Modified gravity models play an important role in contemporary theoretical cosmology. The present book proposes a novel approach to the topic based on techniques from noncommutative geometry, especially the spectral action functional as a gravity model. The book discusses applications to early universe models and slow-roll inflation models, to the problem of cosmic topology, to non-isotropic cosmologies like mixmaster universes and Bianchi IX gravitational instantons, and to multifractal structures in cosmology.Relations between noncommutative and algebro-geometric methods in cosmology is also discussed, including the occurrence of motives, periods, and modular forms in spectral models of gravity.

This book is first of its kind describing a new direction in modeling processes taking place in interplanetary and interstellar space (magnetic fields, plasma, cosmic rays, etc.). This method is based on a special mathematical analysis - fractional calculus. The reader will find in this book clear physical explanation of the fractional approach and will become familiar with basic rules in this calculus and main results obtained in frame of this approach. In spite of its profound subject, the book is not overloaded by mathematical details. It contains many illustrations, rich citation and remains accessible to a wide circle of physicists.This book is addressed to graduate and postgraduate students, young and mature researchers specializing in applications of fractional calculus, astrophysics, solar-terrestrial science and physics of cosmic rays.

This is the first English translation of Simplicius' responses to Philoponus' "Against Aristotle on the Eternity of the World." The commentary is published in two volumes: Ian Mueller's previous book in the series, " Simplicius: On Aristotle On the Heavens 1.2-3," and this book on 1.3-4. Philoponus, the Christian, had argued that Aristotle's arguments do not succeed. For all they show to the contrary, Christianity may be right that the heavens were brought into existence by the only divine being and one moment in time, and will cease to exist at some future moment. Simplicius upholds the pagan view that the heavens are eternal and divine, and argues that their eternity is shown by their astronomical movements coupled with certain principles of Aristotle.Until the launch of this series, the 15,000 volumes of the ancient Greek commentators on Aristotle constituted the largest corpus of Greek philosophical writings which had not been translated into English or other European languages. There are now over 100 volumes in the series.

This book contains a systematic and pedagogical exposition of recent developments in particle physics and cosmology. It starts with two introductory chapters on group theory and the Dirac theory. Then it proceeds with the formulation of the Standard Model (SM) of Particle Physics, particle content and symmetries, fully exploiting the material of the first two chapters. It discusses the concept of gauge symmetries and emphasizes their role in particle physics. It then analyses the Higgs mechanism and the spontaneous symmetry breaking (SSB). It explains how the particles (gauge bosons and fermions) after the SSB acquire a mass and get admixed. The various forms of charged currents are discussed in detail as well as how the parameters of the SM, which cannot be determined by the theory, are fixed by experiment, including the recent LHC data and the Higgs discovery. Quantum chromodynamics is discussed and various low energy approximations to it are presented. The Feynman diagrams are introduced and applied, at the level of first year graduate students. Examples are the evaluation of the decay widths of the gauge bosons and some cross sections for interesting processes such as Rutherford scattering, electron-proton scattering (elementary proton or described by a form factor, and inelastic scattering) and Compton scattering. After that the classic topics like the role of C, P, CP symmetries and the experimental methods needed to verify their conservation or violation are discussed in some detail. Topics beyond the standard model, like supersymmetry for pedestrians and grand unification, are discussed. To this end neutrino oscillations, dark matter and baryon asymmetry are also briefly discussed at the first year graduate level. Finally, the book contains an exhibition of recent developments in cosmology, especially from the elementary particle point of view.

