Fundamental Observations of Modern Cosmology

Ancient cosmology, like modern cosmology, was based on observation. Sometimes, observations lag behind theory. During periods when data are lacking, sometimes cosmologists adopt a new model for aesthetic or philosophical reasons. For instance, Copernicus put the Earth in motion because it made a simpler, more appealing model than the geocentric Greek cosmological model. However, Foucault didn't demonstrate the rotation of the Earth with his pendulum experiment until AD 1851, 308 years after the death of Copernicus.

Although observations sometimes lag behind theory, every hypothesis that is not eventually supported by observational evidence must remain pure speculation. Since cosmology is ultimately based on observation of the universe around us, let's review some of the observations on which modern cosmology is based.

Observation 1: The universe is populated with "Galaxies" like the Milky Way.

In the mid-1920s, Edwin Hubble finally settled the Curtis-Shapley debate. In 1923, Hubble was examining photographic plates of the Andromeda Nebula M31, taken with the 100-inch telescope in order to find novae -- stars that would suddenly increase in brightness (because of cataclysmic explosions). On this place from the night of October 5-6, 1923, Hubble located three novae, each marked with an "N." One of these novae, however, turned out to be a Cepheid variable, a star that changes predictably in brightness, and the "N" was crossed out and the star was relabeled "VAR!"

This Cepheid, and others subsequently discovered in the Andromeda Nebula, enabled Hubble to make the first reliable measurement of the distance to Andromeda, and to prove that the Nebula was not a star cluster within our own Milky Way, but a galaxy more than a million light years away. The estimated distance was much greater than what Shapley and Curtis proposed was the extent of our Milky Way galaxy. This was the start of a systematic survey to measure distances to other spiral galaxies. Hubble's discovery was definitive: as of 1924, all astronomers knew that the spiral nebulae were galaxies, comparable in size to our own Galaxy, the Milky Way.

Observation 2: Galaxies show a redshift proportional to their distance.

With the discovery that spiral nebula were, in fact, other galaxies external to our own, our concept of a Universe became one of in a Newtonian universe of infinite size and mass, galaxies spread out in infinite space. However, there is a problem with a uniform, static Universe, any density enhancements would become unstable to gravitational collapse. Thus, the whole Universe should have collapsed (or be collapsing) into a giant black hole.

By 1925, Vesto Slipher had measured the shift in wavelength for the light from ~40 "extragalactic nebulae", of which nearly all showed positive redshift rather than blueshifted. Redshift, z, is proportional to the velocity of the galaxy divided by the speed of light. Since the vast majority of galaxies display a redshift, i.e. moving away from us, this is referred to as recession velocity.

In the 1930's, Hubble discovered that their redshifts increase proportionally with their increasing distance. In other words, all galaxies were receding from the Milky Way. By the Copernican principle (we are not at a special place in the Universe), we deduce that all galaxies are receding from each other, or we live in a dynamic, expanding Universe.

This solves the problem for gravitational collapse, only small regions will collapse to form galaxies. The rest of space keeps expanding.

The expansion of the Universe is described by a very simple equation called Hubble's law; the velocity of the recession of a galaxy (determined from its redshift) is equal to a constant times its distance (v=Hd). The constant is called Hubble's constant and relates velocity to distance in units of megaparsecs. This law of redshifts has been confirmed by subsequent research and provides the cornerstone of modern relativistic cosmological theories that postulate that the universe is expanding.

Of course, a key parameter in understanding the distance-redshift relation is the calibration of the whole system. This is know as the problem of the extragalactic distance scale, an ongoing research project for the last 70 years. The primary goal of the distance scale project is to compare the redshift, or recession velocity, of a galaxy with some independent measure of its distance.

The distance scale work uses a chain of distance indicators working outward from nearby stars to star clusters in our own Galaxy to stars in nearby galaxies. Unusually bright stars, such as variable stars and supernovae, complete the distance ladder out to cosmological distances. The latest results from the Hubble Space Telescope are shown above, a plot of recession velocity with distance (in megaparsecs). The straight, linear correlation indicates that the Universe is currently expanding at a rate of 72 km per sec for every Mpc. The rate, known as Hubble's constant, may change with time.

Observation 3: The night sky is dark.

The oldest and most basic cosmological observation is the darkness of the night sky, known as Olber's paradox. In a very large (or infinite), ageless Universe the night sky should not be dark. It should glow with the brightness of a stellar surface.

Note that the paradox cannot be resolved by assuming that parts of the Universe are filled with absorbing dust or dark matter, because eventually that material would heat up and emit its own light.

