Fundamental Issues in Cosmology
by Professor Joseph Silk
Cosmological Principles:
The scientist, although not necessarily the poet or the theologian,
commences his study of the Universe by assuming that the laws of physics, which are locally measured in the laboratory,
have more general applicability.
If experiment proves that this assumption is wrong, one then proceeds to explore generalizations of local physics.
In this spirit, cosmology, the science of studies of the Universe,
is developed by extrapolation of locally verified laws of physics to remote locations in space and time,
which can be probed with modern astronomical techniques.
In a theory of cosmology, simplicity is sought on sufficiently large scales.
The successful theories in physics and mathematics are invariably the simplest, with the least number of arbitrary degrees of freedom.
Postulating that Titan held up the heavens (Where did he come from? Why didn't he get bored? or sleepy?)
required many more ad hoc assumptions than the realization that the orbits of the planets in the gravity field of the Sun
suffice to stop them falling onto the Earth like so many shooting stars.
Unlike other branches of science, cosmology is unique in that there is only one Universe available for study.
We cannot tweak one parameter, juggle another, and end up with a different system on which to experiment.
We can never know how unique is our Universe, for we have no other Universe with which to compare.
The Universe denotes everything that is or ever will be observable, so that we can never hope to glimpse another Universe.
Nevertheless, we can imagine other possible Universes. One could have a Universe containing no galaxies, no stars and no planets.
Needless to say, man could not exist in such a Universe.
The very fact that our species has evolved on the planet Earth sets significant constraints on the possible ways our Universe has evolved.
Indeed, some cosmologists think that this may be the only way we can ever tackle such questions as Why does space have three dimensions?,
or, Why does the proton have a mass that is precisely 1,836 times larger than the electron?
If neither were the case, we certainly would not be here.
One can take the argument further:
our actual existence requires the Universe to have had three space dimensions and the proton mass to be 1,836 electron masses.
This conclusion is called the "Anthropic Cosmological Principle":
Namely, that the Universe must be congenial to the origin and development of intelligent life.
Of course, it is not an explanation, and the anthropic principle is devoid of any physical
significance. Rather it limits the possibilities. There could be a host of radically
different Universes that we need not worry about.
It is inevitable that an astronomer studies objects remote in time as well as in space; Light
travels a distance of 300,000 kilometers in one second, or ten thousand billion kilometers
in a year.
The nearest star, Alpha Centauri, is 4.3 light-years from us: we see it as it was more than
four years ago. The nearest galaxy comparable to our own Milky Way is two million light-years
distance: we are seeing the Andromeda Galaxy, a naked eye object in a dark sky, as it was
when homo sapiens had not yet evolved.
A large telescope is a time-machine that can take us part way to creation, to examine regions
from which light emanated more than five billion years ago, before our Sun had ever formed.
To a cosmologist, the issue of creation is inevitable.
There are three possibilities that one may envisage for the creation of the Universe:
- The beginning was a singular state, not describable by physical science.
A skeptic might ask, What did God do before He created the Universe?
The apocryphal answer is that He was preparing Hell for people who might ask such questions
(attributed to St. Augustine).
- The beginning was the most simple and permanent state imaginable, containing within itself
the seeds of future evolution.
This is the modern view, and one searches for the correct physical laws that describe this
initial state.
- There was no creation, and the Universe is unchanging and of infinite age.
We can try to distinguish between the latter two possibilities, the only two options on which
scientific tools can be brought to bear.
The earlier considerations about the simplicity of a successful theory are incorporated into
a simple principle that serves as a guide for building a model of the Universe. There are
various versions of such a cosmological principle.
The "Cosmological Principle" states that the Universe, on the average, looks the same
from any point. It is motivated by the Copernican argument that the Earth is not in a
central, preferred position.
If the Universe is locally isotropic, as viewed from any point, hence it is also uniform.
So the cosmological principle states that the Universe is approximately isotropic and
homogeneous, as viewed by any observer at rest. This allows the possibility of very
different past and future states of the Universe.
A stronger version, the "Perfect Cosmological Principle", goes further: The Universe
appears the same from all points and at all times.
In other words, there can have been no evolution: the Universe must always have been in the
same state, at least as averaged over long times.
Finally, the "Anthropic Cosmological Principle" argues that the Universe must have
been constructed so as to have led to the development of intelligence.
The Darkness of the Night Sky:
Olbers' Paradox is: "Why is the sky dark at night?"
Olbers (and others before him) assumed that both the average space frequency and luminosity
of stars (and galaxies) is approximately constant throughout space and over time.
Consider any large shell of matter of radius r and thickness dr.
The light from this shell is 4 Pi r2 dr n L, where the number of stars per
unit volume is n and the luminosity of a star is L.
So the radiation measured at the centre of the shell is n L dr,
and does not depend on the radius of the shell.
As we add up the contributions of more and more distant concentric shells (each of equal
thickness), the radiation measured at the centre seems to increase without limit.
This is not quite right, since light from a distant star is intercepted by an intervening
star, but we would expect the sky to be about as brilliant as the surface of a star. Any
line of sight must sooner or later run into a star.
This conclusion applies at any arbitrary point, and hence it applies everywhere.
