entropy of black holes on another side, it is shown that the so-called holographic dark energy cannot be mimicked as easily as claimed in the literature. In addition, the limits on the electron $(g-2)$ experiments are taken into account again. It is shown that the corrections to the electron magnetic momentum are of the order of ${\mathcal{O}}(10^{-23})$.
Motivated by the recent work of Wang, Lin, Pavon, and Abdalla [1], we generalize their work to the non-flat case. In particular, we provide a thermodynamical interpretation for the holographic dark energy model in a non-flat universe. For this case, the characteristic length is no more the radius of the event horizon (R_E) but the event horizon radius as measured from the sphere of the horizon (L). Furthermore, when interaction between the dark components of the holographic dark energy model in the non-flat universe is present its thermodynamical interpretation changes by a stable thermal fluc…
We examine the generation and evolution of perturbations in a universe dominated by a fluid with stiff equation of state $p=ρ$. The recently proposed Holographic Universe is an example of such a model. We compute the spectrum of scalar and tensor perturbations, without relying on a microphysical description of the $p=ρ$ fluid. The spectrum is scale invariant deep inside the Hubble horizon. In contrast, infrared perturbations that enter the Hubble horizon during the stiff fluid dominated (holographic) phase yield oscillatory and logarithmic terms in the power spectrum. We show that vector pertu…
A basic understanding of the relevant features of hadron properties from first principles QCD has remained elusive, and should be understood as emergent phenomena which depend critically on the number of dimensions of physical spacetime. These properties include the mechanism of color confinement, the origin of the hadron mass scale, chiral symmetry breaking and the pattern of hadronic bound states. Some of these complex issues have been recently addressed in an effective computational framework of hadron structure based on a semiclassical approximation to light-front QCD, and its holographic …
Holographic theories with a local gravitational dual have a number of striking features. Here I argue that many of these features are controlled by the Eguchi-Kawai mechanism, which is proposed to be a hallmark of such holographic theories. Higher-spin holographic duality is presented as a failure of the Eguchi-Kawai mechanism, and its restoration illustrates the deformation of higher-spin theory into a proper string theory with a local gravitational limit. AdS/CFT is used to provide a calculable extension of the Eguchi-Kawai mechanism to field theories on curved manifolds and thereby introduc…
We examine in details Friedmann-Robertson-Walker models in 2+1 dimensions in order to investigate the cosmic holographic principle suggested by Fischler and Susskind. Our results are rigorously derived differing from the previous one found by Wang and Abdalla. We discuss the erroneous assumptions done in this work. The matter content of the models is composed of a perfect fluid, with a $γ$-law equation of state. We found that closed universes satisfy the holographic principle only for exotic matter with a negative pressure. We also analyze the case of a collapsing flat universe.
