We present a toy model where spacetime is emergent from a more fundamental microscopic system, and investigate the gray area interpolating between the collective and free-particle regimes. For a period of rapid exponential growth in the analogue universe, we argue that the intermediate regime is best described by a coloured potpourri of geometries -- a "rainbow geometry". This can be viewed as an alternative approach towards understanding quantum field theories in the presence of Lorentz-symmetry breaking at ultraviolet scales. Firstly, it is pointed out that cosmological particle production in our emergent FRW-type analogue universe, when compared to conventional semi-classical quantum gravity, is only temporarily robust against model-specific deviations from Lorentz invariance. Secondly, it is possible to carry out a straightforward quantitative analysis to estimate a suitable parameter regime for experimental (analogue) cosmology.
In this work we have investigated the emergent scenario of the universe described by Loop quantum cosmology model, DGP brane model and Kaluza-Klein cosmology. Scalar field along with barotropic fluid as normal matter is considered as the matter content of the universe. In Loop quantum cosmology it is found that the emergent scenario is realized with the imposition of some conditions on the value of the density of normal matter in case of normal and phantom scalar field. This is a surprising result indeed considering the fact that scalar field is the dominating matter component. In case of Tach…
Global variables and dynamics of emergent cosmology in loop gravity
University of the Basque Country EHU（巴斯克大学）；Universidad Complutense de Madrid（马德里康普顿斯大学）；Universidad Autónoma de Madrid（马德里自治大学）；Instituto de Química Física Blas Cabrera (IQF), CSIC（Blas Cabrera物理化学研究所（IQF），西班牙国家研究委员会）
We obtain the analogues of the Friedman equations in an emergent gravity scenario in the presence of dark energy. The background metric is taken to be Friedman-Lemaitre-Robertson-Walker (FLRW). We show that if $\dotϕ^{2}$ is the dark energy density (in units of the critical density) then (a) for total energy density greater than the pressure (non-relativistic scenario, matter domination) the deceleration parameter $q(t)\approx\frac {1}{2} [1 + 27 \dotϕ^{2}+...] > \frac{1}{2}$ (b) for total energy density equal to 3 times the pressure (relativistic case, radiation domination), the deceleration …
We explore the possibility of emergent cosmology using the effective potential formalism. We discover new models of emergent cosmology which satisfy the constraints posed by the cosmic microwave background (CMB). We demonstrate that, within the framework of modified gravity, the emergent scenario can arise in a universe which is spatially open/closed. By contrast, in general relativity (GR) emergent cosmology arises from a spatially closed past-eternal Einstein Static Universe (ESU). In GR the ESU is unstable, which creates fine tuning problems for emergent cosmology. However, modified gravity…
Nonlinear electrodynamics, which acts as a source of gravity Einstein field equations, leads to emergent cosmology, an alternative solution which can avoid Big Bang singularity. In this paper, we explore the emerging universe in models of non-linear electrodynamics (described by dimensional parameter $β$) by using the equation of state parameter $ω$ and see how the parameter $β$ helps the universe to cause a transition from a quasi-static Minkowski phase to the inflationary phase of expansion through the point of emergence and subsequently to the phase of normal thermal expansion. We predict t…
Matrix theory is a proposed non-perturbative definition of superstring theory in which space is emergent. We begin a study of cosmology in the context of matrix theory. Specifically, we show that matrix theory can lead to an emergent non-singular cosmology which, at late times, can be described by an expanding phase of Standard Big Bang cosmology. The horizon problem of Standard Big Bang cosmology is automatically solved. We show that thermal fluctuations in the emergent phase source an approximately scale-invariant spectrum of cosmological perturbations and a scale-invariant spectrum of gravi…
The Dapor-Liegener model of Loop Quantum Cosmology (LQC), which depicts an emergent universe from a de Sitter regime in the contracting phase is studied from the mathematical viewpoint of dynamical systems and compared with the standard model of LQC. Dealing with perturbations, on the contrary to standard LQC where at early times all the scales are inside the Hubble radius, we show that it is impossible to implement the matter bounce scenario due to the fact that an emergent de Sitter regime in the contracting phase implies that all the scales are outside of the Hubble radius in a past epoch.
