Showing papers on "Particle horizon published in 1999"
TL;DR: The cosmic triangle as mentioned in this paper is a way of representing the past, present, and future status of the universe and its current location within the cosmic triangle is determined by the answers to three questions: How much matter is in the universe? Is the expansion rate slowing down or speeding up? And, is the universe flat?
Abstract: The cosmic triangle is introduced as a way of representing the past, present, and future status of the universe. Our current location within the cosmic triangle is determined by the answers to three questions: How much matter is in the universe? Is the expansion rate slowing down or speeding up? And, is the universe flat? A review of recent observations suggests a universe that is lightweight (matter density about one-third the critical value), is accelerating, and is flat. The acceleration implies the existence of cosmic dark energy that overcomes the gravitational self-attraction of matter and causes the expansion to speed up.
1,080 citations
Journal Article•
TL;DR: The cosmic triangle as discussed by the authors is a way of representing the past, present and future status of the universe and its current location within the cosmic triangle is determined by the answers to three questions: How much matter is in the universe? Is the expansion rate slowing down or speeding up? And, is the universe flat?
Abstract: The cosmic triangle is introduced as a way of representing the past, present and future status of the universe. Our current location within the cosmic triangle is determined by the answers to three questions: How much matter is in the universe? Is the expansion rate slowing down or speeding up? And, is the universe flat? A review of recent observations suggests a universe that is lightweight (matter density about one-third the critical value), is accelerating, and is flat. The acceleration implies the existence of cosmic dark energy that overcomes the gravitational self-attraction of matter and causes the expansion to speed up.
800 citations
TL;DR: In this paper, an improved recombination calculation of H, He i, and He ii in the early universe is presented, which involves a line-by-line treatment of each atomic level.
Abstract: We have developed an improved recombination calculation of H, He i, and He ii in the early universe that involves a line-by-line treatment of each atomic level. We find two major differences compared with previous calculations. First, the ionization fraction xe is approximately 10% smaller for redshifts &800 because of nonequilibrium processes in the excited states of H. Second, He i recombination is much slower than previously thought, and it is delayed until just before H recombines. We describe the basic physics behind the new results and present a simple way to reproduce our calculation. This should enable a fast computation of the ionization history (and of the quantities such as the power spectrum of cosmic microwave background anisotropies that depend on it) for arbitrary cosmologies, without the need to consider the hundreds of atomic levels used in our complete model. Subject headings: atomic processes — cosmic microwave background — cosmology: theory — early universe
524 citations
Posted Content•
TL;DR: In this paper, the authors dwell upon the cosmological cornerstones of the very early universe (VEU) theory: Parametric Amplification Effect (PAE) responsible for the generation of Primordial Cosmological Perturbations (PCPs), Chaotic and Stochastic Inflation, Principal Tests of VEU, and others.
Abstract: In these lectures we dwell upon the cosmological corner-stones of the Very Early Universe (VEU) theory: Parametric Amplification Effect (PAE) responsible for the generation of Primordial Cosmological Perturbations (PCPs), Chaotic and Stochastic Inflation, Principal Tests of VEU, and others.
523 citations
TL;DR: In this article, the cosmological implications of light travelling faster in the early universe were considered and a prescription for deriving corrections to cosmology evolution equations while the speed of light $c$ is changing.
Abstract: We consider the cosmological implications of light travelling faster in the early Universe. We propose a prescription for deriving corrections to the cosmological evolution equations while the speed of light $c$ is changing. We then show how the horizon, flatness, and cosmological constant problems may be solved. We also study cosmological perturbations in this scenario and show how one may solve the homogeneity and isotropy problems. As it stands, our scenario appears to most easily produce extreme homogeneity, requiring structure to be produced in the standard big bang epoch. Producing significant perturbations during the earlier epoch would require a rather careful design of the function $c(t).$ The large entropy inside the horizon nowadays can also be accounted for in this scenario.
463 citations
Book•
01 Jan 1999
TL;DR: A brief history of cosmological ideas can be found in this paper, where the authors discuss the evolution of the Standard Cosmological Model (SCM) and Neutrino Cosmology.
