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We examine a class of braneworld models in which the expanding universe encounters a "quiescent" future singularity. At a quiescent singularity, the energy density and pressure of the cosmic fluid as well as the Hubble parameter remain finite while all derivatives of the Hubble parameter diverge (i.e., ${\dot H}$, ${\ddot H}$, etc. $\to \infty$). Since the Kretschmann invariant diverges ($R_{iklm}R^{iklm} \to \infty$) at the singularity, one expects quantum effects to play an important role as the quiescent singularity is approached. We explore the effects of vacuum polarization due to massless conformally coupled fields near the singularity and show that these can either cause the universe to recollapse or, else, lead to a softer singularity at which $H$, ${\dot H}$, and ${\ddot H}$ remain finite while ${\dddot H}$ and higher derivatives of the Hubble parameter diverge. An important aspect of the quiescent singularity is that it is encountered in regions of low density, which has obvious implications for a universe consisting of a cosmic web of high and low density regions -- superclusters and voids. In addition to vacuum polarization, the effects of quantum particle production of non-conformal fields are also likely to be important. A preliminary examination shows that intense particle production can lead to an accelerating universe whose Hubble parameter shows oscillations about a constant value., Comment: 19 pages, 3 figures, text slightly improved and references added. Accepted for publication in Classical and Quantum Gravity

How can a universe coming from a point-like big bang event have infinite spatial extension? It is shown that the relativity of simultaneity is essential in answering this question. Space is finite as defined by the simultaneity of one observer, but it may be infinite as defined by the simultaneity of all the clocks participating in the Hubble flow.

We consider the inverse mean curvature flow in Robertson-Walker spacetimes that satisfy the Einstein equations and have a big crunch singularity and prove that under natural conditions the rescaled inverse mean curvature flow provides a smooth transition from big crunch to big bang. We also construct an example showing that in general the transition flow is only of class $C^3$.

In order to study if the bulk viscosity may induce a big rip singularity on the flat FRW cosmologies, we investigate dissipative processes in the universe within the framework of the standard Eckart theory of relativistic irreversible thermodynamics, and in the full causal Israel–Stewart–Hiscock theory. We have found cosmological solutions which exhibit, under certain constraints, a big rip singularity. We show that the negative pressure generated by the bulk viscosity cannot avoid that the dark energy of the universe to be phantom energy.

The physical process leading to the acceleration of the expansion of the universe is unknown. It may involve new high energy physics or extensions to gravitation. Calling this generically dark energy, we examine the consistencies and relations between these two approaches, showing that an effective equation of state function w(z) is broadly useful in describing the properties of the dark energy. A variety of cosmological observations can provide important information on the dynamics of dark energy and the future looks bright for constraining dark energy, though both the measurements and the interpretation will be challenging. We also discuss a more direct relation between the spacetime geometry and acceleration, via ``geometric dark energy'' from the Ricci scalar, and superacceleration or phantom energy where the fate of the universe may be more gentle than the Big Rip., invited overview at Dark Matter/Dark Energy 2004; 6 pages

It is shown how Einstein's equation can account for the evolution of the universe without an initial singularity and can explain the inflation epoch as a momentum dominated era in which energy from matter and radiation drove extremely accelerated expansion of space. It is shown how an object with momentum loses energy to the expanding universe and how this energy can contribute to accelerated spatial expansion more effectively than vacuum energy, because virtual particles, the source of vacuum energy, can have negative energy, which can cancel any positive energy from the vacuum. Radiation and matter with momentum have positive but decreasing energy in the expanding universe, and the energy lost by them can contribute to accelerated spatial expansion between galactic clusters, making dark energy a classical effect that can be explained by general relativity without quantum mechanics, and, as (13) and (15) show, without an initial singularity or a big bang. This role of momentum, which was overlooked in the Standard Cosmological Model, is the basis of a simpler model which agrees with what is correct in the old model and corrects what is wrong with it.

The purpose of the present paper is to assume that the expanding spacetime of our cosmos was created by the big bang. It then follows that there exists a finite instantaneous radial extent dRU to spacetime as observed from anywhere in spacetime by comoving observers. The consequences for gravity are explored by first considering the scalar field of a central mass that defines the dynamic properties of a circular orbit for each radius R ≤ dRU under the postulate of weak equivalence. These properties include an orbital velocity and an escape velocity. For a central mass of galactic proportion, the escape velocity becomes large even at cosmological distances. By considering the dynamics of a smaller mass occupying the last orbit, we find that the established laws of physics lead to different rotation curves than they do when applied to the solar system. Since galactic rotation curves reveal the existence of dark matter, this is anticipated to have some consequences for our understanding of dark matter.