The aim here is to provide a set of equations for cosmology in terms of information and thermodynamical parameters. The method we implement in order to describe the universe is a development of Padmanabhan\rq{}s approach which is based on the fact that emergence of the cosmic space is provided by the evolution of the cosmic time. In this line we obtain the Friedmann equation or its equivalent the conservation law in terms of information by the implementation of Laundauer\rq{}s principle or in other words the information loss/production rate. Hence, a self consistent description of the universe…
A nonsingular emergent universe cosmology can be realized by a nonconventional spinor field as first developed in \cite{Cai:2012yf}. We study the mechanisms of generating scale-invariant primordial power spectrum of curvature perturbation in the frame of spinor emergent universe cosmology. Particularly, we introduce a light scalar field of which the kinetic term couples to the bilinear of the spinor field. This kinetic coupling can give rise to an effective "Hubble radius" for primordial fluctuations from the scalar field to squeeze at large length scales as well as to form a nearly scale-inva…
Observations indicate that the universe is effectively flat, but they do not rule out a closed universe. The role of positive curvature is negligible at late times, but can be crucial in the early universe. In particular, positive curvature allows for cosmologies that originate as Einstein static universes, and then inflate and later reheat to a hot big bang era. These cosmologies have no singularity, no "beginning of time", and no horizon problem. If the initial radius is chosen to be above the Planck scale, then they also have no quantum gravity era, and are described by classical general re…
In this article, we present an emergent universe scenario that can be derived from DHOST cosmology. The universe starts asymptotically Minkowski in the far past just like the regular Galileon Genesis, but evolves to a radiation dominated period at the late stage, and therefore, the universe has a graceful exit which is absent in the regular Galileon Genesis. We analyze the behavior of cosmological perturbations and show that both the scalar and tensor modes are free from the gradient instability problem. We further analyze the primordial scalar spectrum generated in various situations and disc…
We review a proposal to obtain an emergent metric space-time and an emergent early universe cosmology from the BFSS matrix model. Some challenges and directions for future research are outlined.
We show that in the isentropic scenario the first order thermodynamical particle creation model gives an emergent universe solution even when the chemical potential is non-zero. However there exists no emergent universe scenario in the second order non-equilibrium theory for the particle creation model. We then point out a correspondence between the particle creation model with barotropic equation of state and the equation of state giving rise to an emergent universe without particle creation in spatially flat FRW cosmology.
Here we formulate scenario of emergent universe from particle creation mechanism in spatially flat braneworld models. We consider an isotropic and homogeneous universe in Braneworld cosmology and universe is considered as a non-equilibrium thermodynamical system with dissipation due to particle creation mechanism. Assuming the particle creation rate as a function of the Hubble parameter , we formulate emergent scenario in RS2 and DGP models of Braneworld.
Emergent structure in the binary black hole mass distribution and implications for population-based cosmology
Université de Toulouse, CNRS/IN2P3, L2IT（图卢兹大学）；Laboratoire de Physique de l’ENS, Université Paris Cité, Ecole Normale Supérieure, Université PSL, Sorbonne Université, CNRS（巴黎高等师范学院物理实验室）
The emergent semiclassical time approach to resolving the problem of time in quantum gravity involves heavy slow degrees of freedom providing via an approximately Hamilton-Jacobi equation an approximate timestandard with respect to which the quantum mechanics of light fast degrees of freedom can run. More concretely, this approach involves Born-Oppenheimer and WKB ansatze and some accompanying approximations. In this paper, I investigate this approach for concrete scaled relational particle mechanics models, i.e. models featuring only relative separations, relative angles and relative times. I…
Various choices of the geometry degrees of freedom as the emergent time are tested on the model of an isotropic universe with a scalar field of $ϕ^2$ potential. Potential problems with each choices as well as possible applications in loop quantization are discussed.