Abstract: Preface. Constants conversion factors and symbols. 1. A (Very) Brief History of Cosmological Ideas. 2. Observational Overview. 3. Newtonian Gravity. 4. The Geometry of the Universe. 5. Simple Cosmological Models. 6.Observational Parameters. 7. The Cosmological Constant. 8. The Age of the Universe. 9. The Density of the Universe and Dark Matter. 10. The Cosmic Microwave Background. 11. The Early Universe. 12. Nucleosynthesis: The Origin of the Light Elements. 13. The Inflationary Universe. 14. The Initial Singularity. 15. Overview: The Standard Cosmological Model. Advanced Topic 1: General Relativistic Cosmology Advanced Topic 2: Classic Cosmology: Distances and Luminosities. Advanced Topic 3: Neutrino Cosmology. Advanced Topic 4: Baryogenesis. Advanced Topic 5: Structures in the Universe. Bibliography. Numerical answers and hints to problems. Index.
404 citations
TL;DR: In this article, it was shown that the vacuum energy of a free quantized field of very low mass can significantly alter the recent expansion of the universe, which is consistent with the possibility of inflation in the early universe.
Abstract: We show that the vacuum energy of a free quantized field of very low mass can significantly alter the recent expansion of the universe. The effective action of the theory is obtained from a non-perturbative sum of scalar curvature terms in the propagator. We numerically investigate the semiclassical Einstein equations derived from it. As a result of non-perturbative quantum effects, the scalar curvature of the matter-dominated universe stops decreasing and approaches a constant value. The universe in our model evolves from an open matter-dominated epoch to a mildly inflating de Sitter expansion. The Hubble constant during the present de Sitter epoch, as well as the time at which the transition occurs from matter-dominated to de Sitter expansion, are determined by the mass of the field and by the present matter density. The model provides a theoretical explanation of the observed recent acceleration of the universe, and gives a good fit to data from high-redshift Type Ia supernovae, with a mass of about 10^{-33} eV, and a current ratio of matter density to critical density, Omega_0 <0.4 . The age of the universe then follows with no further free parameters in the theory, and turns out to be greater than 13 Gyr. The model is spatially open and consistent with the possibility of inflation in the very early universe. Furthermore, our model arises from the standard renormalizable theory of a free quantum field in curved spacetime, and does not require a cosmological constant or the associated fine-tuning.
177 citations
TL;DR: In this article, it was shown that the Bekenstein-hawking bound on the black hole entropy is valid for open, flat and closed universes with matter and a small negative cosmological constant.
Abstract: The most radical version of the holographic principle asserts that all information about physical processes in the world can be stored on its surface. This formulation is at odds with inflationary cosmology, which implies that physical processes in our part of the universe do not depend on the boundary conditions. Also, there are some indications that the radical version of the holographic theory in the context of cosmology may have problems with unitarity and causality. Another formulation of the holographic principle, due to Fischler and Susskind, implies that the entropy of matter inside the post-inflationary particle horizon must be smaller than the area of the horizon. Their conjecture was very successful for a wide class of open and flat universes, but it did not apply to closed universes. Bak and Rey proposed a different holographic bound on entropy which was valid for closed universes of a certain type. However, as we will show, neither proposal applies to open, flat and closed universes with matter and a small negative cosmological constant. We will argue, in agreement with Easther, Lowe, and Veneziano, that whenever the holographic constraint on the entropy inside the horizon is valid, it follows from the Bekenstein-Hawking bound on the black hole entropy. These constraints do not allow one to rule out closed universes and other universes which may experience gravitational collapse, and do not impose any constraints on inflationary cosmology.
126 citations
TL;DR: In this paper, the luminosity distance as a function of redshift is obtained accurately using Type Ia supernovae, but the equation of state of the universe cannot be determined uniquely but depends on one free parameter.
Abstract: Even if the luminosity distance as a function of redshift is obtained accurately using, for example, Type Ia supernovae, the equation of state of the Universe cannot be determined uniquely but depends on one free parameter $\Omega_{k0} ={k}/(a_0^2H_0^2)$, where $a_0$ and $H_0$ are the present scale factor and the Hubble parameter, respectively. This degeneracy might be resolved if, for example, the time variations of the redshift of quasars are measured as proposed recently by Loeb. Therefore the equation of state of the Universe (or the metric of the universe) might be determined without any theoretical assumption on the matter content of the Universe in future.