The resolution of Olber's paradox is found in the combined observation that: 1) the speed of light is finite, 2) the Universe has a finite age (~14 Gyrs for Ho= 70 km/s/Mpc) and the oldest stars are only a little younger. Thus, we only see the light from parts of the Universe within the "horizon radius" (i.e., the distance travelled by light since the beginning of the universe: rH~c/Ho, or ~4300 Mpc), and 3) the Universe is expanding and light from distant sources will be redshifted to lower energies.

Observation 4: The baryon mass fraction of the universe is ~75% Hydrogen and ~24% Helium.

Baryon abundance data can be broadly divided into four classes: (i) abundances of the various elements and their isotopes in the Solar System; (ii) composition of the visible layers of individual stars, planetary nebulae, young supernova remnants, cosmic ray sources, etc. due to thermonuclear (or other) processes that have taken place in the course of the internal evolution of the stars themselves; (iii) composition of the interstellar medium (ISM) at different places and times; and (iv) composition of the integalactic medium (IGM) at different places and times.

The Solar System provides the richest source of data that we have. Most of the mass in the Solar System is concentrated in the Sun. The composition of the Sun was first studied by Kirchoff in 1861, who was able to identify the elements responsible for absorption lines observed in the solar spectrum discovered by Fraunhoffer in 1841. (Note that Helium was first observed in the Sun by Janssen in 1868, and postulated to exist as a new, unknown element 27 years before it was actually found on Earth).

Solar Elemental Abundances

Element Number % Mass %

Hydrogen 92.0 73.4
Helium 7.8 25.0
Carbon 0.02 0.20
Nitrogen 0.008 0.09
Oxygen 0.06 0.8
Neon 0.01 0.16
Magnesium 0.003 0.06
Silicon 0.004 0.09
Sulfur 0.002 0.05
Iron 0.003 0.14

Abundances in evolved stars, planetary nebulae, and young supernova remnants (SNR) provide direct information on nuclear and mixing processes in stellar evolution that are believed to be responsible for continuing enrichment of the ISM in heavy elements and to be much like the corresponding processes that have produced the abundance distribution in the ISM today, which - in our own neighborhood - is fairly similar to the standard solar-system distribution. Stellar abundances in the solar neighborhood indicate that the vast majority of stars have values of "metallicity," i.e. [Fe/H] (where [X] denotes the logarithm of any quantity X in a star minus log X in the Sun), that have a Gaussian distribution with mean - 0.15 dex and standard deviation 0.2 dex. In addition, there is a clear trend in stellar age and metallicity, in the sense that the oldest stars are also the most metal-poor. The age-metallicity relation in the solar neighborhood is shown below:

These observations support current ideas in stellar evolution theory, in the sense that elements heavier than hydrogen (all the way till iron) are synthesised in the cores of stars by thermonuclear fusion, the power source for all stars. Supernova explosions will subsenquently enrich the interstellar medium from where new, more metal-rich generations of stars will be born.

A most important question is then: what was the composition of the first stars?. Much observational effort has been dedicated during the XXth century to measure the so-called "primordial abundance of the universe". Observations have focused on three areas of independent research:

(i) Abundances of the IGM in the early-universe:

The dominant baryonic mass component in the universe is the Lyman-alpha forest gas, detected by the trace neutral hydrogen in plasma that fills space as a froth all the way to z = 3. The term "Lyman-alpha forest" is used to denote the plethora of narrow absorption lines seen on the spectra of high-redshift QSOs. The figure below shows a high resolution spectrum of the z = 3.50 quasar Q1159+123, taken with the Keck High Resolution Spectrograph (exposure time 8 h). The Ly-alpha forest is clearly seen in absorption blueward of the atomic hydrogen Ly-alpha emission line from the quasar (the broad peak at 5470 ), and is produced by resonant Ly-alpha scattering in gas clouds along the line-of-sight between us and the quasar.

The neutral hydrogen at z ~ 3 is predominantly in the high column density damped Lyman-alpha absorbers (DLAs). The baryon density parameter needed to correctly reproduce the statistical absorption (mostly due to clouds at HI surface density = 1013 1 cm-2) is OmegaH h2 > 0.017-0.021, depending on the cosmological model, which translates in a Hydrogen mass fraction (X) of ~0.75.

Note that most of the features between the Ly-alpha and CIV emission (the other broad peak just below 7000 ) are CIV intergalactic absorption lines. Most Ly-alpha forest clouds at z ~ 3 observed by Keck have shown some chemical enrichment, as evidenced by weak, but measurable C IV lines down to the detection limit of the data. The typical inferred metallicities range from 0.3% to 1% of solar values, subject to uncertainties of photoionization models. Clearly, these metals were produced in stars that formed in a denser environmemt; the metal-enriched gas was then expelled from the regions of star formation into the IGM.

