DOCSLIB.ORG

Cosmic Inflation and the Arrow of Time1

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Cosmic Inflation and the Arrow of Time1 1 Cosmic Inflation and the Arrow of Time Andreas Albrecht, UC Davis Department of Physics, One Shields Avenue, Davis, CA 95616 Abstract Cosmic inflation claims to make the initial conditions of the standard big bang "generic". But Boltzmann taught us that the thermodynamic arrow of time arises from very non-generic ("low entropy") initial conditions. I discuss how to reconcile these perspectives. The resulting insights give an interesting way to understand inflation and also compare inflation with other ideas that claim to offer alternative theories of initial conditions. 1 Introduction................................................................................................................. 2 2 The everyday perspective on initial conditions .......................................................... 3 3 Arrow of Time Basics................................................................................................. 4 3.1 Overview............................................................................................................. 4 3.2 Without Gravity (ll J ) .................................................................................... 4 3.3 The key roles of the arrow of time...................................................................... 8 3.4 With Gravity (ll J ) ......................................................................................... 9 4 Cosmic Inflation: preliminaries ................................................................................ 11 4.1 The inflationary perspective on initial conditions ............................................ 11 4.2 Illustration 1: Big Bang Nucleosynthesis ......................................................... 12 4.3 Illustration 2: Gas in a block of ice................................................................... 13 4.4 Equilibrium and de Sitter space ........................................................................ 15 4.5 The potential dominated state ........................................................................... 16 5 Cosmic inflation........................................................................................................ 16 5.1 Basic inflation................................................................................................... 16 5.2 Inflation and the arrow of time ......................................................................... 17 6 Initial Conditions: The Big Picture........................................................................... 18 6.1 Data, theory, and the “A” word ........................................................................ 18 6.2 Using the arrow of time as an input.................................................................. 19 6.3 Predictions from cosmic inflation..................................................................... 20 6.4 Boltzmann’s “efficient fluctuation” Problem ................................................... 21 7 Comparing different theories of initial conditions.................................................... 22 1 To appear in “Science and Ultimate Reality: From Quantum to Cosmos”, honoring John Wheeler’s 90th birthday. J. D. Barrow, P.C.W. Davies, & C.L. Harper eds. Cambridge University Press (2003). 8 Further Discussion.................................................................................................... 28 8.1 Emergent Time and Quantum Gravity.............................................................. 28 8.2 Causal Patch Physics......................................................................................... 28 8.3 Measures and other issues................................................................................. 29 9 Some “Wheeler Class” questions.............................................................................. 29 9.1 The arrow of time, classicality and microscopic time ...................................... 29 9.2 The arrow of time in the approach to de Sitter space ....................................... 30 10 Conclusions........................................................................................................... 30 Acknowledgements........................................................................................................... 31 Bibliography ..................................................................................................................... 32 1 Introduction One of the most obvious and compelling aspects of the physical world is that it has an “arrow of time”. Certain processes (such as breaking a glass or burning fuel) appear all the time in our everyday experience, but the time reverse of these processes are never seen. In the modern understanding, special non-generic initial conditions of the universe are used to explain the time-directed nature of the dynamics we see around us. On the other hand, modern cosmologists believe it is possible to explain the initial conditions of the universe. The theory of cosmic inflation (and a number of competitors) claims to use physical processes to set up the initial conditions of the standard big bang. So in one case initial conditions are being used to explain dynamics, and in the other, dynamics are being used to explain initial conditions. In this article I explore the relationship between two apparently different perspectives on initial conditions and dynamics. My goal in pursuing this question is to gain a deeper insight into what we are actually able to accomplish with theories of cosmic initial conditions. Can these two perspectives coexist, perhaps even allowing one to conclude that cosmic