This book contains a systematic and pedagogical exposition of recent developments in particle physics and cosmology. It starts with two introductory chapters on group theory and the Dirac theory. Then it proceeds with the formulation of the Standard Model (SM) of Particle Physics, particle content and symmetries, fully exploiting the material of the first two chapters. It discusses the concept of gauge symmetries and emphasizes their role in particle physics. It then analyses the Higgs mechanism and the spontaneous symmetry breaking (SSB). It explains how the particles (gauge bosons and fermions) after the SSB acquire a mass and get admixed. The various forms of the charged currents are discussed in detail as well as how the parameters of the SM, which cannot be determined by the theory, are fixed by experiment, including the recent LHC data and the Higgs discovery. Quantum chromodynamics is discussed and various low energy approximations to it are presented. The Feynman diagrams are introduced and applied, at the level of first year graduate students.Examples are the evaluation of the decay widths of the gauge bosons and some cross sections for interesting processes such as Rutherford scattering, electron-proton scattering (elementary proton or described by a form factor, and inelastic scattering) and Compton scattering.After that the classic topics like the role of C, P, CP symmetries and the experimental methods needed to verify their conservation or violation are discussed in some detail. Topics beyond the standard model, like supersymmetry for pedestrians and grand unification, are discussed.To this end neutrino oscillations, dark matter and baryon asymmetry are also briefly discussed at the first year graduate level. Finally, the book contains an exhibition of recent developments in cosmology, especially from the elementary particle point of view.

This book is written from the viewpoint that a deep connection exists between cosmology and particle physics. It presents the results and ideas on both the homogeneous and isotropic Universe at the hot stage of its evolution and in later stages. The main chapters describe in a systematic and pedagogical way established facts and concepts on the early and the present Universe. The comprehensive treatment, hence, serves as a modern introduction to this rapidly developing field of science. To help in reading the chapters without having to constantly consult other texts, essential materials from General Relativity and the theory of elementary particles are collected in the appendices. Various hypotheses dealing with unsolved problems of cosmology, and often alternative to each other, are discussed at a more advanced level. These concern dark matter, dark energy, matter-antimatter asymmetry, etc.Particle physics and cosmology underwent rapid development between the first and the second editions of this book. In the second edition, many chapters and sections have been revised, and numerical values of particle physics and cosmological parameters have been updated.

This book is written from the viewpoint that a deep connection exists between cosmology and particle physics. It presents the results and ideas on both the homogeneous and isotropic Universe at the hot stage of its evolution and in later stages. The main chapters describe in a systematic and pedagogical way established facts and concepts on the early and the present Universe. The comprehensive treatment, hence, serves as a modern introduction to this rapidly developing field of science. To help in reading the chapters without having to constantly consult other texts, essential materials from General Relativity and the theory of elementary particles are collected in the appendices. Various hypotheses dealing with unsolved problems of cosmology, and often alternative to each other, are discussed at a more advanced level. These concern dark matter, dark energy, matter-antimatter asymmetry, etc.Particle physics and cosmology underwent rapid development between the first and the second editions of this book. In the second edition, many chapters and sections have been revised, and numerical values of particle physics and cosmological parameters have been updated.

An extraterrestrial civilization created human civilization and all other life on Earth. There was a time when mankind knew about these beings, but as religion and science took over the world, people forgot their true origins.

Religion and science remain at odds, but they continue to work together to erase all knowledge of the extraterrestrials. The only thing that hints at the truth is the continued reports of unidentified flying objects and other unexplained phenomena. Join an electrical engineer as he draws upon his technical knowledge and broad understanding of the world to propose a theory that will change your life. He offers guidance on how to evaluate the impact extraterrestrials had on early civilizations; see through the inaccuracies of religion; evaluate scientific theories.

Relying on unsound theories to create new ones can lead to problems. While science and religion claim to have all the answers, neither one of them explains life on this planet. The truth is out there, and you can find it in "Tarraforming Earth."

Introduction to General Relativity and Cosmology gives undergraduate students an overview of the fundamental ideas behind the geometric theory of gravitation and spacetime. Through pointers on how to modify and generalise Einstein's theory to enhance understanding, it provides a link between standard textbook content and current research in the field.Chapters present complicated material practically and concisely, initially dealing with the mathematical foundations of the theory of relativity, in particular differential geometry. This is followed by a discussion of the Einstein field equations and their various properties. Also given is analysis of the important Schwarzschild solutions, followed by application of general relativity to cosmology. Questions with fully worked answers are provided at the end of each chapter to aid comprehension and guide learning. This pared down textbook is specifically designed for new students looking for a workable, simple presentation of some of the key theories in modern physics and mathematics.