116 citations
TL;DR: The quasi-flatness problem was introduced in this article, where theories incorporating time-varying coupling constants could drive the universe to a late-time near-flat attractor.
111 citations
TL;DR: In this article, an independent constraint on the lower bound to the mass density was derived based on deviations of galaxy velocities from a smooth universal expansion, and together with a nearly flat universe in which the contributions from mass density and the cosmological constant are comparable.
Abstract: Recent observations1,2 of high-redshift supernovae seem to suggest that the global geometry of the Universe may be affected by a ‘cosmological constant’, which acts to accelerate the expansion rate with time. But these data by themselves still permit an open universe of low mass density and no cosmological constant. Here we derive an independent constraint on the lower bound to the mass density, based on deviations of galaxy velocities from a smooth universal expansion3,4,5,6,7. This constraint rules out a low-density open universe with a vanishing cosmological constant, and together the two favour a nearly flat universe in which the contributions from mass density and the cosmological constant are comparable. This type of universe, however, seems to require a degree of fine tuning of the initial conditions that is in apparent conflict with ‘common wisdom’.
TL;DR: In this article, the authors show that an almost isotropic cosmic microwave background (CMB) temperature does not imply that the universe is close to a Friedmann-Lemaitre universe.
Abstract: In this Letter we will show that, contrary to what is widely believed, an almost isotropic cosmic microwave background (CMB) temperature does not imply that the universe is "close to a Friedmann-Lemaitre universe." There are two important manifestations of anisotropy in the geometry of the universe: (1) the anisotropy in the overall expansion, and (2) the intrinsic anisotropy of the gravitational field, described by the Weyl curvature tensor; the former usually receives more attention than the latter in the astrophysical literature. Here we consider a class of spatially homogeneous models for which the anisotropy of the CMB temperature is within the current observational limits but whose Weyl curvature is not negligible, i.e., these models are not close to isotropy even though the CMB temperature is almost isotropic.
TL;DR: A different standard Big Bang model, which includes cold dark matter with a cosmological constant, provides a consistent and absolutely time-calibrated evolutionary sequence for the universe.
Abstract: The age of the universe in the Big Bang model can be calculated from three parameters: Hubble's constant, h; the mass density of the universe, Omegam; and the cosmological constant, OmegaLambda. Recent observations of the cosmic microwave background and six other cosmological measurements reduce the uncertainty in these three parameters, yielding an age for the universe of 13.4 +/- 1.6 billion years, which is a billion years younger than other recent age estimates. A different standard Big Bang model, which includes cold dark matter with a cosmological constant, provides a consistent and absolutely time-calibrated evolutionary sequence for the universe.
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TL;DR: The cosmological constant may be non-zero as mentioned in this paper, which forces us to re-evaluate standard notions about the connection between geometry and the fate of our universe, and it is shown that there is no set of cosmology observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the universe will be.
Abstract: The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.
TL;DR: In this paper, the full linear causal Israel-Stewart-Hiscock theory of bulk viscous processes in relativistic cosmological fluids is reformulated as an effective phenomenological theory for describing particle production processes in the early universe.
Abstract: The full linear causal Israel–Stewart–Hiscock theory of bulk viscous processes in relativistic cosmological fluids is reformulated as an effective phenomenological theory for describing particle production processes in the early universe. Explicit expressions for the particle balance law and particle production rates are obtained that relate the particle creation rate to the bulk viscous (creation) pressure. The general formalism is applied to the case of a full causal cosmological fluid with bulk viscosity coecient proportional to the Hubble function. In this case the general solution of the gravitational field equations can be expressed in an exact parametric form. For an appropriate choice of the physical parameters, the dynamics of the universe can be modelled as starting from a vacuum quasi-Minkowskian geometry, followed by an inflationary period but ending in a non-inflationary phase. The influence of the matter creation processes on the evolution of the universe and the behaviour of the energy density, temperature and entropy are investigated.
TL;DR: In this article, a simple model of the hydrogen atom in a universe without spatial curvature is presented, which admits solutions corresponding to an atom whose radius remains strictly constant during the expansion.