We discuss the present status of the big bang nucleosynthesis and its consistency with the recent observation of the cosmic microwave background radiation. It is found that there exists some discrepancy and the possible solutions to solve the discrepancy by non-standard scenarios such as varying fine structure constant and existence of large neutrino chemical potentials are presented.

Recent astronomical observations suggest that the bulk of energy in the Universe is repulsive and appears like a dark component with negative pressure ($\omega \equiv p_x/\rho_x < 0$). In this work we investigate thermodynamic and statistical properties of such a component. It is found that its energy and temperature grow during the evolution of the Universe since work is done on the system. Under the hypothesis of a null chemical potential, the case of phantom energy ($\omega < -1$) seems to be physically meaningless because its entropy is negative. It is also proved that the wavelengths of the $\omega$-quanta decrease in an expanding Universe. This unexpected behavior explains how their energy may be continuously stored in the course of expansion. The spectrum and the associated Wien-type law favors a fermionic nature with $\omega$ naturally restricted to the interval $-1 \leqslant \omega < -1/2$. Our analysis also implies that the ultimate fate of the Universe may be considerably modified. If a dark energy dominated Universe expands forever, it will become increasingly hot., Comment: 5 pages, 2 figures, to appear in Physics Letters B

The gravitational field of matter and that of antimatter could differ. This might be one signature of quantum gravity. We show that primordial Big Bang Nucleosynthesis restricts such a possibility., 11 pages, 3 figures. Reference added

In this paper we analyze the cosmological dynamics of phantom field in a variety of potentials unbounded from above. We demonstrate that the nature of future evolution generically depends upon the steepness of the phantom potential and discuss the fate of Universe accordingly., Comment: RevTeX4, 5 pages and 3 eps figures; references updated

The article focuses on whether the big bang was really the beginning of time. After string theory made its comeback as a theory of gravity in the 1980s, it was applied to black holes and cosmology. Conditions near the zero time of the big bang were so extreme that no one yet knows how to solve the equations. Nevertheless, string theorists have hazarded guesses about the pre-bang universe. Two popular models are floating around. The first, known as the pre-big bang scenario combines T-duality with the better-known symmetry of time reversal, whereby the equations of physics work equally well when applied backward and forward in time. The other leading model for the universe before the bang is the ekpyrotic ("conflagration") scenario. The pre-big bang and ekpyrotic scenarios share some common features. Both begin with a large, cold, nearly empty universe, and both share the problem of making the transition between the pre- and the post-bang phase. Mathematically, the main difference between the scenarios is the behavior of the dilaton field. Like the details of the inflationary phase, those of a possible pre-bangian epoch could have observable consequences, especially for the small variations observed in the cosmic microwave background temperature. Analysis of the microwave background is not the only way to verify these theories. The pre-big bang scenario should also produce a random background of gravitational waves in a range of frequencies that, though irrelevant for the microwave background, should be detectable by future gravitational-wave observatories. Moreover, because the pre-big bang and ekpyrotic scenarios involve changes in the dilaton field, which is coupled to the electromagnetic field, they would both lead to large-scale magnetic field fluctuations. Vestiges of these fluctuations might show up in galactic and intergalactic magnetic fields.

We construct exact, entropy satisfying shock wave solutions of the Einstein equations for a perfect fluid which extend the Oppeheimer-Snyder (OS) model to the case of non-zero pressure, {\it inside the Black Hole}. These solutions put forth a new Cosmological Model in which the expanding Friedmann-Robertson-Walker (FRW) universe emerges from the Big Bang with a shock wave at the leading edge of the expansion, analogous to a classical shock wave explosion. This explosion is large enough to account for the enormous scale on which the galaxies and the background radiation appear uniform. In these models, the shock wave must lie beyond one Hubble length from the FRW center, this threshhold being the boundary across which the bounded mass lies inside its own Schwarzshild radius, $2M/r>1,$ and thus the shock wave solution evolves inside a Black Hole. The entropy condition, which breaks the time symmetry, implies that the shock wave must weaken until it eventually settles down to a zero pressure OS interface, bounding a {\em finite} total mass, that emerges from the White Hole event horizon of an ambient Schwarzschild spacetime. However, unlike shock matching outside a Black Hole, the equation of state $p=\frac{c^2}{3}\rho,$ the equation of state at the earliest stage of Big Bang physics, is {\em distinguished} at the instant of the Big Bang--for this equation of state alone, the shock wave emerges from the Big Bang at a finite nonzero speed, the speed of light, decelerating to a subluminous wave from that time onward. These shock wave solutions indicate a new cosmological model in which the Big Bang arises from a localized explosion occurring inside the Black Hole of an asymptotically flat Schwarzschild spacetime.