From the Big Bang to the Gaia Mission, this is a very personal history of the universe through the author's favourite 100 stars. Astronomer Florian Freistetter has chosen 100 stars that have almost nothing in common. Some are bright and famous, some shine so feebly you need a huge telescope. There are big stars, small stars, nearby stars and faraway stars. Some died a while ago, others have not even yet come into being. Collectively they tell the story of the whole world, according to Freistetter. There is Algol, for example, the Demon Star, whose strange behaviour has long caused people sleepless nights. And Gamma Draconis, from which we know that the earth rotates around its own axis. There is also the star sequence 61 Cygni, which revealed the size of the cosmos to us. Then there are certain stars used by astronomers to search for extra-terrestrial life, to explore interstellar space travel, or to explain why the dinosaurs became extinct. In 100 short, fascinating and entertaining chapters, Freistetter not only reveals the past and future of the cosmos, but also the story of the people who have tried to understand the world in which we live.

This comprehensive textbook is devoted to classical and quantum cosmology, with particular emphasis on modern approaches to quantum gravity and string theory and on their observational imprint. It covers major challenges in theoretical physics such as the big bang and the cosmological constant problem. An extensive review of standard cosmology, the cosmic microwave background, inflation and dark energy sets the scene for the phenomenological application of all the main quantum-gravity and string-theory models of cosmology. Born of the author's teaching experience and commitment to bridging the gap between cosmologists and theoreticians working beyond the established laws of particle physics and general relativity, this is a unique text where quantum-gravity approaches and string theory are treated on an equal footing. As well as introducing cosmology to undergraduate and graduate students with its pedagogical presentation and the help of 45 solved exercises, this book, which includes an ambitious bibliography of about 3500 items, will serve as a valuable reference for lecturers and researchers.

There are very few with Philip Morrison's gifts, few who can lead us with firm knowledge whispering just the right encouragement as he guides us across the great ideas of science. Take this journey with one of the most astute navigators and you'll find yourself compelled to go deeper into some of the most daring adventures of modern science. Nothing is too grand or seemingly too trivial - the nature of time, the fabric of the atom, what it means to explore scientific horizons, the galaxies, even the search for unknown intelligence in the vast as-yet-uncharted universe. Then as deftly as Morrison takes us on a dazzling tour of the stars, he gently settles down for an intimate stop in the nursery where children have their first encounters with the things of everyday life, everyday things that cause us to wonder and make for discovery. With an equally firm grasp, Morrison, who witnessed the first tests of the atom bomb, takes us unflinchingly through some of the most frightening terrain of modern times, where the arms race can cause our ultimate destruction, but where sanity can still bring us peace. This extraordinary collection of essays by one of the most profound commentators on the successes and failures of the scientific enterprize concludes with lively portraits of men of science - Neils Bohr, Richard Feynman, Charles Babbage, among other notable friends and heroes.

Many books have been written about the Big Bang and how the universe became the way it is today. But what about the future of the universe? What will happen to the Earth and solar system? What about our galaxy? Indeed, how long will the universe as we recognize it survive? The Future of the Universe takes the reader on a journey through space and time, beginning with a long look at the Earth and solar system, voyaging to the outermost galaxies, and finishing with speculations about the life and fate of the entire universe.

Ever since 1911, the Solvay Conferences have shaped modern physics. The format is quite different from other conferences as the emphasis is placed on discussion. The 26th edition held in October 2014 in Brussels and chaired by Roger Blandford continued this tradition and addressed some of the most pressing open questions in the fields of astrophysics and cosmology, gathering many of the leading figures working on a wide variety of profound problems.The proceedings contain the 'rapporteur talks' giving a broad overview with unique insights by distinguished renowned scientists. These lectures cover the five sessions: 'Neutron Stars', 'Black Holes', 'Cosmic Dawn', 'Dark Matter' and 'Cosmic Microwave Background'.In the Solvay tradition, the proceedings also include the prepared comments to the rapporteur talks. The discussions among the participants - expert, yet lively and sometimes contentious - have been edited to retain to retain their flavor and are reproduced in full. The reader is taken on a breathtaking ride through 42 years of extraordinary discovery since astrophysics was last on the Solvay program and 57 years since cosmology was last discussed.

