Definitions

# Physical cosmology

Physical cosmology, as a branch of astronomy, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. Cosmology involves itself with studying the motions of the celestial bodies and the first cause. For most of human history, it has been a branch of metaphysics. Cosmology as a science originates with the Copernican principle, which implies that celestial bodies obey identical physical laws to those on earth, and Newtonian mechanics, which first allowed us to understand those motions. This is now called celestial mechanics. Physical cosmology, as it is now understood, began with the twentieth century development of Albert Einstein's general theory of relativity and better astronomical observations of extremely distant objects.

The twentieth century advances made it possible to speculate about the origins of the universe and allowed scientists to establish the Big Bang as the leading cosmological theory, which most cosmologists now accept as the basis for their theories and observations. Vanishingly few researchers still advocate any of a handful of alternative cosmologies, but professional cosmologists generally agree that the big bang best explains observations. Physical cosmology, roughly speaking, deals with the very largest objects in the universe (galaxies, clusters and superclusters), the very earliest distinct objects to form (quasars) and the very early universe, when it was nearly homogeneous (hot big bang, cosmic inflation, cosmic microwave background radiation and the Weyl curvature hypothesis).

Cosmology is unusual in physics for drawing heavily on the work of particle physicists' experiments, and research into phenomenology and even string theory; from astrophysicists; from general relativity research; and from plasma physics. Thus, cosmology unites the physics of the largest structures in the universe to the physics of the smallest structures in the universe.

## Energy of the cosmos

Light elements, primarily hydrogen and helium, were created in the Big Bang. These light elements were spread too fast and too thinly in the Big Bang process (see nucleosynthesis) to form the most stable medium-sized atomic nuclei, like iron and nickel. This fact allows for later energy release, as such intermediate-sized elements are formed in our era. The formation of such atoms powers the steady energy-releasing reactions in stars, and also contributes to sudden energy releases, such as in novae. Gravitational collapse of matter into black holes is also thought to power the most energetic processes, generally seen at the centers of galaxies (see quasars and in general active galaxies).

Cosmologists are still unable to explain all cosmological phenomena purely on the basis of known conventional forms of energy, for example those related to the accelerating expansion of the universe, and therefore invoke a yet unexplored form of energy called dark energy to account for certain cosmological observations. One hypothesis is that dark energy is the energy of virtual particles (which mathematically must exist in vacuum due to the uncertainty principle).

There is no unambiguous way to define the total energy of the universe in the current best theory of gravity, general relativity. As a result it remains controversial whether one can meaningfully say that total energy is conserved in an expanding universe. For instance, each photon that travels through intergalactic space loses energy due to the redshift effect. This energy is not obviously transferred to any other system, so seems to be permanently lost. Nevertheless some cosmologists insist that energy is conserved in some sense.

Thermodynamics of the universe is a field of study to explore which form of energy dominates the cosmos - relativistic particles which are referred to as radiation, or non-relativistic particles which are referred to as matter. The former are particles whose rest mass is zero or negligible compared to their energy, and therefore move at the speed of light or very close to it; the latter are particles whose kinetic energy is much lower than their rest mass and therefore move much slower than the speed of light.

As the universe expands, both matter and radiation in it become diluted. However, the universe also cools down, meaning that the average energy per particle is getting smaller with time. Therefore the radiation becomes weaker, and dilutes faster than matter. Thus with the expansion of the universe radiation becomes less dominant than matter. In the very early universe radiation dictates the rate of deceleration of the universe's expansion, and the universe is said to be 'radiation dominated'. At later times, when the average energy per photon is roughly 10 eV and lower, matter dictates the rate of deceleration and the universe is said to be 'matter dominated'. The intermediate case is not treated well analytically. As the expansion of the universe continues, matter dilutes even further and the cosmological constant becomes dominant, leading to an acceleration in the universe's expansion.

