Showing papers on "Big Rip published in 2002"

Cosmic Evolution in a Cyclic Universe

Abstract: Based on concepts drawn from the ekpyrotic scenario and M theory, we elaborate our recent proposal of a cyclic model of the universe. In this model, the universe undergoes an endless sequence of cosmic epochs which begin with the universe expanding from a ``big bang'' and end with the universe contracting to a ``big crunch.'' Matching from ``big crunch'' to ``big bang'' is performed according to the prescription recently proposed with Khoury, Ovrut and Seiberg. The expansion part of the cycle includes a period of radiation and matter domination followed by an extended period of cosmic acceleration at low energies. The cosmic acceleration is crucial in establishing the flat and vacuous initial conditions required for ekpyrosis and for removing the entropy, black holes, and other debris produced in the preceding cycle. By restoring the universe to the same vacuum state before each big crunch, the acceleration ensures that the cycle can repeat and that the cyclic solution is an attractor.

Hierarchy problem in the shell-universe model

Abstract: In the model where the Universe is considered as a thin shell expanding in five-dimensional hyper-space there is a possibility to obtain one scale for particle theory corresponding to the five-dimensional cosmological constant and Universe thickness.

New cosmological singularities in braneworld models

Abstract: Higher-dimensional braneworld models which contain both bulk and brane curvature terms in the action admit cosmological singularities of rather unusual form and nature. These 'quiescent' singularities, which can occur both during the contracting as well as the expanding phase, are characterized by the fact that while the matter density and Hubble parameter remain finite, all higher derivatives of the scale factor ( etc) diverge as the cosmological singularity is approached. The singularities are the result of the embedding of the (3 + 1)-dimensional brane in the bulk and can exist even in an empty homogeneous and isotropic (FRW) universe. The possibility that the present universe may expand into a singular state is discussed.

An Alternative to inflation

Abstract: Inflationary models are generally credited with explaining the large scale homogeneity, isotropy, and flatness of our universe as well as accounting for the origin of structure (i.e., the deviations from exact homogeneity) in our universe. We argue that the explanations provided by inflation for the homogeneity, isotropy, and flatness of our universe are not satisfactory, and that a proper explanation of these features will require a much deeper understanding of the initial state of our universe. On the other hand, inflationary models are spectacularly successful in providing an explanation of the deviations from homogeneity. We point out here that the fundamental mechanism responsible for providing deviations from homogeneity—namely, the evolutionary behavior of quantum modes with wavelength larger than the Hubble radius—will operate whether or not inflation itself occurs. However, if inflation did not occur, one must directly confront the issue of the initial state of modes whose wavelength was larger than the Hubble radius at the time at which they were “born.” Under some simple hypotheses concerning the “birth time” and initial state of these modes (but without any “fine tuning”), it is shown that non-inflationary fluid models in the extremely early universe would result in the same density perturbation spectrum and amplitude as inflationary models, although there would be no “slow roll” enhancement of the scalar modes.

Supergravity, Dark Energy and the Fate of the Universe

Abstract: We propose a description of dark energy and acceleration of the universe in extended supergravities with de Sitter (dS) solutions. Some of them are related to M theory with noncompact internal spaces. Masses of ultralight scalars in these models are quantized in units of the Hubble constant: ${m}^{2}{=nH}^{2}.$ If the dS solution corresponds to a minimum of the effective potential, the universe eventually becomes dS space. If the dS solution corresponds to a maximum or a saddle point, which is the case in all known models based on $N=8$ supergravity, the flat universe eventually stops accelerating and collapses to a singularity. We show that in these models, as well as in the simplest models of dark energy based on $N=1$ supergravity, the typical time remaining before the global collapse is comparable to the present age of the universe, ${t=O(10}^{10})\mathrm{yr}.$ We discuss the possibility of distinguishing between various models and finding our destiny using cosmological observations.

