How the Universe Works

Introduction to Modern Cosmology

Serge Parnovsky, Aleksei Parnowski

• Publisher: WSPC
• Year: 2017
• ISBN:
  9789813234963
• Topic: Naturwissenschaften
• Subtopic: Physik

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This book is about the history and the current state of the art in the exciting field of cosmology — the science about the Universe as a whole, which is guaranteed to attract the attention of a wide range of readers. It mostly aims to explain the main ideas of modern cosmology: the expanding Universe, its creation in a Big Bang, its evolution, characteristics, and structure, as well as issues — dark matter and dark energy, black holes and other exotic objects etc. It also answers most frequently asked questions about cosmology.

How the Universe Works stands between a popular science book and a textbook, acting as a sort of a bridge across the great chasm separating popular science from true science. It can be also used as an introductory textbook for undergraduate students. It is also suitable for the non-experts in cosmology who wish to have an overview of the current state of the field. It is different from most popular science books because it avoids cutting corners in explanations and contains justification for various assumptions or estimations made in cosmology. It does not hide problems faced by modern cosmology as well as issues the community has no consensus about. It also does not try to pass hypotheses for established theories, which is not uncommon in scholarly articles.

--> Contents:

• The Laws of the Universe
• The Expanding Universe
• Early Universe
• Dark Matter
• Dark Energy
• Black Holes and Other Exotics

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--> Readership: Students and teachers, also suitable for the general public, together with astronomy enthusiasts. -->
Keywords:Cosmology;Popular Science;Physics;Gravitation;Relativity;Astrophysics;Universe;Big BangReview: Key Features:

• The book offers high-quality popular description of cosmology and related subjects, aimed both at general audience and professional scientists from other fields
• The book contains detailed and comprehensive explanations of all main cosmological issues, as well as the latest available data and results with due discussion
• The book contains the derivation of cosmological equations without the use of the complicated mathematical formalism of General Relativity, and thus can be used as a basic textbook

Chapter 1

The Laws of the Universe

1.1Roots of Cosmology

This book is about cosmology—a science about the structure and evolution of the Universe in its entirety, its past and its future. Cosmology is a very young science; it just celebrated its centennial. Its creation is associated with the publication of Albert Einstein’s 1917 paper “Cosmological Considerations on the General Theory of Relativity” [Einstein et al., 1952]. It was for the first time when physical laws were applied to the whole Universe. Specifically, this article applied the equations of the General Theory of Relativity, formulated by Einstein shortly before.

Technically, nothing prevented this science to appear some 250 years earlier, right after the discovery of the Law of Universal Gravitation by Sir Isaac Newton. The physicists of 17^th–19^th centuries speculated about an infinite Universe filled with stars with planetary systems. Such a Universe existed eternally, and all it took to predict its future state was the knowledge of the laws of mechanics and the current position of all objects. However, the gravitational force in Newtonian mechanics has one peculiarity: it is always the attracting force that never becomes a repulsion force. Therefore, individual stars in an infinite Universe were bound to gather at some point due to attraction. This problem was evaded using a simple, but incorrect, idea. Since the Universe is infinite, each particle is attracted to an infinite number of other particles. If particles fill the Universe with constant density, the resulting force would become zero and the gravitation can be neglected when considering the dynamics of the Universe as a whole.

This idea is as productive as an attempt to set a pencil standing on its tip. The reason for failure in both cases is the instability of the equilibrium. If we somehow managed to make a pencil stand on its tip, any deviation from this position will induce a momentum in the same direction, magnifying the initial deviation and ultimately ruining the equilibrium. In engineering this effect is known as positive feedback.

A closer analogy is an upturned glass of water. Many of you know a classical demonstration when a glass of water covered with a firm sheet is turned upside down and the sheet is held in place by the atmospheric pressure force, which is equivalent to the weight of 10.3 metres of water. But few ponder why the sheet is needed for that demonstration. The answer is Rayleigh–Taylor instability: when a denser liquid (water) is put on top of a rarer liquid (air^a), any deviation from a flat boundary will grow over time exponentially, ruining the boundary very quickly. This is popularly known as spilling of liquid. This is why a firm sheet is needed: it does not apply any forces, but prevents the Rayleigh–Taylor instability from developing.

Note that the mutual attraction of the stars that fill the infinite Universe not only leads to an increase of its density irregularities, but also to the accelerated contraction of the whole Universe, that is, to decreasing distances between the stars.

