Cosmology

I

Introduction

Cosmology, science of the charting of the universe, and of investigating its remote origins in space and time. Galaxies are the fundamental beacons that demarcate the most remote reaches of the universe. The most distant galaxies, visible with the aid of giant telescopes, are billions of light years away. Hence one sees remote galaxies as they were billions of years ago, in their youth, and their evolution can be studied and their origin probed. The science of cosmology involves modelling the beginning of the universe, following its evolution, and predicting its destiny.

II

Ancient Cosmology

The prehistory of cosmology is intimately tied to myths of Creation, with the supposition that there is a supreme maker or deity responsible for the emergence of the universe. The Greek philosophers attempted to propose a self-consistent cosmology, in which the universe could be explained in terms of the interactions of one or a few fundamental elements. Thales of Miletus proposed that water was the basis of everything and subsequently Anaximenes, Heraclitus, and Xenophanes proposed air, fire, and earth as alternatives. Aristotle developed a cosmology based on all four of these elements and the “four fundamental qualities” of hot, cold, dry, and wet. Between the concentric crystal spheres, which he believed carried the Sun, planets, and stars, he added a fifth “divine substance”, known as the ether, or quintessence.

The idea of a harmonious universe based on geometry can be traced to Pythagoras, who proposed a set of two perfect spheres: a central sphere that consisted of the Earth, and an outer sphere supporting the stars. Aristotle elaborated on this model and posited the existence of many spheres. The Earth, which consisted of the four elements, was at the centre, while the planets and stars were located on 55 supporting spheres made of quintessence. It was Ptolemy who, in his Almagest, combined the ideas of Aristotle with the observations of the motions of the stars to propose that the circular motions were slightly off centre. In Ptolemy’s model, the planets followed small circles called epicycles in their circular progress around the Earth. Using this elaborate system, he was able to match the observations with reasonable precision.

The success of the Ptolemaic system made it the standard cosmology until the 15th century. However, an alternative model of the universe, championed by Epicurus in the 4th century bc, and by Lucretius in the 1st century bc, posited the existence of many worlds made of atoms. These universes would be spread out in an infinite void governed by the laws of nature.

III

Classical Cosmology

The first major change to the Ptolemaic universe was proposed by Nicholas Copernicus, who proposed, in De Revolutionibus Orbium Coelestium (On the Revolutions of the Celestial Spheres), published in 1543, that the Earth moves around the Sun. He argued that the planets follow circular orbits around the Sun, but in doing so he constructed a cosmos that could not account for their movements with the same precision as Ptolemy’s epicycles. Building on the accurate planetary observations of Tycho Brahe, Johannes Kepler was able to show in the early 17th century that the planetary orbits were in fact elliptical. In doing so he was able to demonstrate that the heliocentric (Sun-centred) model of the universe matched the precision of the Ptolemaic universe. The observations by Galileo Galilei of the structure of the planets further contributed to the demise of the Ptolemaic and Aristotelian universe by showing that the planets were similar in nature to the Earth. He showed that the Moon has valleys and mountains and that Jupiter has moons, and hence that the outer, celestial spheres are no different from the inner, Earthly sphere.

Later in the 17th century, Sir Isaac Newton proposed that all objects were attracted to each other by an invisible force, which he called gravity. Using his law of gravitation, one could mathematically derive the motion of celestial bodies, the tides, the flattening of the Earth, and a host of natural phenomena. Newton argued that the universe had to be infinite and uniform if it were to remain stable under the effect of the attractive gravitational force.

For the next 200 years, two pictures of the universe competed within the scientific canon. Astronomical observations showed that stars were not distributed uniformly in the sky, but form an arch of light—the Milky Way. The Sun was one of many stars in this structure, albeit with a possibly privileged position. This galaxy of stars—the Galaxy—was claimed by Immanuel Kant to be one of many island universes spread throughout space. Faint patches of light that could not be resolved as individual stars, the nebulae, were examples of distant galaxies just like our own.

The competing view was that these nebulae were merely bright regions of our galaxy where stars and planets may be forming; the Milky Way was claimed to be the only star system of appreciable size, a unique island universe. To resolve this debate it was necessary to develop accurate methods of measuring astronomical distances in order to map out the Galaxy and the distances to the nebulae.

Early in the 19th century, Caroline and William Herschel had mapped out the Galaxy and found it to be a flattened system with the Sun located near the centre. They resolved some of the nebulae to find that they were agglomerations of stars, a tentative indication that they may be distant galaxies. In the 1840s, Friedrich Bessel used the method of parallax to measure the distance to the star 61 Cygni and found it to be 11 light years away, giving a first idea of interstellar distances. The one-island universe hypothesis was supported by the measurements of William Huggins, who showed that the atomic spectra of one nebula were very different from that of the Sun, pointing to the possibility that it was an unformed star or planet.