## History of physical cosmology

Modern cosmology developed along tandem observational and theoretical tracks. In 1915, Albert Einstein developed his theory of general relativity. At the time, physicists were prejudiced to believe in a perfectly static universe without beginning or end. Einstein added a cosmological constant to his theory to try to force it to allow for a static universe with matter in it. The so-called Einstein universe is, however, unstable. It is bound to eventually start expanding or contracting. The cosmological solutions of general relativity were found by Alexander Friedmann, whose equations describe the Friedmann-Lemaître-Robertson-Walker universe, which may expand or contract.

In the 1910s, Vesto Slipher and later Carl Wilhelm Wirtz interpreted the red shift of spiral nebulae as a Doppler shift that indicated they were receding from Earth. However, it is notoriously difficult to determine the distance to astronomical objects: even if it is possible to measure their angular size it is usually impossible to know their actual size or luminosity. They did not realize that the nebulae were actually galaxies outside our own Milky Way, nor did they speculate about the cosmological implications. In 1927, the Belgian Roman Catholic priest Georges Lemaître independently derived the Friedmann-Lemaître-Robertson-Walker equations and proposed, on the basis of the recession of spiral nebulae, that the universe began with the "explosion" of a "primeval atom"—what was later called the big bang. In 1929, Edwin Hubble provided an observational basis for Lemaître's theory. Hubble proved that the spiral nebulae were galaxies and measured their distances by observing Cepheid variable stars. He discovered a relationship between the redshift of a galaxy and its luminosity. He interpreted this as evidence that the galaxies are receding in every direction at speeds (relative to the Earth) directly proportional to their distance. This fact is known as Hubble's law. The relationship between distance and speed, however, was accurately ascertained only relatively recently: Hubble was off by a factor of ten.

Given the cosmological principle, Hubble's law suggested that the universe was expanding. This idea allowed for two opposing possibilities. One was Lemaître's Big Bang theory, advocated and developed by George Gamow. The other possibility was Fred Hoyle's steady state model in which new matter would be created as the galaxies moved away from each other. In this model, the universe is roughly the same at any point in time.

For a number of years the support for these theories was evenly divided. However, the observational evidence began to support the idea that the universe evolved from a hot dense state. Since the discovery of the cosmic microwave background in 1965 it has been regarded as the best theory of the origin and evolution of the cosmos. Before the late 1960s, many cosmologists thought the infinitely dense singularity at the starting time of Friedmann's cosmological model was a mathematical over-idealization, and that the universe was contracting before entering the hot dense state and starting to expand again. This is Richard Tolman's oscillatory universe. In the sixties, Stephen Hawking and Roger Penrose demonstrated that this idea was unworkable, and the singularity is an essential feature of Einstein's gravity. This led the majority of cosmologists to accept the Big Bang, in which the universe we observe began a finite time ago.

## History of the Universe

The history of the universe is a central issue in cosmology. According to the standard theory of cosmology, the history of the universe is divided into different periods called epochs, according to the dominant forces and processes in each period. The standard cosmological model is known as ΛCDM model.

### Equations of motion

The equations of motion governing the universe as a whole are derived from general relativity with a small, positive cosmological constant. The solution is an expanding universe; due to this expansion the radiation and matter in the universe are cooled down and become diluted. At first the expansion is slowed down by gravitation due to the radiation and matter content of the universe. However, as these become diluted, the cosmological constant becomes more dominant and the expansion of the universe starts to accelerate rather than decelerate. In our universe this has already happened, billions of years ago.

### Particle physics in cosmology

Particle physics, which deals with high energies, is extremely important in the behavior of the early universe, since it was so hot that the average energy density was very high. Because of this, scattering processes and decay of unstable particles are important in cosmology.

As a thumb rule, a scattering or a decay process is cosmologically important in a certain cosmological epoch if its relevant time scale is smaller or comparable to the time scale of the universe expansion, which is $1/H$ with $H$ being the Hubble constant at that time. This is roughly equal to the age of the universe at that time.

