Showing papers on "Big Rip published in 2001"
TL;DR: In this article, a review of catalogues of galaxies, clusters of galaxies and superclusters is given, and the power spectrum of density perturbations and correlation functions are discussed.
281 citations
TL;DR: In this article, the authors investigated the possibility of having a late time accelerated phase of the universe, suggested by recent supernova observation, in the context of Brans-Dicke theory with a potential having a time dependent mass squared term which has recently become negative and a matter field.
Abstract: In this work we investigate the possibility of having a late time accelerated phase of the universe, suggested by recent supernova observation, in the context of Brans-Dicke theory with a potential having a time dependent mass squared term which has recently become negative and a matter field. We find that while a perfect fluid (pressureless and with pressure) cannot support this acceleration, a fluid with dissipative pressure can drive this late time acceleration for a simple power-law expansion of the universe. We have also calculated some cosmological parameters in our model to match with observations.
157 citations
[...]
TL;DR: In this article, it was shown that in the simplest theories of spontaneous symmetry breaking one can have a stage of fast-roll inflation, where the standard slow-roll condition |m^2| << H^2 is violated if |m| is sufficiently small.
Abstract: We show that in the simplest theories of spontaneous symmetry breaking one can have a stage of a fast-roll inflation. In this regime the standard slow-roll condition |m^2| << H^2 is violated. Nevertheless, this stage can be rather long if |m| is sufficiently small. Fast-roll inflation can be useful for generating proper initial conditions for the subsequent stage of slow-roll inflation in the very early universe. It may also be responsible for the present stage of accelerated expansion of the universe. We also make two observations of a more general nature. First of all, the universe after a long stage of inflation (either slow-roll or fast-roll) cannot reach anti-de Sitter regime even if the cosmological constant is negative. Secondly, the theories with the potentials with a 'stable' minimum at V(\phi)<0 in the cosmological background exhibit the same instability as the theories with potentials unbounded from below. This instability leads to the development of singularity with the properties practically independent of V(\phi). However, the development of the instability in some cases may be so slow that the theories with the potentials unbounded from below can describe the present stage of cosmic acceleration even if this acceleration occurs due to the fast-roll inflation.
150 citations
TL;DR: It is pointed out that apparent causality violation is possible for the brane universe which contains matter energy and it is shown that there is no "horizon problem" in the Friedmann-Robertson-Walker brane universes.
Abstract: Causal structure of the brane universe with respect to null geodesics in the bulk spacetime is studied. It is pointed out that apparent causality violation is possible for the brane universe which contains matter energy. It is also shown that there is no "horizon problem" in the Friedmann-Robertson-Walker brane universe.
80 citations
TL;DR: In this paper, the authors present a rich class of exact solutions which contain radiation-dominated and matter-dominated models for the early and late universe, including a variable cosmological constant which is derived from a higher dimension and manifests itself in spacetime as an energy density for the vacuum.
Abstract: We present a rich class of exact solutions which contains radiation-dominated and matter-dominated models for the early and late universe. They include a variable cosmological ``constant'' which is derived from a higher dimension and manifests itself in spacetime as an energy density for the vacuum. This is in agreement with observational data and is compatible with extensions of general relativity to string and membrane theory. Our solutions are also typified by a non-singular ``big bounce'' (as opposed to a singular big bang), where matter is created as in inflationary cosmology.
69 citations
TL;DR: The cosmological model best capable of fitting current observational data features two separate epochs during which the universe is accelerating as discussed by the authors, and the possibility that the two epochs may share the same physical description, and give an overview of the current status.
56 citations
TL;DR: In this article, the authors examine the behavior of a closed oscillating universe filled with a homogeneous scalar field and find that, contrary to naive expectations, such a universe expands to larger volumes during successive expansion epochs.