Abstract: I take a simple model of the hydrogen atom in a universe without spatial curvature. The Maxwell equations are formulated on the background cosmic spacetime. For a class of cosmic metrics, which includes the de Sitter universe, these equations admit solutions corresponding to an atom whose radius remains strictly constant during the expansion. In the Einstein-de Sitter universe approximate calculations show that the atom expands, but at a rate which is negligible compared with the general cosmic expansion.
TL;DR: In this article, the evolution of initial metric perturbations is computed using the first 749 eigenmodes of the fundamental cell in the framework of linear perturbation theory using a mixture of radiation and matter.
Abstract: The fluctuations of the cosmic microwave background (CMB) are investigated for a small, open universe, i.e., one that is periodically composed of a small fundamental cell. The evolution of initial metric perturbations is computed using the first 749 eigenmodes of the fundamental cell in the framework of linear perturbation theory using a mixture of radiation and matter. The fluctuations of the CMB are investigated for various density parameters Ω0, taking into account the full Sachs-Wolfe effect. The corresponding angular power spectrum, Cl, is compared with recent experiments.
TL;DR: In this article, a Lagrangian formulation of a toy universe model is given, where the space dimension is not constant, but varies with the expansion of the universe, and the field equations are derived and discussed.
Abstract: Assuming the space dimension is not constant, but varies with the expansion of the universe, a Lagrangian formulation of a toy universe model is given. After a critical review of previous works, the field equations are derived and discussed. It is shown that this generalization of the FRW cosmology is not unique. There is a free parameter in the theory, C, with which we can fix the dimension of space say at the Planck time. Different possibilities for this dimension are discussed. The standard FRW model corresponds to the limiting case C → +∞. Depending on the free parameter of the theory, C, the expansion of the model can behave differently to the standard cosmological models with constant dimension. This is explicitly studied in the framework of quantum cosmology. The Wheeler–De Witt equation is written down. It turns out that in our model universe, the potential of the Wheeler–DeWitt equation has different characteristics relative to the potential of the de Sitter minisuperspace. Using the appropriate boundary conditions and the semiclassical approximation, we calculate the wave function of our model universe. In the limit of C → +∞, corresponding to the case of constant space dimension, our wave function has not a unique behavior. It can either leads to the Hartle–Hawking wave function or to a modified Linde wave function, or to a more general one, but not to that of Vilenkin. We also calculate the probability density in our model universe. It is always more than the probability density of the de Sitter minisuperspace in 3–space as suggested by Vilenkin, Linde, and others. In the limit of constant space dimension, the probability density of our model universe approaches to Vilenkin and Linde probability density being exp(−2|SE|), where SE is the Euclidean action. Our model universe indicates therefore that the Vilenkin wave function is not stable with respect to the variation of space dimension.
TL;DR: Gravitational lenses, besides being interesting in their own right, have been demonstrated to be suitable as "gravitational standard rulers" for the measurement of the rate of expansion of the Universe (Ho), as well as to constrain the values of the cosmological parameters such as Omegao and Lambdao that control the evolution of the volume of the universe with cosmic time.
Abstract: Gravitational lenses, besides being interesting in their own right, have been demonstrated to be suitable as “gravitational standard rulers” for the measurement of the rate of expansion of the Universe (Ho), as well as to constrain the values of the cosmological parameters such as Ωo and Λo that control the evolution of the volume of the Universe with cosmic time.
Posted Content•
TL;DR: In this article, a physically viable big bang is generated without invoking either large ne-tunings or a long period of post-big bang inflation, using a superstring-motivated principle of ''Asymptotic Past Triviality''.
Abstract: Classical and quantum gravitational instabilities, can, respectively, inflate and warm up a primordial Universe satisfying a superstring-motivated principle of \Asymptotic Past Triviality". A physically viable big bang is thus generated without invoking either large ne-tunings or a long period of post-big bang inflation. Properties of the pre-bangian Universe can be probed through its observable relics, which include: i) a (possibly observable) stochastic gravitationalwave background; ii) a (possible) new mechanism for seeding the galactic magnetic elds; iii) a (possible) new source of large-scale structure and CMB anisotropy.
TL;DR: The scale expanding cosmological theory as discussed by the authors assumes that the relationship between space and time could remain constant during the cosmology expansion and all cosmologically locations in time and space could be equivalent, if the metrics of both space and space expand.