inflation explains the arrow of time? Or do these two different ideas about relating dynamics and initial conditions point to some deep contradiction, leading us to conclude that a fundamental explanation of both the arrow of time and the initial conditions of the universe is impossible? Thinking through these issues also leads to interesting comparisons of different theories of initial conditions (e.g. inflation vs. cyclic models). Throughout this article, by the “arrow of time” I mean the thermodynamic arrow of time. As discussed in section 3.3, I regard this to be equivalent to the radiation, psychological, and quantum mechanical arrows of time. The cosmic expansion (or the “cosmological arrow of time”) may or may not be correlated with the thermodynamic arrow of time, depending on the specific model of the universe in question (see for example Hawking 1994) I also should be clear about how I use the phrase “initial conditions”. The classical standard big bang cosmology has a genuine set of (singular) “initial conditions” in the sense that the model cannot be extended arbitrarily far back in time. Much of my discussion in this article involves various ways one can work in a larger context where time, or at least some physical framework, is eternal. In that context, the problem of initial conditions that concerns us here is how some region entered into a state that reflect 2 the “initial” conditions we use for the part of the universe we observe. This state might not be initial at all in a global sense, but it still seems like an initial state from the point of view of our observable universe. I will often use the term “initial conditions” to refer to the state at the end of inflation which forms the initial conditions for the standard big bang phase that follows. I hope in what follows my meaning will be clear from the context. I hope this article will be stimulating and perhaps even provocative for experts on inflation and alternative theories of the initial conditions of the universe. But, In the spirit of the Wheeler volume, I’ve also tried to make this article for the most part accessible to a wider audience of physical scientists who may be experts in other areas but who might find the subject interesting. This article is organized as follows: Section 2 sets the stage by contrasting a cosmologist’s view of initial conditions with that of “everyone else”. Section 3 presents the standard modern view of the origin of the arrow of time. In section 3.2 I discuss the case where gravity is irrelevant (which covers most everyday intuition). Then (section 3.4) I discuss the case where gravity is dominant, which allows the discussion of the arrow of time to be extended to the entire cosmos. Section 4 presents the inflationary perspective on initial conditions, and contrasts them with the perspective taken when discussing the arrow of time. Sections 5 and 6 show how these two perspectives can coexist (still with some tension) in an overarching “big picture” that allows both an explanation of initial conditions and the arrow of time. Section 7 contrasts a variety of different ideas about cosmic initial conditions in light of the insights from earlier sections. Section 8 discusses additional issues, including “causal patch” physics and problems with measures. Section 9 spells out some big open questions for the future. My conclusions appear in section 10. 2 The everyday perspective on initial conditions Scientists other than cosmologists almost never consider the type of question addressed by cosmic inflation. Cosmic inflation tries to explain the initial conditions of the standard big bang phase of the universe. Where else does one try to explain the initial conditions of anything? The typical perspective on initial conditions is very different. Consider the process of testing a scientific theory in the laboratory. A particular experiment is performed in the laboratory, theoretical
Load more

Recommended publications
  • String Theory and Pre-Big Bang Cosmology
    IL NUOVO CIMENTO 38 C (2015) 160 DOI 10.1393/ncc/i2015-15160-8 Colloquia: VILASIFEST String theory and pre-big bang cosmology M. Gasperini(1)andG. Veneziano(2) (1) Dipartimento di Fisica, Universit`a di Bari - Via G. Amendola 173, 70126 Bari, Italy and INFN, Sezione di Bari - Bari, Italy (2) CERN, Theory Unit, Physics Department - CH-1211 Geneva 23, Switzerland and Coll`ege de France - 11 Place M. Berthelot, 75005 Paris, France received 11 January 2016 Summary. — In string theory, the traditional picture of a Universe that emerges from the inflation of a very small and highly curved space-time patch is a possibility, not a necessity: quite different initial conditions are possible, and not necessarily unlikely. In particular, the duality symmetries of string theory suggest scenarios in which the Universe starts inflating from an initial state characterized by very small curvature and interactions. Such a state, being gravitationally unstable, will evolve towards higher curvature and coupling, until string-size effects and loop corrections make the Universe “bounce” into a standard, decreasing-curvature regime. In such a context, the hot big bang of conventional cosmology is replaced by a “hot big bounce” in which the bouncing and heating mechanisms originate from the quan- tum production of particles in the high-curvature, large-coupling pre-bounce phase. Here we briefly summarize the main features of this inflationary scenario, proposed a quarter century ago. In its simplest version (where it represents an alternative and not a complement to standard slow-roll inflation) it can produce a viable spectrum of density perturbations, together with a tensor component characterized by a “blue” spectral index with a peak in the GHz frequency range.