Abstract: We examine the behavior of a closed oscillating universe filled with a homogeneous scalar field and find that, contrary to naive expectations, such a universe expands to larger volumes during successive expansion epochs. This intriguing behavior introduces an arrow of time in a system which is time reversible. The increase in the maximum size of the universe is closely related to the work done on or by the scalar field during one complete oscillatory cycle which, in turn, is related to the asymmetry in the scalar field equation of state during expansion and collapse. Our analysis shows that scalar fields with polynomial potentials $V(\ensuremath{\varphi})=\ensuremath{\lambda}{\ensuremath{\varphi}}^{q},$ $qg1,$ lead to a growing oscillation amplitude for the universe: the increase in amplitude between successive oscillations is more significant for smaller values of q. Such behavior allows for the effective recycling of the universe. A recycled universe can be quite old and can resolve the flatness problem. These results have strong bearing on cosmological models in which the role of dark matter is played by a scalar field. They are also relevant for chaotic inflationary models of the early universe since they demonstrate that, even if the universe fails to inflate the first time around, it will eventually do so during future oscillatory cycles. Thus, the space of initial conditions favorable for chaotic inflation increases significantly.
54 citations
TL;DR: In this article, the authors consider a cosmological setting for which the currently expanding era is preceded by a contracting phase, that is, they assume the Universe experienced at least one bounce, and they show that scalar hydrodynamic perturbations lead to a singular behavior of the Bardeen potential and/or its derivatives.
Abstract: We consider a cosmological setting for which the currently expanding era is preceded by a contracting phase, that is, we assume the Universe experienced at least one bounce. We show that scalar hydrodynamic perturbations lead to a singular behavior of the Bardeen potential and/or its derivatives (i.e. the curvature) for whatever Universe model for which the last bounce epoch can be smoothly and causally joined to the radiation dominated era. Such a Universe would be filled with non-linear perturbations long before nucleosynthesis, and would thus be incompatible with observations. We therefore conclude that no observable bounce could possibly have taken place in the early universe if Einstein gravity together with hydrodynamical fluids is to describe its evolution, and hence, under these conditions, that the Universe has always expanded.
40 citations
Posted Content•
TL;DR: In this article, the ekpyrotic model is proposed as a possible alternative to inflationary cosmology as a description of the very early universe and the authors point out a number of errors in their considerations.
Abstract: We respond to the criticisms by Kallosh, Kofman and Linde concerning our proposal of the ekpyrotic universe scenario. We point out a number of errors in their considerations and argue that, at this stage, the ekpyrotic model is a possible alternative to inflationary cosmology as a description of the very early universe.
33 citations
TL;DR: In this article, the cosmological evolution of a D3-brane universe in a type 0 string background was studied and the energy density induced on the brane because of its motion in the bulk was calculated.
Abstract: We study the cosmological evolution of a D3-brane Universe in a type 0 string background. We follow the brane-universe along the radial coordinate of the background and we calculate the energy density which is induced on the brane because of its motion in the bulk. We find that for some typical values of the parameters and for a particular range of values of the scale factor of the brane-universe, the effective energy density is dominated by a term proportional to $\frac{1}{(loga)^{4}}$ indicating a slow varying inflationary phase. For larger values of the scale factor the effective energy density takes a constant value and the brane-universe enters its usual inflationary period.
31 citations
TL;DR: In this article, the evolution of a flat Friedmann-Robertson-Walker universe, filled with a causal bulk viscous cosmological fluid, in the presence of variable gravitational and cosmology constants is considered.
Abstract: We consider the evolution of a flat Friedmann-Robertson-Walker Universe, filled with a causal bulk viscous cosmological fluid, in the presence of variable gravitational and cosmological constants. The basic equation for the Hubble parameter, generalizing the evolution equation in the case of constant gravitational coupling and cosmological term, is derived, under the supplementary assumption that the total energy of the Universe is conserved. By assuming that the cosmological constant is proportional to the square of the Hubble parameter and a power law dependence of the bulk viscosity coefficient, temperature and relaxation time on the energy density of the cosmological fluid, two classes of exact solutions of the field equations are obtained. In the first class of solutions the Universe ends in an inflationary era, while in the second class of solutions the expansion of the Universe is non-inflationary for all times. In both models the cosmological "constant" is a decreasing function of time, while the gravitational "constant" increases in the early period of evolution of the Universe, tending in the large time limit to a constant value.
TL;DR: In this paper, a dynamical effective Q-cosmological "constant" was proposed to recover some of the L decaying cases found in the literature, and a sort of complementarity between the Q-dominated or L-dominated expansions of the universe was introduced.
Abstract: In this paper we present exactly solved extended quintessence models; furthermore, through a dynamical effective Q-cosmological "constant", we recover some of the L decaying cases found in the literature. Finally we introduce a sort of complementarity between the Q-dominated or L-dominated expansions of the Universe.