How did the Universe begin? Does time have a beginning and an end? Does space have edges? Einstein's theory of relativity replied to these ancient questions with three startling predictions: that the Universe is expanding from a Big Bang; that black holes so distort space and time that time stops at their edges; and that a dark energy could be pulling space apart, sending galaxies forever beyond the edge of the visible Universe. Observations confirm these remarkable predictions, the last finding only four years ago. Yet Einstein's legacy is incomplete. His theory raises – but cannot answer – three profound questions: What powered the Big Bang? What happens to space, time and matter at the edge of a black hole? and, What is the mysterious dark energy pulling the Universe apart? The Beyond Einstein program within NASA's office of space science aims to answer these questions, employing a series of missions linked by powerful new technologies and complementary approaches to shared science goals. The program also serves as a potent force with which to enhance science education and science literacy.

Despite its great popularity, the Big Bang framework for cosmology faces growing contradictions with observation. The Big Bang theory requires three hypothetical entities-the inflation field, nonbaryonic (dark) matter, and the dark energy field-to overcome gross contradictions of theory and observation. Yet, no evidence has ever confirmed the existence of any of these three hypothetical entities. The predictions of the theory for the abundance of /sup 4/He, /sup 7/Li, and D are more than 7/spl sigma/ from the data for any assumed density of baryons and the probability of the theory fitting the data is less than 10/sup -14/. Observations of voids in the distribution of galaxies that are in excess of 100 Mpc in diameter, combined with observed low streaming velocities of galaxies, imply an age for these structure that is at least triple and more likely six times the hypothesized time since the Big Bang. Big Bang predictions for the anisotropy of the microwave background, which now involve seven or more free parameters, still are excluded by the data at the 2/spl sigma/ level. The observed preferred direction in the background anisotropy completely contradicts Big Bang assumptions. In contrast, the predictions of plasma cosmology have been strengthened by new observations, including evidence for the stellar origin of the light elements, the plasma origin of large-scale structures, and the origin of the cosmic microwave background in a "radio fog" of dense plasma filaments. This review of the evidence shows that the time has come, and indeed has long since come, to abandon the Big Bang as the primary model of cosmology.

or millennia, cosmology has been a theorist’s domain, where elegant theory was only occasionally endangered by inconvenient facts. Early in the 20th century, Albert Einstein gave us new conceptual tools to rigorously address the questions of the origins, evolution, and fate of the universe. In recent years, technology has developed to the point where these concepts from general relativity can be substantiated and elaborated by measurements. For example, measurement of the remnant glow from the hot, dense beginnings of the expanding universe—the cosmic microwave background—is yielding increasingly detailed data about the first half-million years and the overall geometry of the cosmos (see the news story on page 21 of this issue). The standard model of particle physics has also begun to play a prominent role in cosmology. The widely accepted idea of exponential inflation in the immediate aftermath of the Big Bang was built on the predicted effect of certain putative particle fields and potentials on the cosmic expansion. Measuring the history of cosmic expansion is no easy task, but in recent years, a specific variety of supernovae, type Ia, has given us a first glimpse at that history—and surprised us with an unexpected plot twist.

By studying the present cosmological data, particularly on CMB, SNeIA and LSS, we find that the future fate of the universe, for simple linear models of the dark energy equation-of-state, can vary between the extremes of (I) a divergence of the scale factor in as little as 7 Gyr; (II) an infinite lifetime of the universe with dark energy dominant for all future time; (III) a disappearing dark energy where the universe asymptotes as $t \to \infty$ to $a(t) \sim t^{2/3}$ {\it i.e.} matter domination. Our dreadful conclusion is that no amount of data from our past light-cone can select between these future scenarios., Comment: 10 pages LaTeX including 4 eps figures. Minor corrections in text

Cosmology, the field that focuses on the origin and evolution of the universe on its largest scales, is undergoing what many have called a “golden era.” New observations, on the ground, in the air, and in space, combined with exciting new theoretical insights, have, over the past decade or two, literally revolutionized our picture of the universe in which we live. Ideas that were essentially pure speculation 20 years ago now rest firmly on the bedrock of experiment. At the same time, many new questions have arisen, and some once firmly held notions about the future of the universe have been displaced. In this article I present a guide to our current understanding of the history and fate of the universe to parallel and supplement the overview presented in the Contemporary Physics Education Project Cosmology Chart.