    [Show full text]
  • The Arrow of Time Volume 7 Paul Davies Summer 2014 Beyond Center for Fundamental Concepts in Science, Arizona State University, Journal Homepage P.O
    The arrow of time Volume 7 Paul Davies Summer 2014 Beyond Center for Fundamental Concepts in Science, Arizona State University, journal homepage P.O. Box 871504, Tempe, AZ 852871504, USA. www.euresisjournal.org [email protected] Abstract The arrow of time is often conflated with the popular but hopelessly muddled concept of the “flow” or \passage" of time. I argue that the latter is at best an illusion with its roots in neuroscience, at worst a meaningless concept. However, what is beyond dispute is that physical states of the universe evolve in time with an objective and readily-observable directionality. The ultimate origin of this asymmetry in time, which is most famously captured by the second law of thermodynamics and the irreversible rise of entropy, rests with cosmology and the state of the universe at its origin. I trace the various physical processes that contribute to the growth of entropy, and conclude that gravitation holds the key to providing a comprehensive explanation of the elusive arrow. 1. Time's arrow versus the flow of time The subject of time's arrow is bedeviled by ambiguous or poor terminology and the con- flation of concepts. Therefore I shall begin my essay by carefully defining terms. First an uncontentious statement: the states of the physical universe are observed to be distributed asymmetrically with respect to the time dimension (see, for example, Refs. [1, 2, 3, 4]). A simple example is provided by an earthquake: the ground shakes and buildings fall down. We would not expect to see the reverse sequence, in which shaking ground results in the assembly of a building from a heap of rubble.
    [Show full text]
  • 30+ Commonly Held Concepts About Cosmology
    30+ Commonly held Concepts about Cosmology Big bang 1. The big bang is unavoidable, as proven by well-known “singularity theorems.” 2. Big bang nucleosynthesis, the successful theory of the formation of the elements, requires a big bang (as the name implies). 3. Extrapolating back in time, the universe must have reached a phase (the Planck epoch) in which quantum gravity effects dominate. 4. Time must have a beginning. 5. In an expanding universe, space expands but time does not. 6. The discovery that the expansion of the universe is accelerating today means that the universe will expand forever into the future. 7. There is no natural mechanism that could cause the universe to switch from its current cosmic acceleration to slow contraction. 8. With the exception of the bang, cosmology probes gravity in the weak coupling limit (in contrast with black hole collisions that probe gravity in the strong coupling limit). Smoothness, flatness and inflation 9. Inflation naturally explains why the universe is smooth (homogeneous), isotropic and flat. 10. You can understand how inflation flattens the universe by imagining an inflating balloon. The more it inflates, the flatter it gets. 11. Inflation is the only known cosmological mechanism for flattening the universe. 12. Inflation is proven because we observe the universe to be homogeneous, isotropic and flat. 13. Inflation is equivalent to a “nearly de Sitter” universe. 14. The parameters ns, r, / etc. extracted from the CMB measurements are “inflationary parameters.” 15. Inflation predicts a nearly scale-invariant spectrum of CMB temperature variations. 16. Inflation is the only mechanism for generating super-Hubble wavelength modes (which is essential for explaining the CMB).