Posted Content•
TL;DR: In this paper, the authors present a review of some central problems, anomalies, paradoxes of Astrophysics, Cosmology and new approaches to its decisions, proposed by the Wave Universe Concept (WU Concept).
Abstract: We present the brief review of some central problems, anomalies, paradoxes of Astrophysics, Cosmology and new approaches to its decisions, proposed by the Wave Universe Concept (WU Concept). All these, anyhow, - Hot Points of modern science of Universe, about which Standard Model have not authentic answers. The represented set of brief (justified) Novels reflects very perspective directions of search. Essential from thems - Headline (and Topics): New Phenomenon-Megaquantization: Observed Megaquantum Effects in Astronimical Systems. Internal Structure of Celestial Bodies and Sun. Where is disposes the Convective Zone? Towards to Stars: Where the Heliopause will be found? Mystery of the Fine Structure Constant (FSC). Answer of the WU Concept: Theoretical Representation of the Fine Structure Constant. FSC - As Micro and Mega Parameter of the Universe. FSC, Orbits, Heliopause. What Quasars with Record Redshifts will be discovered in Future? Observed Universe: Monotonic Homogeneity and Anisotropy or Principal Hierarchy? Is the (Large - Scale) Limit of Universe exist? All answers, proposed by the Wave Universe Concept, in contrast with speculative schemes of Standard Model, are effectively verified by experience, including, - and by justified in observations prognoses. It will be waited, that namely here it is possible the real break in the understanding of these principal problems and enigmas, which Nature, infinite Universe offers (to us).
Posted Content•
TL;DR: In this paper, a space-velocity theory of gravitation in a 4-dimensional curved space is presented, and the solutions of the field equations yield three possibilities for the universe expansion but only the accelerating one is possible.
Abstract: We present a space-velocity theory of gravitation in a 4-dimensional curved space. The solutions of the field equations yield 3 possibilities for the universe expansion but only the accelerating one is possible. Although the theory has no cosmological constant, we exract from it its equivalent value which is shown to be in agreement with measurements. No pressure is used in the theory.
TL;DR: In this paper, the authors study the linear theory of perturbations in a Friedmann-Robertson-Walker universe with a cosmological constant and obtain the equations for the evolution of the perturbation in the fully relativistic case.
Abstract: There is now evidence that the cosmological constant Λ has a non-zero positive value. Alternative scenarios to a pure cosmological constant model are provided by quintessence, an effective negative pressure fluid permeating the Universe. Recent results indicate that the energy density ρ and the pressure p of this fluid are constrained by −ρ≤p≲−0.6ρ. As p=−ρ is equivalent to the pure cosmological constant model, it is appropriate to analyse this particular, but important, case further.
We study the linear theory of perturbations in a Friedmann–Robertson–Walker universe with a cosmological constant. We obtain the equations for the evolution of the perturbations in the fully relativistic case, for which we analyse the single-fluid and two-fluid cases. We obtain solutions to these equations in appropriate limits. We also study the Newtonian approximation. We find that for a positive cosmological constant universe (i) the perturbations will grow more slowly in the relativistic regime for a two-fluid composed of dark matter and radiation, and (ii) in the Newtonian regime the perturbations stop growing.
TL;DR: In this article, the creation of very massive particles in the gravitational background of anisotropic perturbed Minkowski space-time is discussed and the total particle number of the observable universe as well as the present value of photon-to-baryon ratio are obtained in agreement with their accepted values from the observational facts.
Abstract: Quantum creation of very massive particles in the gravitational background of anisotropically perturbed Minkowski space-time is discussed. In this framework of semiclassical gravity the quantum mechanically produced heavy particles which made the initial space-time unstable and ushered into the FRW expansion phase at the Planck order epoch of the universe can account for the energy density at that epoch. Also, both the conformal and nonconformal particle-creations in the FRW era of the early universe after the Planck order epoch are investigated. In this consideration the total particle number of the observable universe as well as the present value of photon-to-baryon ratio are obtained in agreement with their accepted values from the observational facts. The existence of very massive particles at the very early period of the universe is also discussed here with the suggestion of an observational test.
Posted Content•
TL;DR: In this article, it was shown that the universe will continue to accelerate indefinitely if the parameter of the equation of state is a constant, no matter how many different types of energy (matter, radiation, quintessence, cosmological constant and etc) are contained in the universe.