A Two-Field Quintessence Model

Abstract: We study the dynamics of a quintessence model based on two interacting scalar fields. The model can account for the (recent) accelerated expansion of the Universe suggested by astronomical observations. Acceleration can be permanent or temporary and, for both scenarios, it is possible to obtain suitable values for the cosmological parameters while satisfying the nucleosynthesis constraint on the quintessence energy density. We argue that the model dynamics can be made consistent with a stable zero-energy relaxing supersymmetric vacuum.

Generalized Cardassian Expansion: Models in Which the Universe is Flat, Matter Dominated, and Accelerating

Abstract: The Cardassian universe is a proposed modification to the Friedmann Robertson Walker (FRW) equation in which the universe is flat, matter dominated, and accelerating. Here we generalize the original Cardassian proposal to include additional variants on the FRW equation. Specific examples are presented. In the ordinary FRW equation, the right hand side is a linear function of the energy density, $H^2 \sim \rho$. Here, instead, the right hand side of the FRW equation is a different function of the energy density, $H^2 \sim g(\rho)$. This function returns to ordinary FRW at early times, but modifies the expansion at a late epoch of the universe. The only ingredients in this universe are matter and radiation: in particular, there is {\it no} vacuum contribution. Currently the modification of the FRW equation is such that the universe accelerates. The universe can be flat and yet consist of only matter and radiation, and still be compatible with observations. The energy density required to close the universe is much smaller than in a standard cosmology, so that matter can be sufficient to provide a flat geometry. The modifications may arise, e.g., as a consequence of our observable universe living as a 3-dimensional brane in a higher dimensional universe. The Cardassian model survives several observational tests, including the cosmic background radiation, the age of the universe, the cluster baryon fraction, and structure formation. As will be shown in future work, the predictions for observational tests of the generalized Cardassian models can be very different from generic quintessence models, whether the equation of state is constant or time dependent.

Interpretations of the Accelerating Universe

Abstract: It is generally argued that present cosmological observations support the accelerating models of the universe, as driven by a cosmological constant or "dark energy." We argue here that an alternative model of the universe is possible, which explains the current observations of the universe. We demonstrate this with a reinterpretation of the magnitude-redshift relation for Type Ia supernovae, since this was the test that gave a spurt to the current trend in favor of the cosmological constant.

Dynamical compactification, standard cosmology, and the accelerating universe

Abstract: A cosmological model based on Kaluza-Klein theory is studied. A metric, in which the scale factor of the compact space evolves as an inverse power of the radius of the observable universe, is constructed. The Freedmann-Robertson-Walker equations of standard four-dimensional cosmology are obtained precisely. The pressure in our universe is an effective pressure expressed in terms of the components of the higher dimensional energy-momentum tensor. In particular, this effective pressure could be negative and might therefore explain the acceleration of our present universe. A special feature of this model is that, for a suitable choice of the parameters of the metric, the higher dimensional gravitational coupling constant could be negative.

Cosmological magnetic fields from primordial helical seeds

Abstract: Most early Universe scenarios predict negligible magnetic fields on cosmological scales if they are unprocessed during subsequent expansion of the Universe. We present a new numerical treatment of the evolution of primordial fields and apply it to weakly helical seeds as they occur in certain early Universe scenarios. We find that initial helicities not much larger than the baryon to photon number can lead to fields of about 10^{-13} Gauss with coherence scales slightly below a kilo-parsec today.

Mass Power Spectrum in a Universe Dominated by the Chaplygin Gas

Abstract: The mass power spectrum for a Universe dominated by the Chaplygin gas is evaluated numerically from scales of the order of the Hubble horizon to 100 Mpc. The results are compared with a pure baryonic Universe and a cosmological constant model. In all three cases, the spectrum increases with k, the wavenumber of the perturbations. The slope of the spectrum is higher for the baryonic model and smaller for the cosmological constant model, the Chaplygin gas interpolating these two models. The results are analyzed in terms of the sound velocity of the Chaplygin gas and the moment the Universe begins to accelerate.

