We perform a semi-classical analysis of the Emergent Universe scenario for inflation. Fixing the background, and taking the inflaton to be homogenous, we cast the inflaton's evolution as a one-dimensional quantum mechanics problem. We find that the tuning required over a long time scale for this inflationary scenario is unstable quantum mechanically. Considering the inflaton field value as a wavepacket, the spreading of the wavepacket destroys any chance of both starting and ending with a well-formed state. Thus, one cannot have an Einstein static universe to begin with that evolves into a well-defined beginning to inflation a long time later.
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 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 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…
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…
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 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 order to bypass the big bang singularity, we develop an emergent universe scenario within a covariant extension of General Relativity known as \emph{"Energy-Momentum Squared Gravity"}. The extra terms of the model emerge in the high energy regime. Considering dynamics in a Friedmann-Lemaître-Robertson-Walker background, critical points, representing stable Einstein static states of the phase space, result as solutions. It then turns out that as the equation of state parameter $ω$ gradually declines from a constant value as $t\rightarrow-\infty$, eventually some of the static past eternal so…
It has been recently pointed out by Mithani-Vilenkin that certain emergent universe scenarios which are classically stable are nevertheless unstable semiclassically to collapse. Here, we show that there is a class of emergent universes derived from scale invariant two measures theories with spontaneous symmetry breaking (s.s.b) of the scale invariance, which can have both classical stability and do not suffer the instability pointed out by Mithani-Vilenkin towards collapse. We find that this stability is due to the presence of a symmetry in the "emergent phase", which together with the non lin…
We study a composition of normal and exotic matter which is required for a flat Emergent Universe scenario permitted by the equation of state (EOS)($p=Aρ-Bρ^{1/2}$) and predict the range of the permissible values for the parameters $A$ and $B$ to explore a physically viable cosmological model. The permitted values of the parameters are determined taking into account the $H(z)-z$ data obtained from observations, a model independent BAO peak parameter and CMB shift parameter (WMAP7 data). It is found that although $A$ can be very close to zero, most of the observations favours a small and negati…
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 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…
The dilaton-gravity sector of a linear in the scalar curvature, scale invariant Two Measures Field Theory (TMT), is explored in detail in the context of closed FRW cosmology and shown to allow stable emerging universe solutions. The model possesses scale invariance which is spontaneously broken due to the intrinsic features of the TMT dynamics. We study the transition from the emerging phase to inflation, and then to a zero cosmological constant phase. We also study the spectrum of density perturbations and the constraints that impose on the parameters of the theory.
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…
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…
By considering the realization of the emergent universe scenario in Eddington-inspired Born-Infeld (EiBI) theory, we study the stability of the Einstein static universe filled with perfect fluid in EiBI theory against both the homogeneous and inhomogeneous scalar perturbations in this work. We find that in both the spatially flat and closed cases, the emergent universe scenario is no longer viable, since the Einstein static universe cannot be stable against both the homogeneous and inhomogeneous scalar perturbations simultaneously. However, the emergent universe scenario survives in the spatia…
We study the stability of the Einstein static universe in the Hořava-Lifshitz (HL) gravity and a generalized version of it formulated by Sotiriou, Visser and Weifurtner. We find that, for the HL cosmology, there exists a stable Einstein static state if the cosmological constant $Λ$ is negative. The universe can stay at this stable state eternally and thus the big bang singularity can be avoided. However, in this case, the Universe can not exit to an inflationary era. For the Sotiriou, Visser and Weifurtner HL cosmology, if the cosmic scale factor satisfies certain conditions initially, the Uni…
We investigate emergent universe model using recent observational data for the background tests as well as for the growth tests. The background test data comprises of Hubble data, Baryon Acoustic Oscillation (BAO) data, cosmic microwave background (CMB) shift data, Union compilation data. The observational growth data are obtained from Wiggle-Z measurements and rms mass fluctuations data from Lyman-$α$ measurements at different red shifts. The flat emergent universe model obtained by Mukherjee {\it et. al.} is permitted with a non-linear equation of state (in short, EoS) ($p=Aρ-Bρ^{\frac{1}{2}…
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.
