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Showing papers on "Particle horizon published in 2001"


Journal ArticleDOI
TL;DR: In this article, a cosmological scenario in which the hot big bang universe is produced by the collision of a brane in the bulk space with a bounding orbifold plane, beginning from an otherwise cold, vacuous, static universe was proposed.
Abstract: We propose a cosmological scenario in which the hot big bang universe is produced by the collision of a brane in the bulk space with a bounding orbifold plane, beginning from an otherwise cold, vacuous, static universe. The model addresses the cosmological horizon, flatness and monopole problems and generates a nearly scale-invariant spectrum of density perturbations without invoking superluminal expansion (inflation). The scenario relies, instead, on physical phenomena that arise naturally in theories based on extra dimensions and branes. As an example, we present our scenario predominantly within the context of heterotic M theory. A prediction that distinguishes this scenario from standard inflationary cosmology is a strongly blue gravitational wave spectrum, which has consequences for microwave background polarization experiments and gravitational wave detectors.

1,606 citations


Journal ArticleDOI
TL;DR: In this article, a new mechanism for the formation of protogalaxies is proposed, based on the second-order phase transition in the inflation stage and the domain wall formation upon the end of inflation.
Abstract: A new mechanism describing the formation of protogalaxies is proposed, based on the second-order phase transition in the inflation stage and the domain wall formation upon the end of inflation. The presence of closed domain walls with the size markedly exceeding the cosmological horizon at the instant of their formation and the wall collapse in the postinflation epoch (when the wall size becomes comparable with the cosmological horizon) lead to the formation of massive black hole clusters that can serve as nuclei for the future galaxies. The black hole mass distributions obtained do not contradict the available experimental data. The number of black holes with M ∼ 100 solar masses (M⊙) and above is comparable with the number of galaxies in the visible Universe. Development of the proposed approach gives grounds for a principally new scenario of galaxy formation in the model of a hot Universe.

187 citations


Posted Content
TL;DR: In this article, the analog of an S-matrix for space-times that begin with a Big-Bang and asymptote to an FRW universe with nonnegative cosmological constant is discussed.
Abstract: We discuss the construction of the analog of an S-matrix for space-times that begin with a Big-Bang and asymptote to an FRW universe with nonnegative cosmological constant. When the cosmological constant is positive there are many such S-matrices, related mathematically by gauge transformations and physically by an analog of the principle of black hole complementarity. In the limit of vanishing $\Lambda$ these become (approximate) Poincare transforms of each other. Considerations of the initial state require a quantum treatment of space-time, and some preliminary steps towards constructing such a theory are proposed. In this context we propose a model for the earliest semiclassical state of the universe, which suggests a solution for the horizon problem different from that provided by inflation.

170 citations


Journal ArticleDOI
Andrei Linde1
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


Journal ArticleDOI
TL;DR: In this article, the age of the universe as constrained by measurements of the cosmic microwave background (CMB) is shown to be 14.0 ± 0.5 Gyr, with a small uncertainty due to the tight correlation in flat adiabatic models of the age with the angle subtended by the sound horizon on the last scattering surface.
Abstract: If Ωtot = 1 and structure formed from adiabatic initial conditions, then the age of the universe, as constrained by measurements of the cosmic microwave background (CMB), is t0 = 14.0 ± 0.5 Gyr. The uncertainty is surprisingly small given that CMB data alone do not significantly constrain either h or ΩΛ. This small uncertainty is due to the tight (and accidental) correlation in flat adiabatic models of the age with the angle subtended by the sound horizon on the last-scattering surface and, thus, with the well-determined acoustic peak locations. If we assume either the Hubble Space Telescope Key Project result h = 0.72 ± 0.08 or simply that h > 0.55, we find ΩΛ > 0.4 at 95% confidence—another argument for dark energy, independent of supernovae observations. Our analysis is greatly simplified by the Monte Carlo Markov chain approach to Bayesian inference combined with a fast method for calculating angular power spectra.

115 citations


Journal ArticleDOI
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


Journal ArticleDOI
TL;DR: In this paper, the authors discuss evidence for a few percent increase in the fine structure constant between the time of recombination and the present, which would delay the recombination of electrons and protons and also act to suppress secondary oscillations.
Abstract: Recent measurements of a peak in the angular power spectrum of the cosmic microwave background suggest that the geometry of the universe is close to flat. But if other accepted indicators of cosmological parameters are also correct then the best fit model is marginally closed, with the peak in the spectrum at slightly larger scales than in a flat universe. If these observations persevere, one way they might be reconciled with a flat universe is if the fine structure constant had a lower value at earlier times, which would delay the recombination of electrons and protons and also act to suppress secondary oscillations as observed. We discuss evidence for a few percent increase in the fine structure constant between the time of recombination and the present.