Why does inflation start at the top of the hill

Abstract: We show why the universe started in an unstable de Sitter state. The quantum origin of our universe implies one must take a ``top down'' approach to the problem of initial conditions in cosmology, in which the histories that contribute to the path integral depend on the observable being measured. Using the no boundary proposal to specify the class of histories, we study the quantum cosmological origin of an inflationary universe in theories such as trace anomaly driven inflation in which the effective potential has a local maximum. We find that an expanding universe is most likely to emerge in an unstable de Sitter state, by semiclassical tunneling via a Hawking-Moss instanton. Since the top down view is forced upon us by the quantum nature of the universe, we argue that the approach developed here should still apply when the framework of quantum cosmology will be based on M theory.

A new standard model of the universe

Abstract: Up to about four years ago the dynamical properties of the evolution of the universe were assumed to be well described by the Einstein-de Sitter universe model, which is a flat universe model dominated by cold matter. However, the discovery that the cosmic expansion is accelerating made it clear that, at the present time, the evolution of the universe is dominated by some sort of vacuum energy with repulsive gravitation. The most simple type of vacuum energy is the Lorentz invariant vacuum energy which has constant energy density during the expansion of the universe. This type of vacuum may be represented mathematically by including a cosmological constant in Einstein's field equations. Hence, the flat Friedmann-Lemaitre model, which is a universe model with cold matter and vacuum energy, has replaced the Einstein-de Sitter model as the standard model of the universe. In this paper we give a pedagogical presentation of this model, including, among others, a new formula for the point of time when decelerated expansion changed into accelerated expansion.

Inflationary universe and the vacuumlike state of physical medium

Abstract: This paper reviews two cosmologies which assume that the observable universe was initially vacuumlike (i.e., the cosmological medium was Lorentz invariant). In the earlier nonsingular Friedmann cosmology, the Friedmann universe comes into being during the phase transition of an initial vacuumlike state to the state of 'ordinary' matter. In the course of this transition, the emerging matter is accelerated, which causes the universe to expand and attain the Friedmann expansion regime. In the inflationary cosmology, the transition to the Friedmann universe is preceded by an epoch of inflation in which the universe grows spontaneously by many tens of orders of magnitude without or almost without changes in its composition and density. The idea of inflation gives rise to a variety of scenarios involving a cosmological singularity, or the birth of one universe within another, or the world-as-a-whole as an infinite set of universes, etc. The present paper provides arguments against the inflation idea. On dismissing it, both cosmologies are essentially identical from the viewpoint of their application to the observable universe.

Dark Energy and the Observable Universe

Abstract: We consider ever-expanding big bang models with a cosmological constant, Λ, and investigate in detail the evolution of the observable part of the universe. We also discuss quintessence models from the same point of view. A new concept, the Λ-sphere (or Q-sphere, in the case of quintessence) is introduced. This is the surface in our visible universe that bounds the region where dark energy dominates the expansion, and within which the universe is accelerating. We follow the evolution of this surface as the universe expands, and we also investigate the evolution of the particle and event horizons as well as the Hubble surface. We calculate the extent of the observable universe and the portion of it that can be seen at different epochs. Furthermore, we trace the changes in redshift, apparent magnitude and apparent size of distant sources through cosmic history. Our approach is different from, but complementary to, most other contemporary investigations, which concentrate on the past light cone at the present epoch. When presenting numerical results we use the FRW world model with Ωm0 = 0.30 and ΩΛ0 = 0.70 as our standard cosmological model. In this model the Λ-sphere is at a redshift of 0.67, and within a few Hubble times the event horizon will be stationary at a fixed proper distance of 5.1 Gpc (assuming h0 = 0.7). All cosmological sources with present redshift larger than 1.7 have by now crossed the event horizon and are therefore completely out of causal contact.