Strategies intended to resolve the problem of time in quantum gravity by means of emergent or hidden timefunctions are considered in the arena of relational particle toy models. In situations with `heavy' and `light' degrees of freedom, two notions of emergent semiclassical WKB time emerge; these are furthermore equivalent to two notions of emergent classical `Leibniz--Mach--Barbour' time. I futhermore study the semiclassical approach, in a geometric phase formalism, extended to include linear constraints, and with particular care to make explicit those approximations and assumptions used. I p…
Recent developments in string compactifications demonstrate obstructions to the simplest constructions of low energy cosmologies with positive vacuum energy. The existence of obstacles to creating scale-separated de Sitter solutions indicates a UV/IR puzzle for embedding cosmological vacua in a unitary theory of quantum gravity. Motivated by this puzzle, we propose an embedding of positive energy Friedmann-Lemaitre-Robertson-Walker cosmology within string theory. Our proposal involves confining 4D gravity on a brane which mediates the decay from a non-supersymmetric false AdS5 vacuum to a true…
We study the transition from an Emergent Galileon condensate phase of the early universe to a later expanding radiation phase. This "defrosting" or "preheating" transition is a consequence of the excitation of matter fluctuations by the coherent Galileon condensate, in analogy to how preheating in inflationary cosmology occurs via the excitation of matter fluctuations through coupling of matter with the coherent inflaton condensate. We show that the "minimal" coupling of matter (modeled as a massless scalar field) to the Galileon field introduced by Creminelli, Nicolis and Trincherini in order…
The ten-parameter, quadratic Poincaré gauge theory of gravity is a plausible alternative to general relativity. We show that the rich background cosmology of the gauge theory is described by a non-canonical bi-scalar-tensor theory in the Jordan frame: the `metrical analogue'. This provides a unified framework for future investigation by the broader community. For many parameter choices, the non-canonical term reduces to a Cuscuton field of the form $\smash{\sqrt{|X^{ϕϕ}|}}$. The Einstein-Cartan-Kibble-Sciama theory maps to a pure quadratic Cuscuton, whereas the teleparallel theory maps to the …
The BFSS matrix model is a suggested non-perturbative definition of string theory. Starting from a thermal state of this matrix model, we show how space and time can emerge dynamically. Results from the IKKT matrix model indicate that the $SO(9)$ symmetry of space is spontaneously broken to $SO(3) \times SO(6)$, with the three-dimensional subspace becoming large. Given this initial state for the universe, we show that cosmological perturbations and gravitational waves with scale-invariant spectra are generated, without the need of postulating an early phase of cosmological inflation. The Big B…
Emergent dark sector in group field theory cosmology
Universidad Complutense de Madrid（马德里康普顿斯大学）；Università degli Studi di Padova（帕多瓦大学）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Università di Napoli “Federico II”（那不勒斯费德里科二世大学）；INFN, Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）
Operator-ordering in quantum cosmology is a major as-yet unsettled ambiguity with not only formal but also physical consequences. We determine the Lagrangian origin of the conformal invariance that underlies the conformal operator-ordering choice in quantum cosmology. It is particularly naturally and simply manifest in relationalist product-type actions (such as the Jacobi action for mechanics or Baierlein-Sharp-Wheeler type actions for general relativity), for which all that is required for the kinetic and potential factors to rescale in compensation to each other. These actions themselves ma…
We study the cosmological sector of the Lorentzian Barrett-Crane (BC) model coupled to a free massless scalar field in its Group Field Theory (GFT) formulation, corresponding to the mean-field hydrodynamics obtained from coherent condensate states. The relational evolution of the condensate with respect to the scalar field yields effective dynamics of homogeneous and isotropic cosmologies, similar to those previously obtained in $\text{SU}(2)$-based EPRL-like models. Also in this manifestly Lorentzian setting, in which only continuous $\text{SL}(2,\mathbb{C})$-representations are used, we obta…
Constant-torsion emergent gravity (CTEG) has a Lagrangian quadratic in curvature and torsion, but without any Einstein--Hilbert term. CTEG is motivated by a unitary, power-counting renormalisable particle spectrum. The timelike axial torsion adopts a vacuum expectation value, and the Friedmann cosmology emerges dynamically on this torsion condensate. We show that this mechanism -- and the whole background cosmology of CTEG -- may be understood through the effective potential of a canonical single scalar field model. The effective potential allows for hilltop inflation in the early Universe. In…