Oscillating solutions to the effective equations of Loop Quantum Cosmology have been suggested for the role of an `eternal seed', providing a possible starting point for the emergent universe scenario. We investigate the stability of a particular model, sourced by a homogeneous massless scalar field and a negative cosmological constant, with respect to small perturbations and to quantum collapse. We find that the model has perturbatively stable and unstable solutions, with both types of solutions occupying significant regions of the parameter space. All solutions are unstable with respect to c…
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 …
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…
We illustrate that $Λ$MOND cosmology following from E. Verlinde's emergent gravity idea which contains only constant dark energy and baryonic matters governed by linear inverse gravitation forces at and beyond galaxy scales fit with the luminosity distance v.s. redshift relationship, i.e. $d_\ell(z)$ of type Ia supernovae equally well as the standard $Λ$CDM cosmology does. But in a rather broad and reasonable parameter space, $Λ$MOND gives too strong baryon acoustic oscillation, i.e. BAO signals on the matter power spectrum contradicting with observations from various galaxy survey and countin…
Alternative scenarios to the Big Bang singularity have been subject of intense research for several decades by now. Most popular in this sense have been frameworks were such singularity is replaced by a bounce around some minimal cosmological volume or by some early quantum phase. This latter scenario was devised a long time ago and referred as an "emergent universe" (in the sense that our universe emerged from a constant volume quantum phase). We show here that within an improved framework of canonical quantum gravity (the so called Quantum Reduced Loop Gravity) the Friedmann equations for co…
Closed, singularity-free, inflationary cosmological models have recently been studied in the context of general relativity. Despite their appeal, these so called emergent models suffer from a number of limitations. These include the fact that they rely on an initial Einstein static state to describe the past eternal phase of the universe. Given the instability of such a state within the context of general relativity, this amounts to a very severe fine tuning. Also in order to be able to study the dynamics of the universe within the context of general relativity, they set the initial conditions…
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…
Central European Institute for Cosmology and Fundamental Physics (CEICO), Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所中欧宇宙学与基础物理研究所）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo（东京大学大学院理学研究系早期宇宙研究中心）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo（东京大学前沿研究机构宇宙物理与数学卡弗里研究所）；Institut d’Astrophysique de Paris, UMR-7095 du CNRS（巴黎天体物理研究所法国国家科学研究中心联合研究实验室）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）
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…
Following the recent study on the emergent Friedmann equation from the expansion of cosmic space for a flat universe, we apply this method to a nonflat universe, and modify the evolution equation to lead to the Friedmann equation. In order to maintain the same form with the original evolution equation, we have to define the time-dependent Plank constant, which shows that the spatial curvature of $k=0$ and $k=1$ is preferable to $k=-1$ since the Plank constant of the nonflat open universe is divergent. Finally, we discuss its physical consequences.
The Einstein static universe has played a central role in a number of emergent scenarios recently put forward to deal with the singular origin of the standard cosmological model. Here we study the existence and stability of the Einstein static solution in presence of vacuum energy corresponding to conformally-invariant fields. We show that the presence of vacuum energy stabilizes this solution by changing it to a centre equilibrium point, which is cyclically stable. This allows non-singular emergent cosmological models to be constructed in which initially the universe oscillates indefinitely a…
Creation of an inflationary epoch from an Emergent Universe through quantum tunneling
Ben Gurion University of the Negev（内盖夫本-古里安大学）；Frankfurt Institute for Advanced Studies（法兰克福高等研究所）；Bahamas Advanced Studies Institute and Conferences（巴哈马高级研究与会议研究所）
We present a detailed analysis of a quantum model for Loop Quantum Cosmology based on strict application of the Thiemann regularization algorithm for the Hamiltonian in Loop Quantum Gravity, extending the results presented previously in our brief report. This construction 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 spat…
Observations indicate that our universe is characterized by a late-time accelerating phase, possibly driven by a cosmological constant $Λ$, with the dimensionless parameter $ΛL_P^2 \simeq 10^{-122}$, where $L_P = (G \hbar /c^3)^{1/2}$ is the Planck length. In this review, we describe how the emergent gravity paradigm provides a new insight and a possible solution to the cosmological constant problem. After reviewing the necessary background material, we identify the necessary and sufficient conditions for solving the cosmological constant problem. We show that these conditions are naturally sa…