We have a contradiction with the trivial observation that apart from the Milky Way, our own
Galaxy, the night sky is remarkably dark.
Olbers' paradox is not resolved by allowing for interstellar dust, as Olber's suggested,
since this absorbs and radiates energy.
Possible resolutions are:
(A) The Universe is young, so stars have only been shining for about ten billion years, or
(B) The Universe is of infinite age but expanding so as to avoid a state of thermodynamic
equilibrium.
Expansion "cools off" the Universe, due to the "Doppler shift" (which reddens light or
reduces the energy of photons that are received from a receding source).
Of course, the Universe may be both young and expanding, but only hypothesis B
requires expansion.
Steady State Cosmology:
The "Steady State Universe (Bondi, Gold, and Hoyle, 1949) postulates matter creation out of
vacuum, so that the Perfect Cosmological Principle is satisfied (density is constant and the
Universe appears the same averaged over large volumes and times). This postulate was
motivated by an apparent time-scale problem.
The Universe of galaxies was found to be expanding by Hubble at a velocity
V = H0 * R,
that increased systematically with galaxy distance, R.
H0
is the Hubble expansion rate.
This means that if there has been no acceleration or deceleration, all matter must have been
piled-up at the beginning of the expansion; at a time R/V or 1/H0
ago.
The current Hubble expansion rate was found to be H0= 500 km/s/Mpc
in Hubble's original work.
This means that 1/H0 = 2 billion yr. was an upper limit on the age
of the Universe.
One may compare this with radioactive dating technique of old rocks, e.g.
U238 -> Pb205 with a half-life of
4x109 yr.
Measured for different rock and meteorite samples, the present lead isotope abundances allow
an estimate of age. We infer 4.6x109 yr. for the oldest meteoritic or Lunar rocks
(4.6 billion years).
Stellar evolution theory, with hydrogen fusion to helium as an energy source, yields the age
of globular clusters, the oldest stars in our Galaxy.
The main sequence turnoff denotes the duration of the observed era of hydrogen burning, while
the horizontal branch on the H-R diagram indicates the location of helium burning stars.
The inferred age to fit the observed H-R diagram is 10x109 yr.
(10 billion years).
The discrepancy between the Universal expansion age, on the one hand, and meteoritic and
stellar ages on the other hand, was only removed in the 1950s, when a more accurate value
for H0 emerged.
The best modern value is H0 = 50 km/s Mpc,
or 1/H0 = 20x109 yr. (20 billion years).
Key predictions of steady state cosmology were that:
- There was and is creation of one hydrogen atom per cubic metre per 1010 yr.
Creation is assumed to occur out of the vacuum, radically violating the law of conservation
of mass and energy.
One expects antimatter to also be produced, leading to a gamma ray background that results
from occasional annihilations of protons and antiprotons. One does not want to also violate
another fundamental law, namely the law of conservation of electric charge. Hence another
possible form for newly created matter is neutrons. These decay and leave behind hot X-ray
emitting gas pervading the Universe. Neither the expected cosmic gamma rays, or X-rays, were
seen, so that the theory was modified to postulate creation only in dense cores which we
identified with the nuclei of galaxies.
- No evolution at great distance could have occurred.
Radio source counts tested this prediction:
N(>f) is the number observed brighter than flux f, which for a source at distance d,
luminosity L is given by f = L/4Pi d2. So the distance to which one can see in a
flux-limited survey of sources with identical L is d = (L/4Pi f)1/2.
Now, the total number of sources measured in an all-sky survey is N=(4/3)Pi d3n,
where n is the source density.
The steady state model predicts that n = constant, so that N(>f) is proportional to
d3 or (L/f)3/2, predicting that as the survey sensitivity is increased
(or as f is lowered), then N(>f) should increase as f-3/2 in Euclidean space.
Observations revealed a much stronger increase in source counts.
Proponents of the steady state model in the 1950s argued that we might be living in a very
local hole. However, subsequent optical identifications and distance determinations have
shown the radio sources primarily to be radio galaxies and quasars that are several billions
of Mpc away from us, demonstrating that evolution must be occurring over a time-scale of
order 1010 yr. Luminous radio emitting galaxies were far more frequent in the
past than they are seen to be today.
The final blow to the steady state theory came with the discovery of the cosmic microwave
background in 1964.
This was direct evidence of radiation originating in a dense hot phase of the Universe, as
predicted by the Big Bang theory. It is characterized by a blackbody spectrum appropriate to
a blackbody at 2.75 degrees Kelvin. The intensity of such a cold blackbody peaks at a
wavelength of 1mm, in the microwave band.
To explain such radiation in a steady state model requires one to postulate the universal
presence of millimeter sized dust grains that would absorb an intense radiation field
produced by many exceptionally luminous galaxies and reradiate it at the appropriate
temperature.
This interpretation is so contrived and requires so many special assumptions that it is
generally regarded as being highly implausible.
The original information for this page can be found at
Fundamental Issues in Cosmology
In the Smoot Astrophysics Research Program Web site
John C. Mather and George F. Smoot, Nobel Prize in Physics 2006
(Nobel Foundation)
See
The Nobel Prize in Physics 2006
(.pdf)
Updated: October 3 '06
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