(ii) Abundances of pristine ISM in the nearby universe:

The primordial He abundance is best determined from observations of 4HeII -> 4HeI recombination lines in extragalactic HII regions.

There is a good collection of abundance information on the 4He mass fraction (Y), and O/H, and N/H in over 70 such regions. Since 4He is produced in stars along with heavier elements such as Oxygen, it is then expected that the primordial abundance of 4He can be determined from the intercept of the correlation between Y and O/H, namely YP = Y(O/H -> 0). A detailed analysis of the data found: YP = 0.238 +/- 0.002 +/-0.005. The first uncertainty is purely statistical and the second uncertainty is an estimate of the systematic uncertainty in the primordial abundance determination.

(iii) Abundances of the oldest stars in the nearby universe:

The abundance of 7Li has been determined by observations of over 100 hot, population-II halo stars, and is found to have a very nearly uniform abundance. For stars with a surface temperature T > 5500 K and a metallicity less than about 1/20th solar (so that effects such as stellar convection may not be important), the abundances show little or no dispersion beyond that which is consistent with the errors of individual measurements. The Li data indicate a mean 7Li abundance of: Li/H = (1.6 +/- 0.1) 10-10. The small error is statistical and is due to the large number of stars in which 7Li has been observed.

In conclusion, when astronomers study the chemical composition of a wide variety of astronomical objects they find that the baryonic component of the universe can be described, to lowest order, as a mix of three parts hydrogen to one part helium, with only minor "contamination" by heavier elements. The current measurements indicate that 75% of the mass of the Universe is in the form of hydrogen, 24% in the form of helium and the remaining 1% in the rest of the periodic table. Note that since the mass of helium is 4 times the mass of hydrogen, the number of hydrogen atoms is 90% and the number of helium atoms is 9% of the total number of atoms in the Universe.

Observation 5: The universe is filled with a Cosmic Microwave Background.

The discovery of the Cosmic Microwave Background (CMB) has an interesting history:

It was first accidentally discovered in 1941 by McKellar who noticed that the excited states of the CN molecule in his observations indicated excitation by a photon background with a characteristic temperature of 2.3 K. But since the CN molecule could only be found where the Galaxy was, the excitation was attributed to the ambient energy density of starlight in the Galaxy as opposed to being energy external to the galaxy (i.e., a CMB).

It was accidentally discovered again in 1965 by Arno Penzias and Robert Wilson (who won the Nobel Prize). They were employed at Bell Labs and were testing the feasibility of using Microwaves for communication. In experiments conducted in connection with the first Telstar communication satellite, Penzias and Wilson measured excess radio noise that seemed to come from the sky in a completely isotropic fashion. The initial measurements (at one frequency only) indicated that the flux density of photons at their millimeter receiver was independent of position in the sky. Failing to see any 24 hour modulation of this signal, the remaining logical conclusion was that it was indeed of cosmological origin and therefore everywhere. When they consulted Bernard Burke (MIT) about the problem, Burke realized that Penzias and Wilson had most likely found the cosmic background radiation that Robert H. Dicke, P.J.E. Peebles, and their colleagues at Princeton were planning to search for. Put in touch with one another, the two groups published simultaneously in 1965 papers detailing the prediction and discovery of a universal thermal radiation field with a temperature of about 3.5 K, the Cosmic Microwave Background (CMB).

Precise measurements of the CMB required space-based observations because the microwave region of the spectrum is blocked by the Earth's atmosphere. In late 1989, the Cosmic Background Explorer (COBE) satellite was launched. COBE determined the spectrum to be exactly characteristic of a blackbody at 2.735 K.

The CMB is a highly isotropic and uniform radiation field to better than 1 part in 100,000. Maps of the CMB have to go through three stages of analysis to reveal the fluctuations associated with the early Universe. The raw image of the sky looks like the following, where red is hotter and blue is cooler:

The above image has a typical dipole appearance because our Galaxy is moving in a particular direction. The result is one side of the sky will appear redshifted and the other side of the sky will appear blueshifted. The magnitude of this effect--the so-called dipole anisotropy--allows astronomers to determine that the Local Group of galaxies is moving at a speed of about 600 km/sec in a direction that is 45 degrees from the direction of the Virgo cluster of galaxies. Such motion is not measured relative to the galaxies themselves (the Virgo galaxies have an average velocity of recession of about 1,000 km/sec with respect to the Milky Way system) but relative to a local frame of reference in which the cosmic microwave background radiation would appear as a perfect Planck spectrum with a single radiation temperature.