We study a six matrix model with global $SO(3)\times SO(3)$ symmetry containing at most quartic powers of the matrices. This theory exhibits a phase transition from a geometrical phase at low temperature to a Yang-Mills matrix phase with no background geometrical structure at high temperature. This is an exotic phase transition in the same universality class as the three matrix model but with important differences. The geometrical phase is determined dynamically, as the system cools, and is given by a fuzzy four-sphere background ${\bf S}^2_N\times{\bf S}^2_N$, with an Abelian gauge field whic…
In a previous paper (gr-qc/9907063) we described the early inflationary universe in terms of quantum information. In this paper, we analize those results in more detail, and we stress the fact that, during inflation, the universe can be described as a superposed state of quantum registers. The self-reduction of the superposed quantum state is consistent with the Penrose's Objective Reduction (OR) model. The quantum gravity threshold is reached at the end of inflation, and corresponds to a superposed state of 10^9 quantum registers. This is also the number of superposed tubulins-qubits in our b…
We study a model of the emergent dark universe, which lives on the time-like hypersurface in a five-dimensional bulk spacetime. The holographic fluid on the hypersurface is assumed to play the role of the dark sector, mainly including the dark energy and apparent dark matter. Based on the modified Friedmann equations, we present a Markov-Chain-Monte-Carlo analysis with the observational data, including type Ia Supernova and the direct measurement of the Hubble constant. We obtain a good fitting result and the matter component turns out to be small enough, which matches well with our theoretica…
We obtain cosmological solutions which admit emergent universe (EU) scenario in the framework of Einstein Gauss-Bonnet gravity coupled with a dilaton field in four dimensions. The coupling parameter of the Gauss-Bonnet terms and the dilaton in the theory are determined for obtaining an EU scenario. The corresponding dilaton potential which admits such scenario is determined. It is found that the Gauss- Bonnet (GB) terms coupled with a dilaton field plays an important role in describing the dynamics of the evolution of the early as well as the late universe. We note an interesting case where th…
We revisit a non-perturbative formulation leading to a vacuum created gravitational pair of (33)-brane by a Poincare dual higher form U (1) gauge theory on a D4 -brane. In particular, the analysis has revealed a dynamical geometric torsion H 3 for an on-shell Neveu-Schwarz (NS) form on a fat 4-brane. We argue that a D-instanton can be a viable candidate to incorporate the quintessence correction hidden to an emergent (3 + 1)-dimensional brane universe. It is shown that a dynamical non-perturbative correction may be realized with an axionic scalar QFT on an emergent anti 3-brane within a gravit…
The possibility that the universe may have a fundamental and positive cosmological constant has motivated an interesting cosmological model, in which initially the universe is in a cosmological constant sea, then the local quantum fluctuations violating the null energy condition create some islands with matter and radiation, which under certain conditions might corresponds to our observable universe. We in this note study the perturbation spectra of scalar fields not affecting the evolution of background during the fluctuation. We will examine whether they can be interesting, and responsible f…
We provide a comprehensive numerical study of the Emergent Cyclic Inflation scenario. This is a scenario where instead of traditional monotonic slow roll inflation, the universe expands over numerous short asymmetric cycles due to the production of entropy via interactions among different species. This is one of the very few scenarios of inflation which provides a nonsingular geodesically complete space-time and does not require any "reheating" mechanism.
The IKKT matrix model yields an emergent space-time. We further develop these ideas and give a proposal for an emergent metric. Based on previous numerical studies of this model, we provide evidence that the emergent space-time is continuous and infinite in extent, both in space and in time, and that the metric is spatially flat. The time evolution describes the transition from a string-theoretic emergent phase to a phase in which the $SO(9)$ symmetry of the model is spontaneously broken to $SO(6) \times SO(3)$, with three dimensions of space expanding, becoming classical and at later times ev…
We present a simplified dynamic-vacuum-energy model for a time-symmetric Milne-like universe. The big bang singularity in this simplified model, like the one in a previous model, is just a coordinate singularity with finite curvature and energy density. We then calculate the dynamic behavior of scalar metric perturbations and find that these perturbations destabilize the big bang singularity.