64 citations


Journal ArticleDOI
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


Journal ArticleDOI
TL;DR: In this article, the authors investigated the dynamical consequences of a bimetric scalar-tensor theory of gravity with a dynamical light speed in a cosmological setting, and showed that in a universe with matter that has a radiation-dominated equation of state, the model allows solutions with a de Sitter phase that provides sufficient inflation to solve the horizon and flatness problems.

55 citations


Journal ArticleDOI
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


Posted Content
TL;DR: In this paper, the cosmological implications of space-time non-commutativity are examined, and a deformed Planck spectrum, a temperature dependent equation of state, a new Stephan-Boltzmann law and a new entropy relation are found.
Abstract: We examine the cosmological implications of space-time non-commutativity, discovering yet another realization of the varying speed of light model. Our starting point is the well-known fact that non-commutativity leads to deformed dispersion relations, relating energy and momentum, implying a frequency dependent speed of light. A Hot Big Bang Universe therefore experiences a higher speed of light as it gets hotter. We study the statistical physics of this "deformed radiation", recovering standard results at low temperatures, but a number of novelties at high temperatures: a deformed Planck's spectrum, a temperature dependent equation of state $w=p/\rho$ (ranging from 1/3 to infinity), a new Stephan-Boltzmann law, and a new entropy relation. These new photon properties closely mimic those of phonons in crystals, hardly a surprising analogy. They combine to solve the horizon and flatness problems, explaining also the large entropy of the Universe. We also show how one would find a direct imprint of non-commutativity in the spectrum of a cosmic graviton background, should it ever be detected.

Journal ArticleDOI
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.

Journal ArticleDOI
TL;DR: In this article, the authors investigate the possibility of apparent acausality as seen by a brane-based observer resulting from signal propagation through the extra dimensions, and derive the equations of motion for the interbrane distance in a two-brane scenario.
Abstract: Models with extra dimensions are often invoked to resolve cosmological problems. We investigate the possibility of apparent acausality as seen by a brane-based observer resulting from signal propagation through the extra dimensions. Null geodesics are first computed in static and cosmological single-brane models, following which we derive the equations of motion for the inter-brane distance in a two-brane scenario, which we use to examine possible acausality in this more complex setup. Despite observing significant effective acausality in some situations there is no a priori solution to the horizon problem using this mechanism. In the two-brane scenario there can be significant late time violation of gravitational Lorentz invariance, resulting in the gravitational horizon being larger than the particle horizon, leading to potential signals in gravitational wave detectors.

Journal ArticleDOI
TL;DR: In this paper, the authors take a critical look at the cosmological scenario at the turn of the century by examining the available cosmology models in the light of the present observational evidence.
Abstract: ▪ Abstract This review takes a critical look at the cosmological scenario at the turn of the century by examining the available cosmological models in the light of the present observational evidence. The center stage is held by the big bang models, which are collectively referred to here as standard cosmology (SC) and its extensions. SC itself is characterized by a seven parameter set of models based on Einstein's general theory of relativity. The seven parameters are H0, ΩB, ΩDM, ΩΛ, ΩR (describing the background universe, and A, n (specifying the amplitude and power law index of initial fluctuation spectrum). The extended SC includes extrapolations of the SC to earlier epochs when the mean energies of the particles were greater than about 100 GeV. The strength of the SC is seen to lie in its successful prediction of the expansion of the universe, the abundance of light nuclei, and the spectrum and anisotropies of the cosmic microwave background (CMBR). The SC has led to a whole class of theories of stru...

Journal ArticleDOI
22 Jun 2001-Science
TL;DR: Comparisons of the CMB detections with the corresponding acoustic oscillations in the matter-density power spectrum provide further support for the standard Hot Big Bang model of the universe.
Abstract: During its first ≃100,000 years, the universe was a fully ionized plasma with a tight coupling by Thompson scattering between the photons and matter. The trade-off between gravitational collapse and photon pressure causes acoustic oscillations in this primordial fluid. These oscillations will leave predictable imprints in the spectra of the cosmic microwave background and the present-day matter-density distribution. Recently, the BOOMERANG and MAXIMA teams announced the detection of these acoustic oscillations in the cosmic microwave background (observed at redshift ≃ 1000). Here, we compare these CMB detections with the corresponding acoustic oscillations in the matter-density power spectrum (observed at redshift ≃ 0.1). These consistent results, from two different cosmological epochs, provide further support for our standard Hot Big Bang model of the universe.