The first breakthrough came in 1912 when Henrietta Leavitt discovered that Cepheid variables (stars whose brightness varies with time) have a strong correlation between their variability and their intrinsic brightness. Her studies of Cepheids in the Magellanic Clouds led to a new and accurate way of measuring the distances of remote objects. The debate over the one-island universe concept raged for a few more years until, in 1924, Edwin Hubble found Cepheid variables in the spiral arms of the M31 (now known as the Andromeda Galaxy) and M33 nebulae. He was able to use these to measure the distance to M31 and found it to be 1 million light years away, far beyond the outer reaches of the Galaxy. A subsequent re-analysis by Walter Baade showed it to be twice as far away (the error had arisen from the existence of more than one type of Cepheid variable). These measurements firmly pointed to a universe populated with multiple galaxies at vast distances from our own.

IV

Modern Cosmology and the Big Bang

There is currently a successful working hypothesis for the evolution of the universe: the theory of the big bang. This theory, now widely accepted by cosmologists, states that the universe originated from a point or singularity in one massive fireball in which space and time began, and that it has been expanding ever since.

The big bang is predicted by Albert Einstein’s theory of general relativity. General relativity explains the gravitational effect between massive bodies as deformations of space-time. Space-time will be warped in the presence of energy (in the form of matter or otherwise). This warping of space-time will, in response, affect the motion of objects by distorting their paths. The result is an inherently dynamical picture in which space-time is constantly changing due to the motion of the objects which it contains. To describe the evolution of the universe as a whole, one must use general relativity to follow the evolution of all of space-time as it responds to all the energy contained in it. To do so, it is necessary to assume that space is homogeneous and isotropic. Homogeneity requires that all physical quantities have the same value at all points of space, at a given time. Isotropy requires that the universe looks the same in all directions. There is strong evidence from looking at the distribution of light in the sky that these assumptions are valid on very large scales.

In the late 1920s, Alexander Friedman and Georges Lemaître used Einstein’s theory of general relativity to propose a model for a strictly homogeneous and isotropic universe. Consider a perfectly smooth distribution of energy over all space. For homogeneity to be preserved, there are only three possible types of evolution allowed: space stretches or contracts equally at each point in space, or it remains static. Einstein’s theory of general relativity is our modern explanation of gravity, and the basic known fact about gravitating systems is that objects attract each other. This makes the static configuration unstable. Indeed if we set up our universe in such a static configuration, the gravitational pull of the distribution of energy (through its effect on space-time) will lead it to start contracting. We are then left with either an expanding universe that is decelerating due to the pull of gravity, or a contracting universe that is accelerating towards a final collapse. The evidence indicates that the universe is expanding.

According to the big bang model, the universe has been expanding for about 13.7 billion years. As the universe expands, its density and temperature decrease. Hence the universe was much hotter and more energetic in the past. A brief history of the universe would be as follows.

Before the universe was 1 thousandth of a billionth of a second old, it consisted of a hot plasma of essentially mass-less, fundamental particles that interacted with each other through the strong, weak, electromagnetic, and gravitational forces (see Fundamental Forces). When the universe cooled down below 1 million billion Kelvin (K), and was 1 thousandth of a billionth of a second old, many of the fundamental particles acquired a mass through a change in the properties of the electromagnetic and weak forces. The universe was still sufficiently hot for the lighter particles to collide and form short-lived, heavier particles. However, as the universe cooled down, fewer and fewer unstable particles were created, and most of the energy of the universe was deposited in lighter, stable particles. When the temperature of the universe fell below 1 thousand billion K, when it was 1 millionth of a second old, quarks combined into triplets to form baryons or into doublets to form mesons. The most stable baryons are protons and neutrons. These baryons subsequently combined to produce the nuclei of the elements hydrogen, helium, and lithium when the universe had cooled to a temperature of 1 billion K, which occurred when it was a few minutes old.

The universe continued to cool down until its temperature fell below 3,000 K, when it was 300,000 years old. At that time the energy of the negatively charged electrons was sufficiently small for them to be captured by the positively charged nuclei leading to the formation of neutral atoms of hydrogen, helium, and lithium. This is known as the epoch of recombination. Until now, the universe had been opaque. With the formation of atoms, it became optically transparent because light in the form of photons could essentially propagate unhindered throughout space. The relic electromagnetic radiation left over from recombination, now greatly degraded in energy, pervades the universe. It is known as the cosmic microwave background (see Background Radiation).

After the first few million years, slight irregularities in the distribution of energy grew under gravity into dense, massive objects that became the first stars. In the cores of these stars, the heavier elements were synthesized and subsequently expelled into interstellar space when the stars eventually exploded as supernovae. Larger irregularities in the distribution of mass led to the formation of galaxies when the universe was a few billion years old, with the formation of our solar system approximately 4.6 billion years ago. Our universe now has an ambient temperature of a few K.

V

Evidence for the Big Bang