### Timeline of the Big Bang

Observations suggest that the universe as we know it began around 13.7 billion years ago. Since then, the evolution of the universe has passed through three phases. The very early universe, which is still poorly understood, was the split second in which the universe was so hot that particles had energies higher than those currently accessible in particle accelerators on Earth. Therefore, while the basic features of this epoch have been worked out in the big bang theory, the details are largely based on educated guesses. Following this, in the early universe, the evolution of the universe proceeded according to known high energy physics. This is when the first protons, electrons and neutrons formed, then nuclei and finally atoms. With the formation of neutral hydrogen, the cosmic microwave background was emitted. Finally, the epoch of structure formation began, when matter started to aggregate into the first stars and quasars, and ultimately galaxies, clusters of galaxies and superclusters formed. The future of the universe is not yet firmly known, but according to the ΛCDM model it will continue expanding forever.

## Areas of study

Below, some of the most active areas of inquiry in cosmology are described, in roughly chronological order. This does not include all of the big bang cosmology, which is presented in cosmological timeline.

### The very early universe

While the early, hot universe appears to be well explained by the big bang from roughly 10-33 seconds onwards, there are several problems. One is that there is no compelling reason, using current particle physics, to expect the universe to be flat, homogeneous and isotropic (see the cosmological principle). Moreover, grand unified theories of particle physics suggest that there should be magnetic monopoles in the universe, which have not been found. These problems are resolved by a brief period of cosmic inflation, which drives the universe to flatness; smooths out anisotropies and inhomogeneities to the observed level; and exponentially dilutes the monopoles. The physical model behind cosmic inflation is extremely simple, however it has not yet been confirmed by particle physics, and there are difficult problems reconciling inflation and quantum field theory. Some cosmologists think that string theory and brane cosmology will provide an alternative to inflation.

Another major problem in cosmology is what has caused the universe to contain more particles than antiparticles. Cosmologists can use X-ray observations to deduce that the universe is not split into regions of matter and antimatter, but rather is predominantly made of matter. This problem is called the baryon asymmetry, and the theory to describe the resolution is called baryogenesis. The theory of baryogenesis was worked out by Andrei Sakharov in 1967, and requires a violation of the particle physics symmetry, called CP-symmetry, between matter and antimatter. Particle accelerators, however, measure too small a violation of CP-symmetry to account for the baryon asymmetry. Cosmologists and particle physicists are trying to find additional violations of the CP-symmetry in the early universe that might account for the baryon asymmetry.

Both the problems of baryogenesis and cosmic inflation are very closely related to particle physics, and their resolution might come from high energy theory and experiment, rather than through observations of the universe.

### Big bang nucleosynthesis

Big Bang Nucleosynthesis is the theory of the formation of the elements in the early universe. It finished when the universe was about three minutes old and its temperature fell enough that nuclear fusion ceased. Because the time in which big bang nucleosynthesis occurred was so short, only the very lightest elements were produced, unlike in stellar nucleosynthesis. Starting from hydrogen ions (protons), it principally produced deuterium, helium-4 and lithium. Other elements were produced in only trace abundances. While the basic theory of nucleosynthesis has been understood for decades (it was developed in 1948 by George Gamow, Ralph Asher Alpher and Robert Herman) it is an extremely sensitive probe of physics at the time of the big bang, as the theory of big bang nucleosynthesis connects the abundances of primordial light elements with the features of the early universe. Specifically, it can be used to test the equivalence principle, to probe dark matter and test neutrino physics. Some cosmologists have proposed that big bang nucleosynthesis suggests there is a fourth "sterile" species of neutrino.

