Modern Cosmology -
Part I: The Observable Universe
Jacobs University Bremen
Caption: Panoramic view of the entire near-infrared sky reveals the distribution of galaxies beyond the Milky Way. The image is derived from the 2MASS Extended Source Catalog (XSC) - more than 1.5 million galaxies, and the Point Source Catalog (PSC) - nearly 0.5 billion Milky Way stars. The galaxies are color coded by 'redshift' obtained from the UGC, CfA, Tully NBGC, LCRS, 2dF, 6dFGS, and SDSS surveys (and from various observations compiled by the NASA Extragalactic Database), or photo-metrically deduced from the K band (2.2 um). Blue are the nearest sources (z < 0.01); green are at moderate distances (0.01 < z < 0.04) and red are the most distant sources that 2MASS resolves (0.04 < z < 0.1). The map is projected with an equal area Aitoff in the Galactic system (Milky Way at center). [Image courtesy: Jarrett 2004]
|1. History and Overview
Astronomical models of the universe were proposed soon after astronomy began with the Babylonian astronomers, who viewed the universe as a flat disk floating in the ocean, and this forms the premise for early Greek maps like those of Anaximander and Hecataeus of Miletus.
Later Greek philosophers, observing the motions of the heavenly bodies, were concerned with developing models of the universe based more profoundly on empirical evidence. The first coherent model was proposed by Eudoxus of Cnidos. According to this model, space and time are infinite and eternal, the Earth is spherical and stationary, and all other matter is confined to rotating concentric spheres. This model was refined by Callippus and Aristotle, and brought into nearly perfect agreement with astronomical observations by Ptolemy. The success of this model is largely due to the mathematical fact that any function (such as the position of a planet) can be decomposed into a set of circular functions (the Fourier modes). However, not all Greek scientists accepted the geocentric model of the universe. The Pythagorean philosopher Philolaus postulated that at the center of the universe was a "central fire" around which the Earth, Sun, Moon and Planets revolved in uniform circular motion. The Greek astronomer Aristarchus of Samos was the first known individual to propose a heliocentric model of the universe. Though the original text has been lost, a reference in Archimedes' book The Sand Reckoner describes Aristarchus' heliocentric theory.
The Aristotelian model was accepted in the Western world for roughly two millennia, until Copernicus revived Aristarchus' theory that the astronomical data could be explained more plausibly if the earth rotated on its axis and if the sun were placed at the center of the universe. Copernicus' heliocentric model allowed the stars to be placed uniformly through the (infinite) space surrounding the planets, as first proposed by Thomas Digges in his Perfit Description of the Caelestiall Orbes according to the most aunciente doctrine of the Pythagoreans, latelye revived by Copernicus and by Geometricall Demonstrations approved (1576). Giordano Bruno accepted the idea that space was infinite and filled with solar systems similar to our own; for the publication of this view, he was burned at the stake in the Campo dei Fiori in Rome on 17 February 1600.
Caption: Johannes Kepler published the Rudolphinae Tables containing a star catalog and planetary tables using Tycho Brahe's measurements. These data were the basis for the development of Kepler's three fundamental laws of planetary motion.
This cosmology was accepted provisionally by Isaac Newton, Christiaan Huygens and later scientists, although it had several paradoxes that were resolved only with the development of general relativity. The first of these was that it assumed that space and time were infinite, and that the stars in the universe had been burning forever; however, since stars are constantly radiating energy, a finite star seems inconsistent with the radiation of infinite energy. Secondly, Edmund Halley (1720) and Jean-Philippe de Cheseaux (1744) noted independently that the assumption of an infinite space filled uniformly with stars would lead to the prediction that the nighttime sky would be as bright as the sun itself; this became known as Olbers' paradox in the 19th century. Third, Newton himself showed that an infinite space uniformly filled with matter would cause infinite forces and instabilities causing the matter to be crushed inwards under its own gravity. This instability was clarified in 1902 by the Jeans instability criterion. One solution to these latter two paradoxes is the Charlier universe, in which the matter is arranged hierarchically (systems of orbiting bodies that are themselves orbiting in a larger system, ad infinitum) in a fractal way such that the universe has a negligibly small overall density; such a cosmological model had also been proposed earlier in 1761 by Johann Heinrich Lambert. A significant astronomical advance of the 18th century was the realization by Thomas Wright, Immanuel Kant and others that stars are not distributed uniformly throughout space; rather, they are grouped into galaxies.