Ever since 1911, the Solvay Conferences have shaped modern physics. The format is quite different from other conferences as the emphasis is placed on discussion. The 26th edition held in October 2014 in Brussels and chaired by Roger Blandford continued this tradition and addressed some of the most pressing open questions in the fields of astrophysics and cosmology, gathering many of the leading figures working on a wide variety of profound problems.The proceedings contain the 'rapporteur talks' giving a broad overview with unique insights by distinguished renowned scientists. These lectures cover the five sessions: 'Neutron Stars', 'Black Holes', 'Cosmic Dawn', 'Dark Matter' and 'Cosmic Microwave Background'.In the Solvay tradition, the proceedings also include the prepared comments to the rapporteur talks. The discussions among the participants - expert, yet lively and sometimes contentious - have been edited to retain to retain their flavor and are reproduced in full. The reader is taken on a breathtaking ride through 42 years of extraordinary discovery since astrophysics was last on the Solvay program and 57 years since cosmology was last discussed.

1. Standard Model of Primordial Nucleosynthesis and Observations of Light Elements.- Standard Model of Primordial Nucleosynthesis: A Few General Remarks.- The Abundances of D, He and Li Test and Constrain the Standard Model of Cosmology.- Lithium, Beryllium and Boron: Observational Constraints on Primordial Nucleosynthesis.- The Evolution of the Galactic Lithium Abundance.- Chemical Evolution of Galaxies.- The Effect of Some Nonequilibrium Processes on the Primordial Nucleosynthesis.- Analysis of the Reaction 7Li(d, n)8Be at Subcoulomb Energies.- Experimental Study of the Key Reaction to the Nucleosynthesis in the Inhomogeneous Big Bang Models.- Primordial Black Holes and Big Bang Nucleosynthesis.- Constraints from Primordial Nucleosynthesis on Neutrino Degeneracy.- 2. QCD Phase Transition and Nucleosynthesis in Inhomogeneous Universes.- Strange Quark Matter in Physics and Astrophysics.- Primordial Nucleosynthesis in Inhomogeneous Universe.- Sterile Neutrinos in the Early Universe.- Could Cosmic QCD Phase Transition Produce Strange Quark Matter Which Survives until the Present Time?.- Multi-Zone Calculation of Nucleosynthesis in Inhomogeneous Universe and Be-9 Abundance.- Signatures of Inhomogeneity in the Early Universe.- Diffusion Coefficients of Nucleons in the Inhomogeneous Big Bang Model.- Reactions on Carbon-14.- Survival of Strange Matter Lumps Formed in the Early Universe.- Measurement of the Cross Section of the 12C(n, g)13C Reaction at Stellar Energy.- Inhomogeneous Universes in the Framework of Lattice QCD.- 3. Inflation and very Early Universe.- The Beginning of the Universe.- Extended Inflationary Cosmology: A Primer.- The Inflation Sector of Extended Inflation.- Inflation in Generalized Einstein Theories.- Baryogenesis in the Universe.- Formation of Topological Defects in the Inflationary Universe.- Non-Zel'dovich Fluctuations from Inflation.- Magnetic Theory of Gravitation.- Chaotic Inflation and the Omega Problem.- Late-Time Cosmological Phase Transitions.- False-Vacuum Decay in Generalized Extended Inflation.- Reconciling a Small Density Parameter to Inflation.- Soft Inflation: A Model for Easing Constraints.- Stochastic Inflation Lattice Simulations: Ultra-Large Scale Structure of the Universe.- Purely Quantum Derivation of Density Fluctuations in the Inflationary Universe.- Constraints on the Coupling of Weakly-Interacting Particles to Matter from Stellar Evolution.- Formation and Evolution of Domain-Wall-Networks.- Catastrophe of Spacetime in the Early Universe.- (2+1)-Dimensional Quantum Gravity.- A Stringy Universe Scenario.- The Constant-Mean-Curvature Slicing of the Schwarzschild-de Sitter Space-Time.- Schwarzschild-de Sitter Type Wormhole and Cosmological Constant.- 4. Background Radiation.- COBE: New Sky Maps of the Early Universe.- Large Scale Cosmic Instability.- Gas-Induced Primary and Secondary CMB Anisotropies.- Cosmic X-Ray Background.- Large Scale Anisotropy of the CMB in an Open Universe and Constraints on the Models of Galaxy Formation.- 5. Dark Matter.- The Best-Fit Universe.- LEP Physics and the Early Universe.- A Search for Dark Matters in the Kamiokande II.- Baryonic Dark Matter.- Phenomenological Dark Matter Detection Rate-form WIMP to SIMP-.- 6. Galaxies and AGN.- X-Ray Iron Line of Cluster of Galaxies.- Dynamical Evolution of Compact Groups of Galaxies.- Correlations of Spin Angular Momenta of Galaxies.- Formation of Bipolar Radio Jets and Lobes from Accreton Disk around Forming Blackhole at the Center of Protogalaxies.- An Evolutionary Unified Scheme for Radio-Loud Quasars and Blazars.- Magnetohydrodynamical Energy Extraction from a Kerr Black Hole.- Spherical Symmetric Model for Calculating Large Peculiar Velocities of Galaxies.- On the Origin of Cosmological Magnetic Fields.- 7. Large Scale Structure.- The Hawaii Deep Survey-Implications for Cosmology and Galaxy Formation.- Analysis of the Large Scale Structure with Deep Pencil Beam Surveys.- Distance to the Coma Cluster and the Va.