Abstract: The Big Bang model assumes that the Universe expands by continuously changing the relationship between the metrics of space and time. However, the relationship between space and time could remain constant during the cosmological expansion and all cosmological locations in time and space could be equivalent, if the metrics of both space and time expand. The Scale Expanding Cosmos theory accurately models the universe we observe and offers simple and direct explanations for several cosmological enigmas.
15 Jul 1999
TL;DR: In this paper, the authors present results from two research groups that are in excellent agreement with high statistical confidence that the universe is currently accelerating (q 0 0.0 0.1 ).
Abstract: Measurements of type Ia supernova apparent brightnesses over a range of distances allows a measurement of changes in the universe’s expansion rate. This measurement yields information about the mass density and vacuum energy density (“cosmological constant”) of the universe. We present results from two research groups that are in excellent agreement. Both groups’ results indicated with high statistical confidence that the Universe is currently accelerating (q0 0.
Book•
01 Jan 1999TL;DR: Black holes More to light than meets the eye! Invisible stars Beyond the horizon A hole that can never be filled Spinning black holes Falling into a black hole To see a hole Not so black after all White holes Time Times are Changing What is time? Who invented time? The first moment Does time flow? Something called entropy Arrows of time Stephen Hawking gets it wrong A possible solution Einstein's Time What is so special about special relativity? The two faces of light Thought experiments and brain-teasers Slowing down time Shrinking distances Light-the world speed record When time runs
Abstract: SPACE The 4th Dimension To do with shapes What is space? 2Dworld and 2D'ers Curved space Is there really a 4th dimension? Matters of Some Gravity Apples and moons Einstein's gravity Free fall Rubber space Twinkle, twinkle Cooking the elements Champagne supernova in the sky The Universe The night sky How big is the Universe? The expanding Universe Hubble, bubble ... Space is stretching Did the Big Bang really happen? The edge of space A closed universe An open universe What shape is the Universe then? Invisible matter 1998: a big year in cosmology Is the Universe infinite? Why is it dark at night? Before the Big Bang? Summary Black Holes More to light than meets the eye! Invisible stars Beyond the horizon A hole that can never be filled Spinning black holes Falling into a black hole To see a black hole Not so black after all White holes TIME Times Are Changing What is time? Who invented time? The first moment Does time flow? Something called entropy Arrows of time Stephen Hawking gets it wrong A possible solution Einstein's Time What is so special about special relativity? The two faces of light Thought experiments and brain-teasers Slowing down time Shrinking distances Light-the world speed record When time runs backwards Little green men Fast-forward to the future Spacetime-the future is out there Gravitational times Time Travel Paradoxes The Terminator paradox Trying to save the dinosaurs Mona Lisa's sister No way out? Parallel universes Where are all the time travelers? TIME MACHINES Wormholes A bridge to another world Alice through the looking glass When science fact met science fiction Wormholes-keeping the star gate open Visiting a parallel universe How to Build a Time Machine Time loops The Tipler time machine Cosmic string time machines A recipe for a wormhole time machine Insurmountable problems? What Do We Know? The mother of all theories The end of theoretical physics What might new experiments tell us? Astronomy versus astrology The fascination of science Suggestions for Further Reading Index
Posted Content•
TL;DR: The existence of a positive and possibly varying Lambda-term opens a much wider field of possibilities for the future of our universe than it was usually thought before Definite predictions may be made for finite (though very large) intervals of time only in other branches of science as mentioned in this paper.
Abstract: The existence of a positive and possibly varying Lambda-term opens a much wider field of possibilities for the future of our Universe than it was usually thought before Definite predictions may be made for finite (though very large) intervals of time only, as well as in other branches of science In particular, our Universe will continue to expand as far as the Lambda-term remains positive and does not decay to other forms of matter, even if the Universe is closed Two new effects due to the presence of a constant Lambda-term are discussed: reversal of a sign of the redshift change with time for sufficiently close objects and inaccessibility of sufficiently distant objects in the Universe for us A number of more distant and speculative possibilities for the future evolution of the Universe is listed including hitting a space-time singularity during an expansion phase Finally, in fantastically remote future, a part of our Universe surrounding us can become supercurved and superdense due to various quantum-gravitational effects This returns us to the past, to the origin of our Universe from a superdense state about 14 Gy ago According to the inflationary scenario, this state was almost maximally symmetric (de Sitter-like) Though this scenario seems to be sufficient for the explanation of observable properties of the present Universe, and its predictions have been confirmed by observations, the question of the origin of the initial de Sitter (inflationary) state itself remains open A number of conjectures regarding the very origin of our Universe, ranging from "creation from nothing" to "creation from anything", are discussed
TL;DR: A quantum mechanical model for an (N + 1)-dimensional universe arising from a quantumfluctuation is outlined in this article, where it is assumed that gravity and the strong-electroweak (SEW) force had equal strengths in the initial state.