|2. The Observable Universe: Redshift and Distances
In the modern Big Bang Cosmology, the observable universe consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because light (or other signals) from those objects has had time to reach us since the beginning of the cosmological expansion. Assuming the Universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction - that is, the observable universe is a spherical volume (a 3-sphere surface) centered on the observer, regardless of the shape of the Universe as a whole. The actual shape of the Universe may or may not be spherical. However, the portion of it that we (humans, from the perspective of planet Earth) are able to observe is determined by whether or not the light and other signals originating from distant objects has had time to arrive at our point of observation (planet Earth). Therefore, the observable universe appears from our perspective to be spherical. Every location in the Universe has its own observable universe which may or may not overlap with the one centered around the Earth.
|3. The Observable Universe: CMB and Cosmic Web
The cosmic microwave background (CMB) was predicted in 1948 by George Gamow, Ralph Alpher, and Robert Herman. Alpher and Herman were able to estimate the temperature of the cosmic microwave background to be 5 K, though two years later they re-estimated it at 28 K. Although there were several previous estimates of the temperature of space, these suffered from two flaws. First, they were measurements of the effective temperature of space and did not suggest that space was filled with a thermal Planck spectrum. Next, they depend on our being at a special spot at the edge of the Milky Way galaxy and they did not suggest the radiation is isotropic. The estimates would yield very different predictions if Earth happened to be located elsewhere in the Universe.
The 1948 results of Alpher and Herman were discussed in many physics settings through about 1955, when each left the Applied Physics Laboratory at Johns Hopkins University. The mainstream astronomical community, however, was not intrigued at the time by cosmology. Alpher and Herman's prediction was rediscovered by Yakov Zel'dovich in the early 1960s, and independently predicted by Robert Dicke at the same time. The first published recognition of the CMB radiation as a detectable phenomenon appeared in a brief paper by Soviet astrophysicists A. G. Doroshkevich and Igor Novikov, in the spring of 1964. In 1964, David Todd Wilkinson and Peter Roll, Dicke's colleagues at Princeton University, began constructing a Dicke radiometer to measure the cosmic microwave background. In 1965, Arno Penzias and Robert Woodrow Wilson at the Crawford Hill location of Bell Telephone Laboratories in nearby Holmdel Township, New Jersey had built a Dicke radiometer that they intended to use for radio astronomy and satellite communication experiments. Their instrument had an excess 3.5 K antenna temperature which they could not account for. After receiving a telephone call from Crawford Hill, Dicke famously quipped: "Boys, we've been scooped." A meeting between the Princeton and Crawford Hill groups determined that the antenna temperature was indeed due to the microwave background. Penzias and Wilson received the 1978 Nobel Prize in Physics for their discovery.
Measurements of the CMB have made the inflationary Big Bang theory the standard model of the earliest eras of the universe. This theory predicts that the initial conditions for the universe are originally random in nature, and follow a roughly Gaussian probability distribution, which when graphed in cross-section forms bell-shaped curves. By analyzing this distribution at different frequencies, a spectral density or power spectrum is generated. The power spectrum of these fluctuations has been calculated, and agrees with the observations, although certain observables, for example the overall amplitude of the fluctuations, are more or less free parameters of the cosmic inflation model. Therefore, meaningful statements about the inhomogeneities in the universe need to be statistical in nature. This leads to cosmic variance in which the uncertainties in the variance of the largest scale fluctuations observed in the universe are difficult to accurately compare to theory. The model uses a Gaussian random field with a nearly scale invariant or Harrison-Zel'dovich spectrum to represent the primeval inhomogeneities.
|Ex_1||Lecture Notes: Part I
|LN: Part I|