Our universe seems strangely "biophilic," or hospitable to life. Is this happenstance, providence, or coincidence? According to cosmologist Martin Rees, the answer depends on the answer to another question, the one posed by Einstein's famous remark: "What interests me most is whether God could have made the world differently." This highly engaging book explores the fascinating consequences of the answer being "yes." Rees explores the notion that our universe is just a part of a vast "multiverse," or ensemble of universes, in which most of the other universes are lifeless. What we call the laws of nature would then be no more than local bylaws, imposed in the aftermath of our own Big Bang. In this scenario, our cosmic habitat would be a special, possibly unique universe where the prevailing laws of physics allowed life to emerge. Rees begins by exploring the nature of our solar system and examining a range of related issues such as whether our universe is or isn't infinite. He asks, for example: How likely is life? How credible is the Big Bang theory? Rees then peers into the long-range cosmic future before tracing the causal chain backward to the beginning. He concludes by trying to untangle the paradoxical notion that our entire universe, stretching 10 billion light-years in all directions, emerged from an infinitesimal speck. As Rees argues, we may already have intimations of other universes. But the fate of the multiverse concept depends on the still-unknown bedrock nature of space and time on scales a trillion trillion times smaller than atoms, in the realm governed by the quantum physics of gravity. Expanding our comprehension of the cosmos, Our Cosmic Habitat will be read and enjoyed by all those--scientists and nonscientists alike--who are as fascinated by the universe we inhabit as is the author himself.

This is a presentation of the progress and current problems in the early universe, cosmic microwave background radiation, large scale structure formation, and the interplay between them. The emphasis is on the mutual impact of fundamental physics and cosmology, both at theoretical and experimental (observational) levels within a deep, well-focused and well-defined programme. The nature of the domain itself leads to different aspects, approaches and points of view on the same topic. Special care has been taken to provide the reader the basis of the different, sometimes competing lines of research.

"The dominant figures of postwar astrophysical cosmology have been the late Yakov Ze'ldovich, of Moscow, and Jim Peebles, of Princeton. But running a close third in influence has been Joseph Silk.... This collection is essential reading for the cosmological enthusiast." Nature These essays represent Joseph Silk's own meandering around cosmic themes. The topics span the beginning of time until its end and encompass the enigma of the evolution of large-scale structure, culminating in the formation of the galaxies. Dr. Silk has taken these writings from pieces written over the years, many commissioned to highlight a new look at a new discovery in cosmology. Some have been rewritten to capture a modern perspective while others remain as written to encapsulate his thoughts of a decade ago.