Naturally, it was known by that time that deviations from a homogeneous distribution of matter density led to their growth, but this mechanism was then considered only on the spatial scale of the Solar System. According to Laplace hypothesis, the planets in the Solar System were formed from a primordial nebula made of gas and dust due to mutual gravitational attraction. Such a treatment was not extended to larger scales. In the big picture of that time, the growth of matter density inhomogeneities led to the formation of planets which did not fall on the Sun only because they orbited it. On scales larger than distances between nearest stars, the Universe was considered as something homogeneous and a belief was held that the attraction force of any body to different stars is fully compensated.

The only problem which marred this glorious picture was the so-called Olbers paradox, formulated in 1823 by a German amateur astronomer Heinrich Olbers, a medic by trade. Its point was that in an infinite static Universe instead of a night sky we would see a burning sphere as bright as the Sun. It can be explained in the following way. Let us divide the Universe into geocentric nested spherical layers with constant thickness. The number of stars in each layer will grow as a square of distance, and the flux from each single star will decrease as a square of distance. Thus, the flux from each layer will be the same. Since the number of layers if infinite, the total flux will be also infinite.

However, if we take into account that stars can cover each other, we obtain that the luminosity will be finite, because no matter which direction we look at, our line of sight will inevitably reach some star. Although, anyone who looked up in the sky at night knows that it looks quite different. A simple way to resolve the Olbers paradox was to write it off for the absorption of light by interstellar dust. However, this solution sounds credible only for those who studied physics poorly, as after long enough exposure this dust would be heated to the temperature of surrounding stars and become luminous.

The progress in astronomy led to a new model of the Universe proposed by William Herschel in the end of 18^th century. In this model the stars did not fill the whole Universe, but formed a single lens-shaped cluster called Galaxy. Why did they not fall on the centre of the Galaxy? The answer was the same as to why the planets did not fall on the Sun — they orbited it. Likewise, individual stars in the Galaxy orbited its centre. In 1783 Herschel discovered Sun’s movement around the centre of the Galaxy. This model with minor corrections was generally accepted till the beginning of the 20^th century. The idea of the Galaxy solved the Olbers paradox, since the matter now filled a finite volume in the Universe. Nevertheless, the discovery of other galaxies revived the Olbers paradox.

So, cosmology, which could potentially emerge in late 17^th century, appeared only in the beginning of the 20^th century. Usually new sciences are created in the simplest formulation and then evolve towards more complex models and calculations and use modern physical theories. For example, condensed matter physics relied on classical mechanics for centuries and successfully switched to quantum mechanics much later.

The cosmology is curious because it was created in its most complex form — relativistic cosmology. Only several decades later cosmologists reached a surprising conclusion that they could consider a much simpler non-relativistic cosmology. This is possible because a uniform Universe evolves identically in every point of space, and to study it in its entirety it is sufficient to consider a small volume, e.g. 1 cm³. And when studying 1 cm³ one can ignore space-time curvature and other complicated problems of General Relativity. But this is true only in the case of a homogeneous and isotropic Universe. In such a world there are no chosen places and preferred directions, every point is not better or worse than any other, and each direction is not better or worse than any other; this is known as the Copernicus principle.

Not every result of relativistic cosmology can be obtained in this way, but the main ones can be obtained quite easily. To derive, understand, and analyze these results it is sufficient to know physics at college level. For this reason, when we simply can not resist the urge to write some formulae in this book, we shall limit ourselves to non-relativistic cosmology.

We marked the parts containing mathematics “Advanced material”. They can be skipped without much loss to the understanding.

Question: What is the principal difference between cosmology and other areas of physics?

Answer: Cosmology studies a unique object, only one copy of which exists, which is changing in time, and containing us as a part. Thus, we can achieve neither repeatability nor reproducibility, and we can forget about active experiments. As a result, it is very difficult to check cosmological theories for falsifiability, which is required of any scientific theory. A similar situation is encountered in some other scientific disciplines, such as history and evolutionary biology.

1.2Principles of General Relativity

The emergence of cosmology as a science was preceded by the creation of the General Theory of Relativity (GTR), finally formulated by Einstein in 1916. This theory is one of the pinnacles of modern physics. Since its ideas and terminology are widely used in cosmology, we decided to describe the basics of GTR, which are simple enough to understand and can be explained without the use of its very sophisticated mathematical formalism. We start with the three classical GTR effects.