Cosmological evolution in a type-0 string theory

Abstract: We study the cosmological evolution of a type-0 string theory by employing non-criticality, which may be induced by fluctuations of the D3 brane worlds. We check the consistency of the approach to in the corresponding σ-model. The ten-dimensional theory is reduced to an effective four-dimensional model, with only time dependent fields. We show that the four-dimensional universe has an inflationary phase and graceful exit from it, while the other extra dimensions are stabilized to a constant value, with the fifth dimension much larger than the others. We pay particular attention to demonstrating the role of tachyonic matter in inducing these features. The universe asymptotes, for large times, to a nonaccelerating linearly-expanding universe with a time-dependent dilaton and a relaxing to zero vacuum energy a la quintessence. Our perturbative string solution appears to have initial singularities (Big Bang type), which however, we believe, may be lifted in a nonperturbative way, and they do not represent true singularities of the string theory.

Shear free rotating inflation

Abstract: We demonstrate the existence of shear-free cosmological models with rotation and expansion which support inflationary scenarios. The corresponding metrics belong to the family of spatially homogeneous models with the geometry of the closed universe (Bianchi type IX). We show that the global vorticity does not prevent inflation and can even accelerate it.

Back reaction and the effective Einstein equation for the universe with ideal fluid cosmological perturbations

Abstract: We investigate the back reaction of cosmological perturbations on the evolution of the Universe using the renormalization group method. Starting from the second order perturbed Einstein's equation, we renormalize a scale factor of the Universe and derive the evolution equation for the effective scale factor which includes back reaction due to inhomogeneities of the Universe. The resulting equation has the same form as the standard Friedman-Robertson-Walker equation with the effective energy density and pressure which represent the back reaction effect.

How the Universe Got Its Spots

Abstract: The universe displays a three-dimensional pattern of hot and cold spots in the radiation remnant from the big bang. The global geometry of the universe can be revealed in the spatial distribution of these spots. In a topologically compact universe, distinctive patterns are especially prominent in spatial correlations of the radiation temperature. Whereas these patterns are usually washed out in statistical averages, we propose a scheme which uses the universe’s spots to observe global geometry in a manner analogous to the use of multiple images of a gravitationally lensed quasar to study the geometry of the lens. To demonstrate how the geometry of space forms patterns, we develop a simple real-space approximation to estimate temperature correlations for any set of cosmological parameters and any global geometry. We present correlated spheres which clearly show topological pattern formation for compact flat universes as well as for the compact negatively curved space introduced by Weeks and another discovered by Best. These examples illustrate how future satellite-based observations of the microwave background can determine the full geometry of the universe. @S0556-2821~98!02124-9# PACS number~s!: 98.70.Vc, 98.80.Hw From the zebra’s stripes to the leopard’s spots, the animal kingdom displays a diversity of coat patterns. Following the innovative ideas of Turing @1#, mathematical biologists have posed and partly answered the question of how the leopard got its spots. The fluctuation of enzymes diffusing through the developing embryo can lead to the spatial pattern formation displayed by animal coats. Both the geometry and size of the animal exert a strong influence on differentiating patterns. For instance, the broad cylindrical shape of the leopard’s body favors spots while the tapered tail induces stripes @2#. Remarkably, these diverse features can arise from the properties of simple solutions to second-order partial differential equations on the geometry and topology appropriate for animal limbs, tails, or bodies. 1

Accelerating Universe: Theory versus Experiment

Abstract: We present gravitation as a theory in which the coordinates are distances and velocities between galaxies. We show that there are three possibilities for the Universe to expand: decelerating, constant and accelerating, and it is shown that the Universe is now in the latter phase. Assuming "Omega"_m=0.245, the time at which the Universe goes over from a decelerating to an accelerating expansion, occurs at 8.5 Gyr ago, at which time the cosmic radiation temperature was 146K. The theory predicts also that now there is a positive pressure, p=0.034g/cm^2, in the Universe. Although the theory has no cosmological constant, we extract from it its equivalence and show that "Lambda"=1.934x10^{-35}s^{-2}, which is in excellent agreement with measurements. It is also shown that the three-dimensional space of the Universe is Euclidean. Comparison with general relativity theory is finally made and it is shown that the classical experiments as well as the gravitational radiation prediction follow from the present theory, too.