### Cosmic microwave background

The cosmic microwave background is radiation left over from decoupling, when atoms first formed, and the radiation produced in the big bang stopped Thomson scattering from charged ions. The radiation, first observed in 1965 by Arno Penzias and Robert Woodrow Wilson, has a perfect thermal black-body spectrum. It has a temperature of 2.7 kelvins today and is isotropic to one part in 105. Cosmological perturbation theory, which describes the evolution of slight inhomogeneities in the early universe, has allowed cosmologists to precisely calculate the angular power spectrum of the radiation, and it has been measured by the recent satellite experiments (COBE and WMAP) and many ground and balloon-based experiments (such as Degree Angular Scale Interferometer, Cosmic Background Imager, and Boomerang). One of the goals of these efforts is to measure the basic parameters of the Lambda-CDM model with increasing accuracy, as well as to test the predictions of the big bang model and look for new physics. The recent measurements made by WMAP, for example, have placed limits on the neutrino masses.

Newer experiments, such as the Atacama Cosmology Telescope and the QUIET telescope, are trying to measure the polarization of the cosmic microwave background, which will provide further confirmation of the theory as well as information about cosmic inflation, and the so-called secondary anisotropies, such as the Sunyaev-Zel'dovich effect and Sachs-Wolfe effect, which are caused by interaction between galaxies and clusters with the cosmic microwave background.

### Formation and evolution of large-scale structure

Understanding the formation and evolution of the largest and earliest structures (ie, quasars, galaxies, clusters and superclusters) is one of the largest efforts in cosmology. Cosmologists study a model of hierarchical structure formation in which structures form from the bottom up, with smaller objects forming first, while the largest objects, such as superclusters, are still assembling. The most straightforward way to study structure in the universe is to survey the visible galaxies, in order to construct a three-dimensional picture of the galaxies in the universe and measure the matter power spectrum. This is the approach of the Sloan Digital Sky Survey and the 2dF Galaxy Redshift Survey.

An important tool for understanding structure formation is simulations, which cosmologists use to study the gravitational aggregation of matter in the universe, as it clusters into filaments, superclusters and voids. Most simulations contain only non-baryonic cold dark matter, which should suffice to understand the universe on the largest scales, as there is much more dark matter in the universe than visible, baryonic matter. More advanced simulations are starting to include baryons and study the formation of individual galaxies. Cosmologists study these simulations to see if they agree with the galaxy surveys, and to understand any discrepancy.

Other, complementary techniques will allow cosmologists to measure the distribution of matter in the distant universe and to probe reionization. These include:

• The Lyman alpha forest, which allows cosmologists to measure the distribution of neutral atomic hydrogen gas in the early universe, by measuring the absorption of light from distant quasars by the gas.
• The 21 centimeter absorption line of neutral atomic hydrogen also provides a sensitive test of cosmology
• Weak lensing, the distortion of a distant image by gravitational lensing due to dark matter.

These will help cosmologists settle the question of when the first quasars formed.

### Dark matter

Evidence from big bang nucleosynthesis, the cosmic microwave background and structure formation suggests that about 25% of the mass of the universe consists of non-baryonic dark matter, whereas only 4% consists of visible, baryonic matter. The gravitational effects of dark matter are well understood, as it behaves like cold, non-radiative dust which forms haloes around galaxies. Dark matter has never been detected in the laboratory: the particle physics nature of dark matter is completely unknown. However, there are a number of candidates, such as a stable supersymmetric particle, a weakly interacting massive particle, an axion, and a massive compact halo object. Alternatives to the dark matter hypothesis include a modification of gravity at small accelerations (MOND) or an effect from brane cosmology.

The physics at the center of galaxies (see active galactic nuclei, supermassive black hole) may give some clues about the nature of dark matter.

### Dark energy

If the universe is to be flat, there must be an additional component making up 74% (in addition to the 22% dark matter and 4% baryons) of the energy density of the universe. This is called dark energy. In order not to interfere with big bang nucleosynthesis and the cosmic microwave background, it must not cluster in haloes like baryons and dark matter. There is strong observational evidence for dark energy, as the total mass of the universe is known, since it is measured to be flat, but the amount of clustering matter is tightly measured, and is much less than this. The case for dark energy was strengthened in 1999, when measurements demonstrated that the expansion of the universe has begun to gradually accelerate.