1.2.1Perihelion precession

The first effect was discovered by the astronomers long before the emergence of General Relativity. It is the perihelion^b precession^c of Mercury, which is manifested as the rotation of Mercury’s orbit as a whole around the Sun with very small angular velocity — less than 6 arcseconds per year. This was not the first deviation from the laws of celestial mechanics since their discovery by Johann Kepler. Earlier in the middle of 19^th century a similar behaviour of Uranus’ orbit was successfully explained by interference from a then-unknown planet, later called Neptune. One of Neptune’s predictors, Urbain Le Verrier, carried over the same approach to Mercury’s orbit, assuming the existence of a new planet Vulcan, which should have been located very close to the Sun and was hidden by his light. This hypothetical planet’s transits over solar disk were reported by both professional and amateur astronomers for a few decades afterwards, but these were later dismissed with the improvement of telescopes. Now we know for certain that Vulcan does not exist, and this was almost certain 100 years ago. Thus, perturbations of Mercury’s orbit should have been explained in a different way.

General Relativity not only explained the perihelion precession of Mercury but also provided an accurate quantitative agreement with the observed precession rate. With further improvement of the observational accuracy, a similar perihelion precession of Venus was discovered, which, together with other effects described below, heavily supported GTR. As a result, the International Astronomical Union (IAU) — the supreme world authority on astronomy—issued a resolution on the mandatory inclusion of the General Relativity effects in precise orbit calculation of celestial bodies in the Solar System. An even more impressive manifestation of this effect is displayed in binary systems with pulsars,^d where two massive bodies rotate at a small distance with a period of a few days. GTR describes their motion up to 0.01 per cent accuracy. The discovery of such systems brought a 1993 Nobel Prize in Physics to Russell Alan Hulse and Joseph Hooton Taylor, Jr.

1.2.2Deviation of light

The second effect is the bending of light rays in the gravitational field of massive objects. The bending itself was not a humbling sensation at the time and could be explained within the framework of the Newtonian mechanics. But the General Relativity predicted the angle of deviation to be twice as large compared to the Newtonian prediction. The nature of this coefficient will be discussed slightly later, in Subsection 1.3.2.

At that time the effect was purely hypothetical but this discrepancy prompted astronomers to measure its value. To do so, it was necessary to measure the position of a star, whose light travelled near the Sun and deviated in his gravitational field, changing the star’s apparent position. With modern accuracy using a very-long base radio interferometer (VLBI) this effect can be measured even in the perpendicular direction to the Sun, but in the beginning of the 20^th century, it could be measured only in a very small area around the Sun.

This was done by the expedition of Sir Arthur Eddington which measured star positions during the total solar eclipse of 1919. The total solar eclipse was required because at that time astronomers could perform observations only in visible light and the sunshine would make it impossible to observe stars. Eddington and his collaborators performed observations from Brazil and from the west coast of Africa. Comparing the photographs of the sky near the eclipsed Sun and of the same area far from the Sun, they measured the deviation angle, which appeared to be in favour of Einstein’s prediction. These observations were plagued by poor accuracy, which was substantially improved only with the invention of radio telescopes.

This effect is the basis for the so-called gravitational lensing, which produces several images of the same object. It is actively studied today and even used as an exotic tool for observing extremely distant objects. We discuss this in Subsection 4.2.7.

1.2.3Gravitational redshift

The third effect is called gravitational redshift^e and describes the difference in the rate of time at different gravity potentials.^f Simply speaking, time runs faster on the top floor of the building than in the basement. A source transmits, say, 1000 signals per second. They propagate to the receiver, but for the receiver a second has a different duration, so during that second it receives not 1000, but, e.g. 999 signals. In other words, the frequency at the receiver is shifted with respect to the frequency of the source.

Astronomers observed gravitational redshift in white dwarf stars, in particular, in Sirius B, which packs roughly the mass of...

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• Dedication
• Preface
• Contents
• List of Table
• List of Figures
• Chapter 1. The Laws of the Universe
• Chapter 2. The Expanding Universe
• Chapter 3. Early Universe
• Chapter 4. Dark Matter
• Chapter 5. Dark Energy
• Chapter 6. Black Holes and Other Exotics
• Summary
• Appendix A. Cosmological Evolution with a Cosmological Constant*
• Bibliography
• Index