Molecules in the early Universe acted as natural temperature regulators, keeping the primordial gas cool and, in turn, allowing galaxies and stars to be born. Even now, such similarly simple chemistry continues to control a wide variety of the exotic objects that populate our cosmos. What are the tools of the trade for the cosmic chemist? What can they teach us about the Universe we live in? These are the questions answered in this engaging and informative guide, The Chemically Controlled Cosmos. In clear, non-technical terms, and without formal mathematics, we learn how to study and understand the behaviour of molecules in a host of astronomical situations. We study the secretive formation of stars deep within interstellar clouds, the origin of our own Solar System, the cataclysmic deaths of many massive stars that explode as supernovae, and the hearts of active galactic nuclei, the most powerful objects in the Universe. We are given an accessible introduction to a wealth of astrophysics, and an understanding of how cosmic chemistry facilitates the investigation of many of the most exciting questions concerning astronomy today.

Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in motion, relativistic addition of velocities, and the twin paradox, as well as new material on gravitational waves, amongst other topics.

Christians often claim to hold a biblical worldview. But what about a biblical cosmos view? From the beginning of Genesis we encounter a vaulted dome above the earth, a "firmament," like the ceiling of a planetarium. Elsewhere we read of the earth sitting on pillars. What does the dome of heaven have to do with deep space? Even when the biblical language is clearly poetic, it seems to be funded by a very different understanding of how the cosmos is put together. As Kyle Greenwood shows, the language of the Bible is also that of the ancient Near Eastern palace, temple and hearth. There was no other way of thinking or speaking of earth and sky or the sun, moon and stars. But when the psalmist looked at the heavens, the delicate fingerwork of God, it evoked wonder. Even today it is astronomy and cosmology that invoke our awe and point toward the depths of divine mystery. Greenwood helps us see how the best Christian thinkers have viewed the cosmos in light of Scripture-and grappled with new understandings as science has advanced from Aristotle to Copernicus to Galileo and the galaxies of deep space. It's a compelling story that both illuminates the text of Scripture and helps us find our own place in the tradition of faithful Christian thinking and interpretation.

Just what is Einstein's Theory of Relativity? The Big Bang Theory? Curvature of Spacetime? What do astronomers mean when they talk of a 'flat universe'? This approachable and authoritative guide to the cosmos answers these questions, and more. Taking advantage of the distinctive Companion format, readers can use the extensive, cross-referenced background chapters as a fascinating and accessible introduction to the current state of cosmological knowledge - or, they can use the convenient A-Z body of entries as a quick reference to a wide range of terms and concepts. Entries include topics such as: Black Hole; Doppler Effect; Fermi, Enrico; Heat Death of the Universe; Life in the Universe; Olber's Paradox; Quantum Field Theory; Supernova; and much more.

The aim of this book is to analyze the all important implications of Heisenberg's Uncertainty Principle for a finite universe with very large mass-energy content such as ours. The earlier and main contributors to the formulation of Quantum Mechanics are briefly reviewed regarding the formulation of Heisenberg's Principle. After discussing "indeterminacy" versus "uncertainty", the universal constants of physics are reviewed and Planck's units are given. Next, a novel set of units, Heisenberg-Lemaitre units, are defined in terms of the large finite mass of the universe. With the help of Heisenberg's principle, the time evolution of the finite zero-point energy for the universe is investigated quantitatively. Next, taking advantage of the rigorous solutions of Einstein's cosmological equation for a flat, open and mixed universe of finite mass, the most recent and accurate data on the "age" (to) and the expansion rate (Ho) of the universe and their implications are reconsidered.

The cutting-edge science that is taking the measure of the universe The Little Book of Cosmology provides a breathtaking look at our universe on the grandest scales imaginable. Written by one of the world's leading experimental cosmologists, this short but deeply insightful book describes what scientists are revealing through precise measurements of the faint thermal afterglow of the Big Bang-known as the cosmic microwave background, or CMB-and how their findings are transforming our view of the cosmos. Blending the latest findings in cosmology with essential concepts from physics, Lyman Page first helps readers to grasp the sheer enormity of the universe, explaining how to understand the history of its formation and evolution in space and time. Then he sheds light on how spatial variations in the CMB formed, how they reveal the age, size, and geometry of the universe, and how they offer a blueprint for the formation of cosmic structure. Not only does Page explain current observations and measurements, he describes how they can be woven together into a unified picture to form the Standard Model of Cosmology. Yet much remains unknown, and this incisive book also describes the search for ever deeper knowledge at the field's frontiers-from quests to understand the nature of neutrinos and dark energy to investigations into the physics of the very early universe.