    [Show full text]
  • Loop Quantum Gravity: the First 25 Years Carlo Rovelli
    Loop quantum gravity: the first 25 years Carlo Rovelli To cite this version: Carlo Rovelli. Loop quantum gravity: the first 25 years. Classical and Quantum Gravity, IOP Publishing, 2011, 28 (15), pp.153002. 10.1088/0264-9381/28/15/153002. hal-00723006 HAL Id: hal-00723006 https://hal.archives-ouvertes.fr/hal-00723006 Submitted on 7 Aug 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Loop quantum gravity: the first twenty five years Carlo Rovelli Centre de Physique Th´eorique de Luminy∗, Case 907, F-13288 Marseille, EU (Dated: January 27, 2011) I give a synthetic presentation of loop quantum gravity. I spell-out the aims of the theory and compare the results obtained with the initial hopes that motivated the early interest in this research direction. I give my own perspective on the status of the program and attempt of a critical evaluation of its successes and limits. I. INTRODUCTION The history of quantum gravity is full of great hopes later disappointed. I remember as a young student sitting in a major conference where a world-renowned physicists Loop gravity is not quite twenty-five years old, but announced that the final theory of quantum gravity and is getting close to such a venerable age: several basic everything had finally been found.
    [Show full text]
  • The Cosmic Gravitational Wave Background in a Cyclic Universe
    The Cosmic Gravitational-Wave Background in a Cyclic Universe Latham A. Boyle1, Paul J. Steinhardt1, and Neil Turok2 1Department of Physics, Princeton University, Princeton, New Jersey 08544 2Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 OWA, United Kingdom (Dated: July 2003) Inflation predicts a primordial gravitational wave spectrum that is slightly “red,” i.e. nearly scale-invariant with slowly increasing power at longer wavelengths. In this paper, we compute both the amplitude and spectral form of the primordial tensor spectrum predicted by cyclic/ekpyrotic models. The spectrum is exponentially suppressed compared to inflation on long wavelengths, and the strongest constraint emerges from the requirement that the energy density in gravitational waves should not exceed around 10 per cent of the energy density at the time of nucleosynthesis. The recently-proposed cyclic model[1, 2] differs radi- V(φ) cally from standard inflationary cosmology [3, 4], while retaining the inflationary predictions of homogeneity, 4 5 φ 6 flatness, and nearly scale-invariant density perturbations. end It has been suggested that the cosmic gravitational wave 3 1 φ background provides the best experimental means for dis- tinguishing the two models. Inflation predicts a nearly 2 scale-invariant (slightly red) spectrum of primordial ten- sor perturbations, whereas the cyclic model predicts a blue spectrum.[1] The difference arises because inflation involves an early phase of hyper-rapid cosmic accelera- tion, whereas the cyclic model does not. In this paper, we compute the gravitational wave spec- trum for cyclic models to obtain both the normalization and spectral shape as a function of model parameters, im- V proving upon earlier heuristic estimates.
    [Show full text]
  • Chaos, Dissipation, Arrow of Time, in Quantum Physics I the National Institute of Standards and Technology Was Established in 1988 by Congress to "Assist
    Chaos, Dissipation, Arrow of Time, in Quantum Physics i The National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability . and to facilitate rapid commercialization . of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied research in the physical sciences and engineering and performs related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. Major technical operating units and their principal activities are listed below. For more information contact the Public Inquiries Desk, 301-975-3058. Technology Services Manufacturing Engineering Laboratory • Manufacturing Technology Centers Program • Precision
    [Show full text]
  • Quantum Cosmic No-Hair Theorem and Inflation
    PHYSICAL REVIEW D 99, 103514 (2019) Quantum cosmic no-hair theorem and inflation † Nemanja Kaloper* and James Scargill Department of Physics, University of California, Davis, California 95616, USA (Received 11 April 2018; published 13 May 2019) We consider implications of the quantum extension of the inflationary no-hair theorem. We show that when the quantum state of inflation is picked to ensure the validity of the effective field theory of fluctuations, it takes only Oð10Þ e-folds of inflation to erase the effects of the initial distortions on the inflationary observables. Thus, the Bunch-Davies vacuum is a very strong quantum attractor during inflation. We also consider bouncing universes, where the initial conditions seem to linger much longer and the quantum “balding” by evolution appears to be less efficient. DOI: 10.1103/PhysRevD.99.103514 I. INTRODUCTION As we will explain, this is resolved by a proper Inflation is a simple and controllable framework for application of EFT to fluctuations. First off, the real describing the origin of the Universe. It relies on rapid vacuum of the theory is the Bunch-Davies state [2]. This cosmic expansion and subsequent small fluctuations follows from the quantum no-hair theorem for de Sitter described by effective field theory (EFT). Once the space, which selects the Bunch-Davies state as the vacuum slow-roll regime is established, rapid expansion wipes with UV properties that ensure cluster decomposition – out random and largely undesirable initial features of the [3 5]. The excited states on top of it obey the constraints – Universe, and the resulting EFT of fluctuations on the arising from backreaction, to ensure that EFT holds [6 14].