The nature of time in quantum mechanics is closely related to the use of a complex, rather than say real, Hilbert space. This becomes particularly clear when considering quantum field theory in time dependent backgrounds, such as in cosmology, when the notion of positive frequency ceases to be well defined. In spacetimes lacking time orientation, i.e without the possibility of defining an arrow of time, one is forced to abandon complex quantum mechanics. One also has to face this problem in quantum cosmology. I use this to argue that this suggests that, at a fundamental level, quantum mechanic…
The quantum nature of the Big Bang is reexamined in the framework of Loop Quantum Cosmology. The strict application of a regularization procedure to the Hamiltonian, originally developed for the Hamiltonian in loop quantum gravity, leads to a qualitative modification of the bounce paradigm. Quantum gravity effects still lead to a quantum bounce connecting deterministically large classical Universes. However, the evolution features a large epoch of de Sitter Universe, with emergent cosmological constant of Planckian order, smoothly transiting into a flat expanding Universe.
Boltzmann Dynamics in K-essence Cosmology: Photon Propagation in an Emergent Spacetime
University of Calcutta（加尔各答大学）；Sister Nivedita University（西塔·尼维迪塔大学）；Inter-University Center for Astronomy and Astrophysics（跨大学天文与天体物理中心）；Prabhat Kumar College（普拉巴特·库马尔学院）；Institute of Astronomy, Space and Earth Science（天文、空间与地球科学研究院）
A new class of gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold are studied in some detail. These models involve an additional $R^2$ (square of the scalar curvature) term as well as scalar matter field potentials of appropriate form so that the pertinent action is invariant under global Weyl-scale symmetry. Scale invariance is spontaneously broken upon integration of the equations of motion for the auxiliary volume-form degrees of freedom. After performing transition …
We study the anisotropic Bianchi I loop quantum cosmology in 2+1 dimensions. Both the $\mubar$ and $\mubar'$ schemes are considered in the present paper and the following expected results are established: (i) the massless scalar field again play the role of emergent time variables and serves as an internal clock; (ii) By imposing the fundamental discreteness of length operator, the total Hamiltonian constraint is obtained and gives rise the evolution as a difference equation; and (iii) the exact solutions of Friedmann equation are constructed rigorously for both classical and effective level. …
In this paper, a new Hamiltonian constraint operator for loop quantum cosmology is constructed by using the Chern-Simons action. The quantum dynamics of the $k=0$ cosmological model with respect to a massless scalar field as an emergent time is determined by a difference equation. The semiclassical analysis shows that the new quantum dynamics has the correct classical limit, and the classical big-bang singularity is again replaced by the quantum bounce. Interestingly, the inverse time evolution of the flat Friedmann-Robertson-Walker cosmological model determined by the effective Hamiltonian wi…
Several software packages for relativistic cosmological simulations that do not fully implement the Einstein equation have recently been developed. Two of the free-licensed ones are inhomog and gevolution. A key question is whether globally emergent volume evolution that is faster than that of a Friedmannian reference model results from the averaged effects of structure formation. Checking that emergent volume evolution is correctly modelled by the packages is thus needed. We numerically replace the software's default random realisation of initial seed fluctuations by a fluctuation of spatiall…
The way physics of loop quantum gravity is affected by the underlying quantization ambiguities is an open question. We address this issue in the context of loop quantum cosmology using gauge-covariant fluxes. Consequences are explored for two choices of regularization parameters: $μ_0$ and $\bar μ$ in presence of a positive cosmological constant, and two choices of regularizations of the Hamiltonian constraint in loop quantum cosmology: the standard and the Thiemann regularization. We show that novel features of singularity resolution and bounce, occurring due to gauge-covariant fluxes, exist …
This introductory review is addressed to beginning researchers. Some of the distinguishing features of loop quantum gravity are illustrated through loop quantum cosmology of FRW models. In particular, these examples illustrate: i) how `emergent time' can arise; ii) how the technical issue of solving the Hamiltonian constraint and constructing the \emph{physical} sector of the theory can be handled; iii) how questions central to the Planck scale physics can be answered using such a framework; and, iv) how quantum geometry effects can dramatically change physics near singularities and yet natura…
In recent works, a construction was proposed resulting emergent universes inside black holes. This result can be obtained from a 4D black hole embedded in a 5D space time with the fifth dimension compactified on a circle [0, 2] (0 and 2 are identified) such that the two branes are at 0 and 1. In the present work, we study this setup by deriving particles equations of motion in the new universes, based on redefining energy and angular momentum. This leads to disappearance of the singularity in centres of black holes in classical General Relativity.