However, apart from its density and its clustering properties, nothing is known about dark energy. Quantum field theory predicts a cosmological constant much like dark energy, but 120 orders of magnitude too large. Steven Weinberg and a number of string theorists (see string landscape) have used this as evidence for the anthropic principle, which suggests that the cosmological constant is so small because life (and thus physicists, to make observations) cannot exist in a universe with a large cosmological constant, but many people find this an unsatisfying explanation. Other possible explanations for dark energy include quintessence or a modification of gravity on the largest scales. The effect on cosmology of the dark energy that these models describe is given by the dark energy's equation of state, which varies depending upon the theory. The nature of dark energy is one of the most challenging problems in cosmology.

A better understanding of dark energy is likely to solve the problem of the ultimate fate of the universe. In the current cosmological epoch, the accelerated expansion due to dark energy is preventing structures larger than superclusters from forming. It is not known whether the acceleration will continue indefinitely, perhaps even increasing until a big rip, or whether it will eventually reverse.

### Other areas of inquiry

Cosmologists also study:

## References

### Textbooks

• Cheng, Ta-Pei (2005). Relativity, Gravitation and Cosmology: a Basic Introduction. Oxford and New York: Oxford University Press. ISBN 0-19-852957-0. Cosmology is introduced in the framework of general relativity -- but without the full tensor apparatus, which is presented in the last part of the book. Particularly suitable for an introductory GR course with an emphasis on cosmology.
• Dodelson, Scott (2003). Modern Cosmology. Academic Press. ISBN 0-12-219141-2. Released slightly before the WMAP results, this is the most modern introductory textbook.
• Grøn, Øyvind; Hervik, Sigbjørn (2007). Einstein's General Theory of Relativity with Modern Applications in Cosmology. New York: Springer. ISBN 978-0-387-69199-2.
• Harrison, Edward (2000). Cosmology: the science of the universe. Cambridge University Press. ISBN 0-521-66148-X. A relatively unmathematical textbook.
• Kutner, Marc (2003). Astronomy: A Physical Perspective. Cambridge University Press. ISBN 0-521-52927-1. An introductory astronomy textbook.
• Kolb, Edward; Michael Turner (1988). The Early Universe. Addison-Wesley. ISBN 0-201-11604-9. This is the classic reference for cosmologists.
• Liddle, Andrew (2003). An Introduction to Modern Cosmology. John Wiley. ISBN 0-470-84835-9. An introduction to cosmology without General Relativity
• Liddle, Andrew; David Lyth (2000). Cosmological Inflation and Large-Scale Structure. Cambridge. ISBN 0-521-57598-2. An introduction to cosmology with a thorough discussion of inflation.
• Mukhanov, Viatcheslav (2005). Physical Foundations of Cosmology. Cambridge University Press. ISBN 0-521-56398-4.
• Padmanabhan, T. (1993). Structure formation in the universe. Cambridge University Press. ISBN 0-521-42486-0. Describes the formation of large-scale structures in detail.
• Peacock, John (1998). Cosmological Physics. Cambridge University Press. ISBN 0-521-42270-1. An introduction with more background on general relativity and quantum field theory than most.
• Peebles, P. J. E. (1993). Principles of Physical Cosmology. Princeton University Press. ISBN 0-691-01933-9. Peebles' book has a strong historical focus.
• Peebles, P. J. E. (1980). The Large-Scale Structure of the Universe. Princeton University Press. ISBN 0-691-08240-5. The classic work on large scale structure, in particular the discussion of correlation functions.
• Rees, Martin (2002). New Perspectives in Astrophysical Cosmology. Cambridge University Press. ISBN 0-521-64544-1.
• Weinberg, Steven (1971). Gravitation and Cosmology. John Wiley. ISBN 0-471-92567-5. An older book, but still a standard reference for a lot of the mathematical formalism.

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