Journal ArticleDOI
TL;DR: In this paper, the authors investigate the possibility that large distance modifications of the curvature of the universe would perhaps offer an alternative explanation of the SNIa data, although inconclusive, when combined with other observations makes a strong case that our universe is presently dominated by dark energy.
Abstract: The SNIa data, although inconclusive, when combined with other observations makes a strong case that our universe is presently dominated by dark energy We investigate the possibility that large distance modifications of the curvature of the universe would perhaps offer an alternative explanation of the observation Our calculations indicate that a universe made up of no dark energy but instead, with a modified curvature at large scales, is not scale invariant; therefore quite likely it is ruled out by the CMB observations The sensitivity of the CMB spectrum is checked for the whole range of mode modifications of large or short distance physics The spectrum is robust against modifications of short-distance physics and the UV cutoff when the initial state is the adiabatic vacuum, and the inflationary background space is de Sitter space

Book
01 Aug 2001
TL;DR: In this paper, a cosmological constant is used to model the relationship between redshift and time in an expanding universe, and the exponential deceleration parameter is defined for the age of the universe The steady state theory The evolving universe Problems with big bang cosmology The flatness problem Alternative cosmologies Problems HOT BIG BANG
Abstract: Preface RECONSTRUCTING TIME The patterns of the stars Structural relics Material relics Ethereal relics Cosmological principles Theories Problems EXPANSION The redshift The expanding universe The distance scale The Hubble constant The deceleration parameter The age of the universe The steady state theory The evolving universe Problems MATTER The mean mass density of the universe Determining the matter density The mean luminosity density The mass to luminosity ratios of galaxies The virial theorem The mass to luminosity ratios of rich clusters Baryonic matter Intracluster gas The gravitational lensing method The intercluster medium The non-baryonic dark matter Dark matter candidates The search for WIMPS Antimatter Appendix A: Derivation of the virial theorem Problems RADIATION Sources of background radiation The microwave background The hot big bang Radiation and expansion Nevertheless it moves The x-ray background Problems RELATIVITY Introduction Space geometry Relativistic geometry Isotropic and homogeneous geometry Other forms of the metric Open and closed spaces Fundamental (or comoving) observers Redshift The velocity-distance law Time dilation The field equations The dust universe The relationship between redshift and time Explicit solutions Models with a cosmological constant The radiation universe Light propagation in an expanding universe The Hubble sphere The particle horizon Alternative equations of state Problems MODELS The classical tests The Mattig relation The angular diameter - redshift test The apparent magnitude - redshift test The geometry of number counts: theory The timescale test The lensed quasar test Problems with big bang cosmology The flatness problem Alternative cosmologies Problems HOT BIG BANG Introduction Equilibrium thermodynamics The plasma universe The matter era The radiation era The era of equilibrium The GUT era: baryogenesis Photon to baryon ratio Nucleosynthesis The plasma era Decoupling Recombination Last scattering Perturbations Appendix A: Thermal distributions Appendix B: The Saha Equation Appendix C: Constancy of ? Problems INFLATION The horizon problem The flatness problem Origin of structure Mechanisms Fluctuations Starting Inflation Stopping inflation Topological defects Problems STRUCTURE The problem of structure Observations Surveys and catalogues Large scale structures Correlations Bias Growth of perturbations The Jeans' mass Adiabatic perturbations Isocurvature (isothermal) perturbations Superhorizon size perturbations Dissipation The spectrum of fluctuations Structure formation in baryonic models Dark matter models Observations of the microwave background Appendix A Appendix B Problems EPILOGUE Homogeneous anisotropy Growing modes The rotating universe The arrow of time REFERENCE MATERIAL REFERENCES

Journal ArticleDOI
TL;DR: In this article, it was shown that in the case of positively-curved Friedmann-lema universes, an inflationary period in the early universe will for most initial conditions not solve the horizon problem, no matter how long inflation lasts.
Abstract: We show that in the case of positively-curved Friedmann-Lema\^itre universes $(k=+1)$, an inflationary period in the early universe will for most initial conditions not solve the horizon problem, no matter how long inflation lasts. It will only do so for cases where inflation starts in an almost static state, corresponding to an extremely high value of $\Omega_{\Lambda}$, $\Omega_{\Lambda} \gg 1$, at the beginning of inflation. For smaller values, it is not possible to solve the horizon problem because the relevant integral asymptotes to a finite value (as happens also in the de Sitter universe in a $k=+1$ frame). Thus, for these cases, the causal problems associated with the near-isotropy of the Cosmic Background Radiation have to be solved already in the Planck era. Furthermore both compact space sections and event horizons will exist in these universes even if the present cosmological constant dies away in the far future, raising potential problems for M-theory as a theory of gravity.