The origin of the "peculiar velocity" of 600 km/sec for the Local Group presents an interesting problem. A component of this velocity may be induced by the gravitational attraction of the excess mass above the cosmological mean represented by the Virgo cluster; however, it is now believed that the Virgo component is relatively small, at best 200-300 km/sec. A more important contribution may come from the mass of a "Great Attractor" at a distance of 65 Mpc, as inferred by the peculiar velocity field of galaxies within this volume. However, this interpretation is somewhat controversial since much of the peculiar velocity masurements turned out to be seriously affected by systematic uncertainties in the distance indicators.

Removing the Galaxy's motion produces the following map:

This map is dominated by the far-infrared emission from gas in our own Galaxy. This gas is predominately in the plane of our Galaxy's disk, thus the dark red strip around the equator. The gas emission can be removed, with some assumptions about the distribution of matter in our Galaxy, to reveal the following map:

Patches of light and dark represented temperature fluctuations that amount to about one part in 100,000--not much higher than the accuracy of the measurements. Nevertheless, the statistics of the distribution of angular fluctuations appeared different from random noise. As we will discuss later on in this course, in the context of the Hot Big Bang model this CMB image is a picture of the last scattering epoch, i.e. it is an image of the moment when matter and photons decoupled, literally an image of the recombination wall. This is the last barrier to our observations about the early Universe, where the early epochs behind this barrier are not visible to us.

The clumpyness of the CMB image is due to fluctuations in temperature of the CMB photons. Changes in temperature are due to changes in density of the gas at the moment of recombination (higher densities equal higher temperatures). Since these photons are coming to us from the last scattering epoch, they represent fluctuations in density at that time.

The origin of these fluctuations are believed to be primordial quantum fluctuations from the very earliest moments of the universe and are echoed in the CMB at recombination. The members of the COBE investigative team believe that they have found the first evidence for the departure from exact isotropy that theoretical cosmologists have long predicted must be there in order for galaxies and clusters of galaxies to condense from an otherwise structureless universe.

Observation 6: On large scales, the universe is isotropic and homogeneous.

After the introduction of General Relativity a number of scientists, including Einstein, tried to apply the new gravitational dynamics to the universe as a whole. At the time this required an assumption about how the matter in the universe was distributed. The simplest assumption to make is that if you viewed the contents of the universe with sufficiently poor vision, it would appear roughly the same everywhere and in every direction. That is, the matter in the universe is uniform when averaged over very large scales. This makes the universe models simpler and ``more reasonable''---if we lived in an unusual part of the universe, then it would be almost impossible to understand the universe as a whole from observing our surroundings.

The idea of a uniform universe is called the Cosmological Principle. There are two aspects of the cosmological principle:

test of
homogeneity and isotropy

The cosmological principle is also known as the Copernican principle: "There is nothing special about our location in the universe". Every observer at a given cosmological time will see the same thing, such as the same Hubble law. ``Cosmological time'' in this context means the time measured from some common event like the beginning of the universe. Everyone at the same cosmological time will measure the same age of the universe. The cosmological principle allows the universe to change, or evolve, throughout time.

This basic assumption of the cosmological principle is being tested continuously as we actually observe the distribution of galaxies on ever larger scales. The key observations in support of this principle are: the observed homogeneity of the Universe at the largest scales sampled by redshift surveys; and the isotropy of the cosmic microwave background radiation.

Although cosmologists accept the cosmological principle, which states that all locations in space are very much the same, they do not accept the so-called perfect cosmological principle, which states that all locations in time are very much the same, i.e., the universe does not change with time; there is no evolution. Therefore, in an expanding universe, new matter must be continually created. This violates a central rule of nature known as the law of the conservation of mass. This law says that the total amount of mass does not change---mass is not created from nothing or destroyed. However, the amount of new matter that would need to be created for the perfect cosmological principle to be true is quite small---only one hydrogen atom per cubic centimeter every 1015 years. This is approximately one hydrogen atom/Ben Hill Griffin Stadium every 1000 years---a very small amount! (and very difficult to measure). There is, however, independent evidence that the universe DOES evolve, as we will review later on in this course.

The Cosmological Principle and the General Relativity form the entire theoretical basis for the Hot Big Bang model and lead to very specific predictions for observable properties of the universe. The observational evidence cited so far ---the expansion of the universe, the dark night sky, the baryon mass fraction, the presence of the CMB, and the homogeneity and isotropy if the universe on large scales--- is consistent with the predictions of the Hot Big Bang model.

Based in part on class notes by Barbara Ryden, Greg Bothum, and James Schombert, and review articles by Keith Olive,and by Bernard Pagel and Mike Edmunds.