Abstract: A quantum mechanical model for an (N +1)-dimensional universe arising from a quantumfluctuation is outlined (3 + 1) dimensions are aclosed, infinitely expanding universe, and the remainingN - 3 dimensions are compact The (3 + 1) noncompact dimensionsare modeled by quantizing a canonical Hamiltoniandescription of a homogeneous isotropic universe It isassumed that gravity and the strong-electroweak (SEW) force had equal strengths in the initial stateInflation occurred when the compact (N - 3)-dimensionalspace collapsed after a quantum transition from theinitial state of the universe during its evolution to the present state where gravity is muchweaker than the SEW force The model suggests theuniverse has no singularities and the large size of ourpresent universe is determined by the relative strength of gravity and the SEW force today A smallcosmological constant, resulting from the zero-pointenergy of the scalar field corresponding to the compactdimensions, makes the model universe expandforever
TL;DR: In this article, the authors investigated higher dimensional cosmological models in the semiclassical approximation with Hartle-Hawking Boundary conditions, assuming a gravitational action which is described by the scalar curvature with a cosmology constant.
Abstract: We investigate higher dimensional cosmological models in the semiclassical approximation with Hartle-Hawking Boundary conditions, assuming a gravitational action which is described by the scalar curvature with a cosmological constant. In the framework the probability for quantum creation of an inflationary universe with a pair of black holes in a multidimensional universe is evaluated. The probability for creation of a universe with a spatial section with $S^{1}XS^{D -2}$ topology is then compared with that of a higher dimensional de Sitter universe with $S^{D -1}$ spatial topology. It is found that a higher dimensional universe with a product space with primordial black holes pair is less probable to nucleate when the extra dimensions scale factors do not vary in an inflating universe.
Posted Content•
TL;DR: In this article, it is shown how the quark picture emerges at the Compton wavelength and the Big Bang scenario at the Planck length, and a theoretical justification for the peculiar characteristics of the quarks namely their fractional charge, handedness and confinement, as also the order of magnitude of their masses, all of which were hitherto ad hoc features.
Abstract: We throw further light on a recently discussed Kerr-Newman type formulation of Fermions and the related cosmological scheme which predicted an ever expanding universe, as indeed has subsequently been confirmed In the spirit of the correspondence principle, it is shown how the quark picture emerges at the Compton wavelength and the Big Bang scenario at the Planck length At the same time we obtain a theoretical justification for the peculiar characteristics of the quarks namely their fractional charge, handedness and confinement, as also the order of magnitude of their masses, all of which were hitherto adhoc features
TL;DR: The big bang model of the universe makes a number of profound and testable predictions as mentioned in this paper, and these predictions are testable in a uniform and uniform way in the real world.
Abstract: The big bang model of the universe makes a number of profound and testable predictions. In a uniform…
TL;DR: In this article, the authors discuss different approaches to the cosmological constant issue including the possibility that Λ could be generated by vacuum polarization in a static universe, and the inflationary scenario therefore, could give rise to a universe that is both flat and Λ-dominated, in agreement with observations.
Abstract: The close relationship between the cosmological constant and the vacuum has been emphasized in the past by Zeldovich amongst others. We briefly discuss different approaches to the cosmological constant issue including the possibility that Λ could be generated by vacuum polarization in a static universe. Fresh possibilities occur in an expanding universe. An inflationary universe generically leads to particle creation from the vacuum, the nature and extent of particle production depending upon the mass of the field and its coupling to gravity. For ultra-light, non-minimally coupled scalar fields, particle production can be large and the resulting vacuum energy–momentum tensor will have the form of an effective cosmological constant. The inflationary scenario therefore, could give rise to a universe that is both flat andΛ-dominated, in agreement with observations.