This Resource Letter treats the nascent discipline of physical eschatology, which deals with the future evolution of astrophysical objects, including the universe itself, and is thus both a counterpart and a complement to conventional cosmology. While sporadic interest in these topics has flared up from time to time during the entire history of humanity, a truly physical treatment of these issues has only become possible during the last quarter century. This Resource Letter deals with these recent developments. It offers a starting point for understanding what the physical sciences might say about the future of our universe and its constituents. Journal articles, books, and web sites are provided for the following topics: history and epistemology of physical eschatology, the future of the Solar system, the future of stars and stellar systems, the global future of the universe, information processing and intelligent communities, as well as some side issues, like the possible vacuum phase transition and the so-called Doomsday Argument.

We model the standard [Formula: see text]CDM model of the universe by the spatially flat FLRW line element [Formula: see text] which we extend for all time [Formula: see text]. Although there is a cosmological singularity at the big bang [Formula: see text], since the spatial part of the metric collapses to zero, nevertheless, this line element is defined for all time [Formula: see text], is [Formula: see text] for all [Formula: see text], is [Formula: see text] differentiable at [Formula: see text], and is non-degenerate and solves Friedmann’s equation for all [Formula: see text]. Thus, we can use this extended line element to model the universe from its past-asymptotic initial state [Formula: see text] at [Formula: see text], through the big bang at [Formula: see text], and onward to its future-asymptotic final state [Formula: see text] at [Formula: see text]. Since in this model the universe existed before the big bang, we conclude that (1) the universe was not created de novo at the big bang and (2) cosmological singularities such as black holes or the big bang itself need not be an end to spacetime. Our model shows that the universe was asymptotically created de novo out of nothing at [Formula: see text] from an unstable vacuum negative half de Sitter [Formula: see text] initial state and then dies asymptotically at [Formula: see text] as the stable positive half de Sitter [Formula: see text] final state. Since the de Sitter states are vacuum matter states, our model shows that the universe was created from nothing at [Formula: see text] and dies at [Formula: see text] to nothing.

In his ambitious book Life Through Time and Space , Wallace Arthur tack­les an extraordinarily difficult set of topics. What is the origin and fate of the universe? How did life, and eventually intelligent life, come into existence on Earth? How does a fertilized human egg trans­form into a complex person with only DNA to guide development?

Inflation leads to omega=1 for the big bang universe, and which is indeed observed. However, two mysterious constituents – dark energy and dark matter – have to be present in the big bang universe for omega = 1. This paper utilizes propositions about the nature of dark energy and dark matter to trace their origins to the contents of the inflationary universe.

The main pillar of the Big Bang paradigm is the expansion of the Universe predicted by the cosmological redshift. Singularity is inevitable in the Big Bang model. The Universe is hyperbolic as we did prove mathematically; where the cosmological redshift is no longer a distance indicator. After all, in the hyperbolic spacetime a group of objects would grow apart even when not moving as their worldlines would be divergent. We show the manifold of the hyperbolic Universe is complete with no singular points. While the distance horizon in the Big Bang flat spacetime is finite, the distance horizon is infinite in the hyperbolic universe. The pillars of the big Bang and its consequences had been refuted and disproved or reinterpreted.

The present accelerated expansion of the universe has enriched the list of possible scenarios for its fate, singular or not. In this paper a unifying framework for analyzing such behaviors is proposed, based on generalized power and asymptotic expansions of the barotropic index $w$, or equivalently of the deceleration parameter $q$, in terms of the time coordinate. Besides well known singular and non-singular future behaviors, other types of strong singularities appear around the phantom divide in flat models, with features similar to those of big rip or big bang/crunch, which we have dubbed grand rip and grand bang/crunch respectively, since energy density and pressure diverge faster than $t^{-2}$ in coordinate time. In addition to this, the scale factor does not admit convergent generalized power series around these singularities with a finite number of terms with negative powers., 19 pages, 2 figures. Typos amended

Cosmology is the study of the origin and fate of the universe. We address the current model of the origin of the universe focusing on the Big Bang theory and evidence in support of the model. The scenario of the ultimate fate of the universe based on its total mass estimate with the involvement of dark matter and dark energy is also discussed. Finally, modern physical theories including the standard model with the basics of elementary particle physics and symmetry principles (and their violation), superstring (M) theory, the multiverse, and wormholes are addressed.