Brane Gas Inflation

Abstract: We consider the brane gas picture of the early universe. At later stages, when there are no winding modes and the background is free to expand, we show that a moving 3-brane, which we identify with our universe, can inflate even though it is radiation-dominated. The crucial ingredients for successful inflation are the coupling to the dilaton and the equation of state of the bulk. If we suppose the brane initially forms in a collision of higher-dimensional branes, then the spectrum of primordial density fluctuations naturally has a thermal origin.

Quantum Origin of the Universe

Abstract: The quantum origin of the Universe due to a positive cosmological constant is studied.

The origin of neutrino mass

Abstract: IF WE look deep into the universe, we see stars and galaxies of all shapes and sizes. What we do not see, however, is that the universe is filled with particles called neutrinos. These particles – which have no charge and have little or no mass – were created less than one second after the Big Bang, and large numbers of these primordial low-energy neutrinos remain in the universe today because they interact very weakly with matter. Indeed, every cubic centimetre of space contains about 300 of these uncharged relics.

A model of the universe including dark energy

Abstract: In this work we explore a model of the universe in which dark energy is modelled explicitely with both a dynamical quintessence field (with a double exponential self-interaction potential) and a cosmological constant. For a given region of the parameter space, our results confirm the possibility of a collapsing universe, which is necessary for an adequate definition of both perturbative quantum field and string theories. We have also reproduced the measurements of modulus distance from supernovae with good accuracy.

Properties of the quantum universe in quasistationary states and cosmological puzzles

Abstract: Old and new puzzles of cosmology are reexamined from the point of view of the quantum theory of the universe developed here. It is shown that in the proposed approach the difficulties of the standard cosmology do not arise. The theory predicts the observed dimensions of the non-homogeneities of matter density and the amplitude of fluctuations of the cosmic background radiation temperature in the Universe and points to a new quantum mechanism of their origin. The large-scale structure in the Universe is explained by the growth of non-homogeneities which arise from primordial quantum fluctuations due to the finite width of the quasistationary states. The theory allows one to obtain the value of the deceleration parameter, which is in good agreement with the recent SNe Ia measurements. It explains the large value of the entropy of the Universe and describes other parameters.

Volume expansion of a Swiss-cheese universe

Abstract: In order to investigate the effect of inhomogeneities on the volume expansion of the universe, we study a modified Swiss-cheese universe model. Since this model is an exact solution of Einstein's equations, we can get insight into the nonlinear dynamics of an inhomogeneous universe from it. We find that inhomogeneities make the volume expansion slower than that of the background Einstein--de Sitter universe when they can be regarded as small fluctuations in the background universe. This result is consistent with the previous studies based on the second order perturbation analysis. On the other hand, if the inhomogeneities cannot be treated as small perturbations, the volume expansion of the universe depends on the type of fluctuations. Although the volume expansion rate approaches the background value asymptotically, the volume itself can be finally arbitrarily smaller than the background one and can be larger than that of the background, but there is an upper bound on it.

Is the universe inflating? Dark energy and the future of the universe

Abstract: We consider the fate of the observable universe in the light of the discovery of a dark energy component to the cosmic energy budget. We extend results for a cosmological constant to a general dark energy component and examine the constraints on phenomena that may prevent the eternal acceleration of our patch of the universe. We find that the period of accelerated cosmic expansion has not lasted long enough for observations to confirm that we are undergoing inflation; such an observation will be possible when the dark energy density has risen to between 90% and 95% of the critical. The best we can do is make cosmological observations in order to verify the continued presence of dark energy to some high redshift. Having done that, the only possibility that could spoil the conclusion that we are inflating would be the existence of a disturbance (the surface of a true vacuum bubble, for example) that is moving toward us with sufficiently high velocity, but is too far away to be currently observable. Such a disturbance would have to move toward us with speed greater than about $0.8c$ in order to spoil the late-time inflation of our patch of the universe and yet avoid being detectable.