    [Show full text]
  • In the Experiments in Which Alpha-Activity Was Measured Using Collimators Directed at East and West
    Volume 1 PROGRESS IN PHYSICS January, 2010 “The Arrow of Time” in the Experiments in which Alpha-Activity was Measured Using Collimators Directed at East and West Simon E. Shnoll, Ilya A. Rubinsteiny, and Nikolai N. Vedenkiny Department of Physics, Moscow State University, Moscow 119992, Russia Inst. of Theor. and Experim. Biophysics, Russian Acad. of Sci., Pushchino, Moscow Region, 142290, Russia Puschino State University, Prospect Nauki 3, Pushchino, Moscow Region, 142290, Russia ySkobeltsin’s Institute of Nuclear Physics, Moscow State University, Moscow 119991, Russia E-mail: [email protected] In our previous paper (Shnoll and Rubinstein, Progress in Physics, 2009, v. 2, 83–95), we briefly reported about a phenomenon, which can be called the “arrow of time”: when we compared histograms constructed from the results of 239-Pu alpha-activity measurements that were obtained using West- and East-directed collimators, daytime series of the “eastern” histograms were similar to the inverted series of the following night, whereas daytime series of the “western” histograms resembled the inverted series of the preceding night. Here we consider this phenomenon in more detail. 1 Introduction As follows from all our past results, the fine structure of the spectrum of amplitude fluctuations (the shape of the corre- sponding histograms) is determined by the motion (orienta- tion) of the object studied (the laboratory) in relation to spa- tial inhomogeneities [2]. The spatial pattern (arrangement in space) of these inhomogeneities is stable: as the Earth ro- tates about its axis and moves along the circumsolar orbit, similar histogram shapes are realized repeatedly with the cor- responding periods (daily, near-monthly, yearly) [3, 4].
    [Show full text]
  • The Cyclic Model Simplified∗
    The Cyclic Model Simplified∗ Paul J. Steinhardt1;2 and Neil Turok3 1Department of Physics, Princeton University, Princeton, New Jersey 08544, USA 2 School of Natural Sciences, Institute for Advanced Study, Olden Lane, Princeton, New Jersey 08540, USA 3 Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, U.K. (Dated: April 2004) The Cyclic Model attempts to resolve the homogeneity, isotropy, and flatness problems and gen- erate a nearly scale-invariant spectrum of fluctuations during a period of slow contraction that precedes a bounce to an expanding phase. Here we describe at a conceptual level the recent de- velopments that have greatly simplified our understanding of the contraction phase and the Cyclic Model overall. The answers to many past questions and criticisms are now understood. In partic- ular, we show that the contraction phase has equation of state w > 1 and that contraction with w > 1 has a surprisingly similar properties to inflation with w < −1=3. At one stroke, this shows how the model is different from inflation and why it may work just as well as inflation in resolving cosmological problems. I. THE CYCLIC MANIFESTO Two years ago, the Cyclic Model [1] was introduced as a radical alternative to the standard big bang/inflationary picture [2]. Its purpose is to offer a new solution to the homogeneity, isotropy, flatness problems and a new mechanism for generating a nearly scale-invariant spectrum of fluctuations. One might ask why we should consider an alternative when inflation [2{4] has scored so many successes in explaining a wealth of new, highly precise data [5].