We confront the big bang for the beginning of the universe with an equivalent picture of a slow freeze - a very cold and slowly evolving universe. In the freeze picture the masses of elementary particles increase and the gravitational constant decreases with cosmic time, while the Newtonian attraction remains unchanged. The freeze and big bang pictures both describe the same observations or physical reality. We present a simple "crossover model" without a big bang singularity. In the infinite past space-time is flat. Our model is compatible with present observations, describing the generation of primordial density fluctuations during inflation as well as the present transition to a dark energy dominated universe., Comment: new material on absence of singularity, 9 pages, 1 figure

We explore the cosmological consequences of kinetically mixed dark photons with a mass between 1 MeV and 10 GeV, and an effective electromagnetic fine structure constant as small as $10^{-38}$. We calculate the freeze-in abundance of these dark photons in the early Universe and explore the impact of late decays on BBN and the CMB. This leads to new constraints on the parameter space of mass $m_V$ vs kinetic mixing parameter $\kappa$., Comment: 14 pages, 11 figures, references added

The Born-Infeld determinantal gravity has been recently proposed as a way to smooth the Big Bang singularity. This theory is formulated on the Weitzenbock space-time and the teleparallel representation is used instead of the standard Riemannian representation. We find that although this theory is shown to be singularity-free for certain region of the parameter space in which the divergence of the Hubble rate at the high energy regime is substituted by a de-Sitter stage or a bounce in a Friedmann-Lemaitre-Robertson-Walker universe, cosmological singularities such as Big Rip, Big Bang, Big Freeze, and Sudden singularities can emerge in other regions of the configuration space of the theory. We also show that all these singular events exist even though the Universe is filled with a perfect fluid with a constant equation of state., 6 pages, 2 figures, RevTex4-1. A minor change. Version accepted in PRD

We exploit the complementarity among supersymmetry, inflation, axions, Big Bang Nucleosynthesis (BBN) and Cosmic Microwave Background Radiation (CMB) to constrain supersymmetric axion models in the light of the recent Planck and BICEP results. In particular, we derive BBN bounds coming from altering the light element abundances by taking into account hadronic and electromagnetic energy injection, and CMB constraints from black-body spectrum distortion. Lastly, we outline the viable versus excluded region of these supersymetric models that might account for the mild dark radiation observed., 8 pages, 2 figures. To appear in Phys. Rev. D

In this paper we investigate the fate of the universe with an anisotropic background sourced by anisotropic matter. We see the behaviour of the Raychaudhuri Equation and investigate wheather a congrurence of time like geodesics focus to a point in a universe with Bianchi I background which is dictated by anisotropic sources like cosmic strings, domain walls, magnetic field and lorentz violating magnetic field each separately. Thus, Focussing theorem has been checked both for initially contracting and diverging universe with each of these anisotropic sources., 6 pages, 10 figures

Measurements of the Higgs boson and top quark masses indicate that the Standard Model Higgs potential becomes unstable around $\Lambda_I \sim 10^{11}$ GeV. This instability is cosmologically relevant since quantum fluctuations during inflation can easily destabilize the electroweak vacuum if the Hubble parameter during inflation is larger than $\Lambda_I$ (as preferred by the recent BICEP2 measurement). We perform a careful study of the evolution of the Higgs field during inflation, obtaining different results from those currently in the literature. We consider both tunneling via a Coleman-de Luccia or Hawking-Moss instanton, valid when the scale of inflation is below the instability scale, as well as a statistical treatment via the Fokker-Planck equation appropriate in the opposite regime. We show that a better understanding of the post-inflation evolution of the unstable AdS vacuum regions is crucial for determining the eventual fate of the universe. If these AdS regions devour all of space, a universe like ours is indeed extremely unlikely without new physics to stabilize the Higgs potential; however, if these regions crunch, our universe survives, but inflation must last a few e-folds longer to compensate for the lost AdS regions. Lastly, we examine the effects of generic Planck-suppressed corrections to the Higgs potential, which can be sufficient to stabilize the electroweak vacuum during inflation., Comment: 26 pages, 7 figures. Clarifications added. Matches published version in JHEP