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.
In the context of Effective Field Theory, the Hilbert space of states increases in an expanding universe. Hence, the time evolution cannot be unitary. The formation of structure is usually studied using effective field theory techniques. We study the constraints on effective field theory analyses of early universe models which come from demanding that the factor of the space of states corresponding to length scales where the primordial fluctuations are manifest does not suffer from the unitarity problem. For bouncing and emergent cosmologies, no constraints arise provided that the energy scale…
We investigate the emergent time scenario in quantum cosmology based on the Page-Wotters approach. Using a quantum cosmological model with a qubit clock, it is demonstrated how the entanglement between the qubit clock and the geometry derives emergence of a time parameter which defines evolution of the timeless quantum state of the universe. We show the universe wave function conditioned by a qubit clock obeys the standard Schrödinger equation and the Fisher information for the clock state, which quantifies entanglement between the universe and the clock, contributes as a negative energy densi…
The comprehensive formulation for loop quantum cosmology in the spatially flat, isotropic model was recently constructed. In this paper, the methods are extended to the anisotropic Bianchi I cosmology. Both the precursor and the improved strategies are applied and the expected results are established: (i) the scalar field again serves as an internal clock and is treated as emergent time; (ii) the total Hamiltonian constraint is derived by imposing the fundamental discreteness and gives the evolution as a difference equation; and (iii) the physical Hilbert space, Dirac observables and semi-clas…
We consider a universe with an arbitrary number of extra dimensions, $N$. We present a new method for constructing the cosmological equations of motion and find analytic solutions with an explicit dependence on $N$. When we take the $N\rightarrow\infty$ limit we find novel, emergent behaviour which distinguishes it from normal Kaluza-Klein universes.
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…
Recently, a de-Sitter epoch has been found in the new model of loop quantum cosmology which is governed by the scalar constraint with both of Euclidean and Lorentz terms. The singularity free bounce in the new LQC model and the emergent cosmology constant strongly suggest that the effective stress energy tensor induced by quantum corrections must violate the standard energy conditions. In this paper, we do an explicit calculation to analyze the behaviours of specific representative energy conditions, i.e., average null, strong and dominant energy conditions. It turns out that the averaging nul…
In this paper, we will study the effect of having a minimum measurable length on inflationary cosmology. We will analyze the inflationary cosmology in the Jacobson approach. In this approach, gravity is viewed as an emergent thermodynamical phenomenon. We will demonstrate that the existence of a minimum measurable length will modify the Friedmann equations in the Jacobson approach. We will use this modified Friedmann equation to analyze the effect of minimum measurable length scale on inflationary cosmology. This analysis will be performed using the Hamiltonian-Jacobi approach. We compare our …
We study the dynamics and predictions of a new emergent-universe model recently derived within Quantum Reduced Loop Gravity and based on the so-called statistical regularization scheme. These effective geometries show a dynamical transition from a stationary spacetime, with nearly constant scale factor at very early times, to a late-time semiclassical phase well approximated by a classical Friedmann-Robertson-Walker spacetime. We show that this is always the case when the matter content is a minimally coupled scalar field subject to a quadratic potential, including the massless case. Besides, …