We argue that all homogeneous and isotropic solutions in nonlinear massive gravity are unstable. For this purpose, we study the propagating modes on a Bianchi type--I manifold. We analyze their kinetic terms and dispersion relations as the background manifold approaches the homogeneous and isotropic limit. We show that in this limit, at least one ghost always exists and that its frequency tends to vanish for large scales, meaning that it cannot be integrated out from the low energy effective theory. This ghost mode is interpreted as a leading nonlinear perturbation around a homogeneous and iso…
We consider scalar field perturbations of the asymptotically Gödel 5-dimensional charged rotating black holes with two equal angular momenta. It is shown that the spectrum of proper oscillations of the perturbation includes superradiant unstable modes. The reason for the instability is the confining Dirichlet boundary condition at the asymptotically far region of the Gödel Universe. The confining box makes superradiant modes extract rotational energy from the black hole and, after repeated reflections from the black hole, grow unboundedly. A similar instability takes place for rotating black h…
Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the ar…
We study the emergent scenario, which is proposed to avoid the big bang singularity, in the Einstein-Cartan (EC) theory with a positive cosmological constant and a perfect fluid by analyzing the existence and stability of the Einstein static (ES) solutions. We find that there is no stable ES solution for a spatially flat or open universe. However, for a spatially closed universe, the stable ES solution does exist, and in the same existence parameter regions, there also exists an unstable one. With the slow decrease of the equation of state $w$ of the perfect fluid, the stable and unstable crit…
We propose that the existence of the string landscape suggests the universe can be in a quantum glass state, where an extremely large viscosity is generated, and long distance dynamics slows down. At the same time, the short distance dynamics is not altered due to the separation of time scales. This scenario can help to understand some controversies in cosmology, for example the natural existence of slow roll inflation and dark energy in the landscape, the apparent smallness of the cosmological constant. We see also that moduli stabilization is no longer necessary. We further identify the glas…
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 present the results from the analysis of galaxy rotation curves with Verlinde's emergent gravity. We use the data in the SPARC (Spitzer Photometry and Accurate Rotation Curves) database, which contains a sample of 175 nearby disk galaxies with 3.6 $μ$m surface photometry and rotation curves. We compute the gravitational acceleration at different galactocentric radii expected from the baryon distribution of the galaxies with the emergent gravity, and compare it with the observed gravitational acceleration derived from galactic rotation curves. The predicted and observed accelerations agree w…
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.
Eternal inflation produces pocket universes with all physically allowed vacua and histories. Some of these pocket universes might contain a phase of slow-roll inflation, some might undergo cycles of cosmological evolution and some might look like the galilean genesis or other "emergent" universe scenarios. Which one of these types of universe we are most likely to inhabit depends on the measure we choose in order to regulate the infinities inherent in eternal inflation. We show that the currently leading measure proposals, namely the global light-cone cut-off and its local counterpart, the cau…
We use higher derivative classical gravity to study the nonlinear coupling between the cosmological expansion of the universe and metric oscillations of Planck frequency and very small amplitude. We derive field equations at high orders in the derivative expansion and find that the nature of the new dynamics is extremely restricted. For the equation of state parameter $w>0$ the relative importance of the oscillations grows logarithmically. Their effect on the cosmological expansion resembles that of dark energy.
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.
In this work, we investigated the electroweak vacuum instability during or after inflation. In the inflationary Universe, i.e., de Sitter space, the vacuum field fluctuations $\left< {δϕ}^{ 2 } \right>$ enlarge in proportion to the Hubble scale $H^{2}$. Therefore, the large inflationary vacuum fluctuations of the Higgs field $\left< {δϕ}^{ 2 } \right>$ are potentially catastrophic to trigger the vacuum transition to the negative-energy Planck-scale vacuum state and cause an immediate collapse of the Universe. However, the vacuum field fluctuations $\left< {δϕ}^{ 2 } \right>$, i.e., the vacuum …