Inspired by quantum gravity proposal, we construct a deformed phase space which supports the UV and IR cutoffs. We show that the Liouville theorem is satisfied in the deformed phase space which allows us to formulate the thermodynamics of the early Universe in the semiclassical regime. Applying the proposed method to the Snyder noncommutative space, we find a temperature dependent equation of state which opens a new window for natural realization of inflation as a phase transition from quantum gravity regime to the standard radiation dominated era. Also we obtain finite energy and entropy densities for the Universe, when at least the Weak Energy Condition is satisfied. We show that there is a minimum size for the Universe which is proportional to the Planck length and consequently the Big Bang singularity is removed., 11 pages, 4 figures, Revised for PRD, title changed

In a recent series of papers, we have shown that theories with scalar fields coupled to gravity (e.g., the standard model) can be lifted to a Weyl-invariant equivalent theory in which it is possible to unambiguously trace the classical cosmological evolution through the transition from big crunch to big bang. The key was identifying a sufficient number of finite, Weyl-invariant conserved quantities to uniquely match the fundamental cosmological degrees of freedom across the transition. In so doing we had to account for the well-known fact that many Weyl-invariant quantities diverge at the crunch and bang. Recently, some authors rediscovered a few of these divergences and concluded based on their existence alone that the theories cannot be geodesically complete. In this note, we show that this conclusion is invalid. Using conserved quantities we explicitly construct the complete set of geodesics and show that they pass continuously through the big crunch-big bang transition., Comment: 3 pages, 1 figure. In version v2 the last three paragraphs include a response to the Note added to Ref. 18

We introduce some algebraic geometric models in cosmology related to the ''boundaries'' of space-time: Big Bang, Mixmaster Universe, Penrose's crossovers between aeons. We suggest to model the kinematics of Big Bang using the algebraic geometric (or analytic) blow up of a point x. This creates a boundary which consists of the projective space of tangent directions to x and possibly of the light cone of x. We argue that time on the boundary undergoes the Wick rotation and becomes purely imaginary. The Mixmaster (Bianchi IX) model of the early history of the universe is neatly explained in this picture by postulating that the reverse Wick rotation follows a hyperbolic geodesic connecting imaginary time axis to the real one. Penrose's idea to see the Big Bang as a sign of crossover from ''the end of previous aeon'' of the expanding and cooling Universe to the ''beginning of the next aeon'' is interpreted as an identification of a natural boundary of Minkowski space at infinity with the Big Bang boundary.

Throughout this book I have tried to convey the incredible amount of knowledge that we have obtained about our universe and our physical world. The cumulative effort of scientists over several thousand years has led to this understanding. There is still a final chapter on this to come, but before contemplating the ultimate fate of the universe and of life itself, let us look from a more critical viewpoint at the knowledge that we have acquired and ask the question, What do we really know? I have made quite a big deal of the fact that, at this moment in our history, we have determined our place in space and time within our universe. And that is a truly incredible achievement from which I do not wish to distract in this chapter. But it is good to question things at an even deeper level and to reveal some of the basic things that we do not completely understand, which include space and time itself.

Primordial nucleosynthesis remains as one of the pillars of modern cosmology. It is the test-ing ground upon which all cosmological models must ultimately rest. It is our only probe of the universe during the first few minutes of cosmic expansion and in particular during the important radiation-dominated epoch. These lectures review the basic equations of space-time, cosmology, and big bang nucleosynthesis. We will then review the current state of observational constraints on primordial abundances along with the key nuclear reactions and their uncertainties. We summarize which nuclear measure-ments are most crucial during the big bang. We also review various cosmological models and their constraints. In particular, we summarize the constraints that big bang nucleosynthesis places upon the possible time variation of fundamental constants, along with constraints on the nature and origin of dark matter and dark energy, long-lived supersymmetric particles, gravity waves, and the primordial magnetic field.

Using a combination of algebraic and computer work, we embed the standard spatially flat four-dimensional cosmological models and inflationary models in a flat five-dimensional space and thereby obtain pictures of the big bang. Such embeddings have important implications for astrophysics, notably in regard to particle masses and background radiation. This approach can be extended to superstrings, supergravity, and membrane theory.