Proceedings ArticleDOI
23 Apr 2001
TL;DR: In this article, it was shown that galaxies with recession velocities faster than the speed of light are observable and that in all viable cosmological models, galaxies above a redshift of three are receding superluminally.
Abstract: Hubble’s Law, v=HD (recession velocity is proportional to distance), is a theoretical result derived from the Friedmann-Robertson-Walker metric. v=HD applies at least as far as the particle horizon and in principle for all distances. Thus galaxies with distances greater than D=c/H are receding from us with velocities greater than the speed of light and superluminal recession is a fundamental part of the general relativistic description of the expanding universe. This apparent contradiction of special relativity (SR) is often mistakenly remedied by converting redshift to velocity using SR. Here we show that galaxies with recession velocities faster than the speed of light are observable and that in all viable cosmological models, galaxies above a redshift of three are receding superluminally.

Journal ArticleDOI
TL;DR: In this article, a mixed dark matter model with cosmological constant (Lambda$MDM) with parameters was proposed, and the model was shown to have a good performance.
Abstract: We use observational data on the large scale structure (LSS) of the Universe measured over a wide range of scales from sub-galactic up to horizon scale and on the cosmic microwave background anisotropies to determine cosmological parameters within the class of adiabatic inflationary models. We show that a mixed dark matter model with cosmological constant ($\Lambda$MDM model) with parameters

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).

Journal ArticleDOI
TL;DR: In this article, the authors investigate the possibility of apparent acausality as seen by a brane-based observer resulting from signal propagation through the extra dimensions, and derive the equations of motion for the interbrane distance in a two-brane scenario.
Abstract: Models with extra dimensions are often invoked to resolve cosmological problems. We investigate the possibility of apparent acausality as seen by a brane-based observer resulting from signal propagation through the extra dimensions. Null geodesics are first computed in static and cosmological single-brane models, following which we derive the equations of motion for the inter-brane distance in a two-brane scenario, which we use to examine possible acausality in this more complex setup. Despite observing significant effective acausality in some situations there is no a priori solution to the horizon problem using this mechanism. In the two-brane scenario there can be significant late time violation of gravitational Lorentz invariance, resulting in the gravitational horizon being larger than the particle horizon, leading to potential signals in gravitational wave detectors.

Posted Content
TL;DR: In this paper, the authors considered the Brane Gas Cosmology (BGC) model, where the initial state of the universe is assumed to be small, dense and hot, with all fundamental degrees of freedom near thermal equilibrium.
Abstract: In Brane Gas Cosmology (BGC) the initial state of the universe is taken to be small, dense and hot, with all fundamental degrees of freedom near thermal equilibrium. This starting point is in close analogy with the Standard Big Bang (SBB) model. In the simplest example, the topology of the universe is assumed to be toroidal in all nine spatial dimensions and is filled with a gas of $p$-branes. The dynamics of winding modes allow, at most, three spatial dimensions to become large, providing a possible explanation to the origin of our macroscopic (3+1)-dimensional universe. Specific solutions are found within the model that exhibit loitering, i.e. the universe experiences a short phase of slow contraction during which the Hubble radius grows larger than the physical extent of the universe. This phase is studied by combining the dilaton gravity background equations of motion with equations that determine the annihilation of string winding modes into string loops. Loitering provides a solution to the brane problem (generalised domain wall problem) in BGC and the horizon problem of the SBB scenario. In BGC the initial singularity problem of the SBB scenario is solved, without relying on an inflationary phase due to the presence of the T-duality symmetry in the theory.

Journal ArticleDOI
TL;DR: In this paper, a cosmological model representing a flat viscous universe with variable G and Λ in the context of higher dimensional spacetime was considered. But the model was not considered in this paper, and it was shown that the model generated all models obtained by Arbab and Singh et al. in four-dimensional space-time.
Abstract: In this paper we have considered a cosmological model representing a flat viscous universe with variable G and Λ in the context of higher dimensional spacetime. It has been observed that in this model the particle horizon exists and the cosmological term varies as inverse square of time. The deceleration parameter and temperature are well within the observational limits. The model indicates matter and entropy generation in the early stages of the universe. Further, it is shown that our model generates all models obtained by Arbab and Singh et al. in four-dimensional space-time.

Book ChapterDOI
20 Dec 2001

Journal ArticleDOI
S. S. De1
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 generalize the spherical collapse model for the formation of bound objects to apply in a universe with arbitrary positive cosmological constant and give exact values of the characteristic densities and redshifts of its evolution.
Abstract: We generalize the spherical collapse model for the formation of bound objects to apply in a Universe with arbitrary positive cosmological constant. We calculate the critical condition for collapse of an overdense region and give exact values of the characteristic densities and redshifts of its evolution.

Journal ArticleDOI
02 Mar 2001-Science
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.