    [Show full text]
  • Solutions to the Cosmic Initial Entropy Problem Without Equilibrium Initial Conditions
    1 Solutions to the Cosmic Initial Entropy Problem without Equilibrium Initial Conditions Vihan M. Patel 1 and Charles H. Lineweaver 1,2,3,* 1 Research School of Astronomy and Astrophysics, Australian National University, Canberra 2600, Australia; [email protected] 2 Planetary Science Institute, Australian National University, Canberra 2600, Australia 3 Research School of Earth Sciences, Australian National University, Canberra 2600, Australia * Correspondence: [email protected] Abstract: The entropy of the observable universe is increasing. Thus, at earlier times the entropy was lower. However, the cosmic microwave background radiation reveals an apparently high entropy universe close to thermal and chemical equilibrium. A two-part solution to this cosmic initial entropy problem is proposed. Following Penrose, we argue that the evenly distributed matter of the early universe is equivalent to low gravitational entropy. There are two competing explanations for how this initial low gravitational entropy comes about. (1) Inflation and baryogenesis produce a virtually homogeneous distribution of matter with a low gravitational entropy. (2) Dissatisfied with explaining a low gravitational entropy as the product of a ‘special’ scalar field, some theorists argue (following Boltzmann) for a “more natural” initial condition in which the entire universe is in an initial equilibrium state of maximum entropy. In this equilibrium model, our observable universe is an unusual low entropy fluctuation embedded in a high entropy universe. The anthropic principle and the fluctuation theorem suggest that this low entropy region should be as small as possible and have as large an entropy as possible, consistent with our existence. However, our low entropy universe is much larger than needed to produce observers, and we see no evidence for an embedding in a higher entropy background.
    [Show full text]
  • Black Holes and String Theory
    Black Holes and String Theory Hussain Ali Termezy Submitted in partial fulfilment of the requirements for the degree of Master of Science of Imperial College London September 2012 Contents 1 Black Holes in General Relativity 2 1.1 Black Hole Solutions . 2 1.2 Black Hole Thermodynamics . 5 2 String Theory Background 19 2.1 Strings . 19 2.2 Supergravity . 23 3 Type IIB and Dp-brane solutions 25 4 Black Holes in String Theory 33 4.1 Entropy Counting . 33 Introduction The study of black holes has been an intense area of research for many decades now, as they are a very useful theoretical construct where theories of quantum gravity become relevant. There are many curiosities associated with black holes, and the resolution of some of the more pertinent problems seem to require a quantum theory of gravity to resolve. With the advent of string theory, which purports to be a unified quantum theory of gravity, attention has naturally turned to these questions, and have remarkably shown signs of progress. In this project we will first review black hole solutions in GR, and then look at how a thermodynamic description of black holes is made possible. We then turn to introduce string theory and in particular review the black Dp-brane solutions of type IIB supergravity. Lastly we see how to compute a microscopic account of the Bekenstein entropy is given in string theory. 1 Chapter 1 Black Holes in General Relativity 1.1 Black Hole Solutions We begin by reviewing some the basics of black holes as they arise in the study of general relativity.
    [Show full text]
  • Time in Cosmology
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Philsci-Archive Time in Cosmology Craig Callender∗ C. D. McCoyy 21 August 2017 Readers familiar with the workhorse of cosmology, the hot big bang model, may think that cosmology raises little of interest about time. As cosmological models are just relativistic spacetimes, time is under- stood just as it is in relativity theory, and all cosmology adds is a few bells and whistles such as inflation and the big bang and no more. The aim of this chapter is to show that this opinion is not completely right...and may well be dead wrong. In our survey, we show how the hot big bang model invites deep questions about the nature of time, how inflationary cosmology has led to interesting new perspectives on time, and how cosmological speculation continues to entertain dramatically different models of time altogether. Together these issues indicate that the philosopher interested in the nature of time would do well to know a little about modern cosmology. Different claims about time have long been at the heart of cosmology. Ancient creation myths disagree over whether time is finite or infinite, linear or circular. This speculation led to Kant complaining in his famous antinomies that metaphysical reasoning about the nature of time leads to a “euthanasia of reason”. But neither Kant’s worry nor cosmology becoming a modern science succeeded in ending the speculation. Einstein’s first model of the universe portrays a temporally infinite universe, where space is edgeless and its material contents unchanging.
    [Show full text]