Every open FRW universe can be completely foliated by spacelike slices of finite volume, each intersecting every fundamental worldline. The volumes tend to zero in the past, suggesting a point-like big bang. Embedding diagrams confirm this. How finite slices can contain an infinite amount of matter is explained by time-reversed gravitational collapse.

The radiation temperature–redshift relation for Friedmann–Robertson–Walker geometries is rediscussed in connection with recent observational data based on the fine-structure splitting of atomic and singly ionized carbon lines in quasar absorption-line systems. Indirect measurement of T(z) is one of the most powerful cosmological tests available because it may exclude even the presence of a cosmological constant. Unlike recent claims, we argue that the temperature at high z may be smaller than the standard prediction, thereby opening a window to alternative (big bang) models. By including new ingredients like a phenomenological decaying vacuum energy density and gravitational ‘adiabatic’ photon creation as well as late inflationary models driven by a scalar field, a new temperature law is deduced and its predictions are compared with the standard result.

Cosmology, the study of the universe, has a past, which is reviewed here. The standard model—the Big Bang, or the hot, dense early universe that is still expanding—is based on observations that are basically consistent but which require additional input to improve the agreement. Out of the early universe came the galaxies and stars that shine today. The future of the universe depends on the density of matter: too much mass leads to the Big Crunch; too little leads to eternal expans ion and cooling. The dark-matter problem prevents us from knowing which will be the fate of the universe. Thelimits of what may be called “scientific” are addressed.

We describe some single-sided BPS domain wall configurations in M-theory. These are smooth non-singular resolutions of Calabi--Yau orbifolds obtained by identifying the two sides of the wall under reflection. They may thus be thought of as domain walls at the end of the universe. We also describe related domain wall type solutions with a negative cosmological constant., Comment: 38 pages, LaTeX

Superstring theory suggests a new cosmology whereby a long inflationary phase preceeded a non singular big bang-like event. After discussing how pre-big bang inflation naturally arises from an almost trivial initial state of the Universe, I will describe how present or near-future experiments can provide sensitive probes of how the Universe behaved in the pre-bang era.

This is a review of an alternative cosmology, recently proposed by Fred Hoyle, Geoffrey Burbidge and this author. It begins with a brief discussion of why one needs an alternative cosmology, when the standard hot big bang cosmology is claimed to be doing well. It is argued that the observational and theoretical constraints on the standard big bang cosmology, from various directions, leave a very narrow window, if any, in the parameter space of plausible models. There is thus a strong case for alternative cosmologies. The rest of the review concentrates on one alternative, the quasi steady state cosmology (QSSC) and summarises the recent work on this model. This includes, the theoretical formulation and simple exact solutions of the basic equations, their relationship to various observations, the stability of solutions and the toy model for understanding the growth of structures in the Universe.

Current observations of Type Ia supernovae provide evidence for cosmic acceleration out to a redshift of $z \lsim 1$, leading to the possibility that the universe is entering an inflationary epoch. However, inflation can take place only if vacuum-energy (or other sufficiently slowly redshifting source of energy density) dominates the energy density of a region of physical radius 1/H. We argue that for the best-fit values of $\Omega_\Lambda$ and $\Omega_m$ inferred from the supernovae data, one must confirm cosmic acceleration out to at least $z \simeq 1.8$ to infer that the universe is inflating., Comment: 4 pages;important changes in conclusion; published in Phys. Rev. Lett

This article takes a critical look at the Hot Big Bang Cosmology (HBBC). It shows that two of its strongest lines of evidence, viz the cosmic microwave background and the abundance of light nuclei are capable of being interpreted differently, and in a physically more realistic way the HBBC is shown to have shifted its ground frequently under observational constraints, changing its parameters like Ω0, Ωb, Ωλ and q0, reinterpreting inflation, bedging options on dark matter, etc. Many of its present deductions are seen to be based on untested physics and unobservable events of the very early Universe, while its beginning in a spacetime singularity indicates its incompleteness as a physical theory. The example of the quasi steady singularity indicates its incompleteness as a physical theory. The example of the quasi-steady state cosmology (QSSC) is given to demonstrate that an alternative cosmology relying more on the ongoing astrophysical properties of the Universe and directly observable events is possible. The case is therefore made that the HBBC does not hold the ‘monopoly’ to be THE model of the Universe.