Abstract: It has been argued in the literature that if a universe is expanding with an accelerating rate indefinitely, it presents a challenge to string theories due to the existence of event horizons. We study the fate of a currently accelerating universe. We show that the universe will continue to accelerate indefinitely if the parameter $\omega = p/\rho$ of the equation of state is a constant, no matter how many different types of energy (matter, radiation, quintessence, cosmological constant and etc) are contained in the universe. This type of universe will always exhibit an event horizon indicating that such a universe may not be derived from string theories. We also comment on some related issues.
Posted Content•
TL;DR: In this paper, the authors derived a new 95% confidence level lower limit on the age of the universe of 11 Gyr, which is consistent with the expansion age for a flat universe for the currently allowed range of the Hubble constant unless the cosmic equation of state is dominated by a component that violates the strong energy condition.
Abstract: New estimates of globular cluster distances, combined with revised ranges for input parameters in stellar evolution codes and recent estimates of the earliest redshift of cluster formation allow us to derive a new 95% confidence level lower limit on the age of the Universe of 11 Gyr. This is now definitively inconsistent with the expansion age for a flat Universe for the currently allowed range of the Hubble constant unless the cosmic equation of state is dominated by a component that violates the strong energy condition. This solidifies the case for a dark energy-dominated universe, complementing supernova data and direct measurements of the geometry and matter density in the Universe. The best-fit age is consistent with a cosmological constant-dominated (w=pressure/energy density = -1) universe. For the Hubble Key project best fit value of the Hubble Constant our age limits yields the constraints w < -0.4 and Omega_matter < 0.38 at the 68 % confidence level, and w < -0.26 and Omega_matter < 0.58 at the 95 % confidence level.
TL;DR: The Cosmic Microwave Background Radiation (CMBR) as discussed by the authors is relic radiation which last interacted with matter more than 10 billion years ago, when free electrons and ionized nuclei recombined to form atoms.
Abstract: The Cosmic Microwave Background Radiation (CMBR) which we observe today is relic radiation which last interacted with matter more than 10 billion years ago, when the expanding universe cooled to the point that free electrons and ionized nuclei recombined to form atoms. Prior to recombination, scattering between photons and free electrons was a very frequent occurrence, and the distance light could penetrate was small; afterwards, with free electrons out of circulation, the universe became largely transparent to light. Thus, the CMBR photons we observe today give us a clear view of the state of the early universe. Measured deviations in the intensity of the CMBR trace the small perturbations in the primordial matter density, which have been amplified by gravitational forces to form the magnificent, complex structures which comprise the present-day universe.
Posted Content•
[...]
TL;DR: The cyclic universe model as mentioned in this paper is a modification of the ekpyrotic universe and the pyrotechnic universe models, which goes through six transitions: the triplet universe, the inflation, the big bang, the quintessence, and the deflation transitions.
Abstract: The cyclic universe model is a modification of the ekpyrotic universe and the pyrotechnic universe models. The cyclic universe goes through the six transitions: the triplet universe, the inflation, the big bang, the quintessence, the big crush, and the deflation transitions. The universe starts with eleven dimensional space-time with two boundary 9-branes separated by a finite gap spanning an intervening bulk volume. The triplet transition starts when the bulk 9-brane is generated from the hidden boundary 9-brane, and collides with the pre-observable 9-brane. The collision starts the inflation transition. The collision is the brane dimensional interference mixing between the pre-observable 9-brane and the bulk 9-brane. The results are the mixed branes (combined brane dimensions), the internal space (cancelled brane dimensions), the bulk space, 3-brane vacuum, and cosmic radiation. Cosmic radiation generated during the inflation leads to the big bang. Meanwhile, the hidden brane undergoes stepwise fractionalization, changing in stepwise manner from 9-brane to 3-brane. The observable universe expands in a constant rate until the quintessence transition. Afterward, there are the big crush transition (the reverse of the big bang) and the deflation (the reverse of the inflation). The cosmic cycle of the fractionalization and condensation starts over again. The masses of all elementary particles and hadrons can be calculated.
TL;DR: In this article, the neutrino masses inferred from the solar and atmospheric neutrinos anomalies are consistent with the hypothesis that the observed cosmological matter density has been created in decays of heavy Majorana Neutrinos in the early universe.
Abstract: The asymmetry of the universe between matter and antimatter in the universe is related to neutrino properties due to non-perturbative processes in the high-temperature symmetric phase of the standard model. We show that the neutrino masses inferred from the solar and atmospheric neutrino anomalies are consistent with the hypothesis that the observed cosmological matter density has been created in decays of heavy Majorana neutrinos in the early universe.
TL;DR: In this paper, a localized scalar on the brane as a stress-energy tensor is used to find the quintessence which gives an accelerating universe, where the initial bulk spacetime consists of two 5D topological anti de Sitter black holes joined by the moving domain wall.
Abstract: We study issues of the quintessence in the brane cosmology. The initial bulk spacetime consists of two 5D topological anti de Sitter black hole joined by the brane (moving domain wall). Here we do not introduce any conventional radiation and matter. Instead we include a localized scalar on the brane as a stress-energy tensor, and thus we find the quintessence which gives an accelerating universe. Importantly, we obtain a $\rho^2$-term as well as a holographic matter term of $\alpha/a^4$ from the masses of the topological black holes. We discuss a possibility that in the early universe, $\rho^2$-term makes a large kinetic term which induces a decelerating universe. This may provide a hint of avoiding from the perpetually accelerating universe of the present-day quintessence. If a holographic matter term exists, it will plays the role of a CFT-radiation in the early universe.
Posted Content•
TL;DR: The existence of future horizons in spacetime geometries poses serious problems for string theory and quantum field theories as discussed by the authors, since the existence of a future horizon for an eternally accelerating universe does not allow the formulation of physical S-matrix observables.
Abstract: The existence of future horizons in spacetime geometries poses serious problems for string theory and quantum field theories. The observation that the expansion of the universe is accelerating has recently been shown to lead to a crisis for the mathematical formalism of string and M-theories, since the existence of a future horizon for an eternally accelerating universe does not allow the formulation of physical S-matrix observables. Postulating that the speed of light varies in an expanding universe in the future as well as in the past can eliminate future horizons, allowing for a consistent definition of S-matrix observables.
Posted Content•
TL;DR: In this article, the authors investigated some solutions of Einstein's field equations which go smoothly between Schwarzschild's relativistic gravitational solution near a mass concentration to the Friedmann-Lemaitre expanding universe solution.
Abstract: Recent experimental results from supernovae Ia observations have been interpreted to show that the rate of expansion of the universe is increasing Other recent experimental results find strong indications that the universe is ``flat'' In this paper, I investigate some solutions of Einstein's field equations which go smoothly between Schwarzschild's relativistic gravitational solution near a mass concentration to the Friedmann-Lemaitre expanding universe solution In particular, the static, curved-space extension of the Lemaitre- Schwarzschild solution in vacuum is given Uniqueness conditions are discussed One of these metrics preserves the ``cosmological equation'' We find that when the rate of expansion of the universe is increasing, space is broken up into domains of attraction Outside a domain of attraction, the expansion of the universe is strong enough to accelerate a test particle away from the domain boundary I give a domain-size--mass relationship This relationship may very well be important to our understanding of the large scale structure of the universe
TL;DR: In this paper, a method of distinguishing an almost flat universe from a precisely flat universe using a single observational data set, without using any microwave background information, is presented, which assumes that a standard ruler should have no preferred orientation (radial versus tangential) to the observer, and requires that the (comoving) length of the standard ruler be known independently (e.g. from low redshift estimates).
Abstract: Several recent observations using standard rulers and standard candles now suggest, either individually or in combination, that the Universe is close to flat, i.e. that the curvature radius is about as large as the horizon radius (10h 1 Gpc) or larger. Here, a method of distinguishing an almost flat universe from a precisely flat universe using a single observational data set, without using any microwave background information, is presented. The method (i) assumes that a standard ruler should have no preferred orientation (radial versus tangential) to the observer, and (ii) requires that the (comoving) length of the standard ruler be known independently (e.g. from low redshift estimates). The claimed feature at xed comoving length in the power spectrum of density perturbations, detected among quasars, Lyman break galaxies or other high redshift objects, would provide an adequate standard candle to prove that the Universe is curved, if indeed it is curved. For example, a combined intrinsic and measurement uncertainty of 1% in the length of the standard ruler L applied at a redshift of z =3 would distinguish an hyperbolic (m =0 :2; =0 :7) or a spherical (m =0 :4; =0 :7) universe from a flat one to 1 P> 95% condence.
TL;DR: In this paper, a new equation for the density contrast is derived in the framework of reexamined Newtonian cosmology if we take into account adiabatic matter creation in the universe.
Abstract: A new equation for the density contrast is derived in the framework of reexamined Newtonian cosmology if we take into account adiabatic matter creation in the universe. The age of the universe and the reach of non linear regime of the density contrast are usually treated separately in the literature and this may leadtocontroversial conclusions regarding the most adequate scenario to describe the universe. We relate the age of the universe and the growing mode of the density contrast by introducing a variable x that relates both of them, so that both aspects are treated simultaneously. We apply this procedure to the Friedmann type model where the source of particle production is Y = 3nbH.
TL;DR: In the early universe, gravity was extremely strong and highly nonlinear as discussed by the authors, which is the case in the deep cores of astronomical objects and dense environs of the early Universe.
Abstract: The new millennium will see the upcoming of several ground-based interferometric gravitational wave antennas. Within the next decade a space-based antenna may also begin to observe the distant Universe. These gravitational wave detectors will together operate as a network taking data continuously for several years, watching the transient and continuous phenomena occurring in the deep cores of astronomical objects and dense environs of the early Universe where gravity was extremely strong and highly nonlinear. The network will listen to the waves from rapidly spinning non-axisymmetric neutron stars, normal modes of black holes, binary black hole inspiral and merger, phase transitions in the early Universe, quantum fluctuations resulting in a characteristic background in the early Universe. The gravitational wave antennas will open a new window to observe the dark Universe unreachable via other channels of astronomical observations.
Posted Content•
TL;DR: In this article, the mutual consistency of the Bekenstein Bound, the Standard Model (SM) of particle physics, and general relativity implies that the universe began in a unique state, and this plausibly yields a (small) positive cosmological constant.
Abstract: I show that the mutual consistency of the Bekenstein Bound, the Standard Model (SM) of particle physics, and general relativity implies that the universe began in a unique state. I solve the coupled EYM equations for this unique state, show how the horizon problem is solved, and how SM baryogenesis naturally results from the triangle anomoly. Since the SU(2) winding number state is thus non-zero, the universe is not in the QCD ground state, and this plausibly yields a (small) positive cosmological constant. Since the initial state is unique, it is necessarily homogeneous and isotropic, as required by the Bekenstein Bound. Wheeler-DeWitt quantization implies an $S^3$ cosmology must be very close to flat if the universe is to be classical today. I show that the spectrum of any classical gauge field (or interacting massless scalar field) in a FRW universe necessarily obeys the Wien displacement law and the corresponding quantized field the Planck distribution law with the reciprocal of the scale factor playing the role of temperature, even if the fields have zero temperature. Thus the CBR could even today be a pure SU(2) electroweak field at zero temperature coupled to the Higgs field, in spite of early universe inverse double Compton and thermal bremsstrahlung.Such a CBR would not couple to right-handed electrons, and this property can be detected with a Penning trap or even using the late 1960's CBR detector with appropriate filters. I argue that ultrahigh energy (UHE) Genesisf.tex Genesisf.tex cosmic ray protons would not produce pions by interacting with such a CBR, and thus the existence of such protons may constitute an observation of this CBR property.
01 Jan 2001
TL;DR: In this paper, a general-relativistic cosmological theory that gives a direct relationship between distances and redshifts in an expanding universe is presented, which is actually a generalization of Hubble's law taking gravity into account by means of Einstein's theory of general relativity.
Abstract: Recent observations of distant supernovae imply, in defiance of expectations, that the universe growth is accelerating, contrary to what has always been assumed that the expansion is slowing down due to gravity. In this paper a general-relativistic cosmological theory that gives a direct relationship between distances and redshifts in an expanding universe is presented. The theory is actually a generalization of Hubble’s law taking gravity into account by means of Einstein’s theory of general relativity. The theory predicts that the universe can have three phases of expansion, decelerating, constant and accelerating, but it is shown that at present the first two cases are excluded, although in the past it had experienced them. Our theory shows that the universe now is definitely in a stage of accelerating expansion, confirming the recent experimental results.