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The Observable Universe

Contents
The Observable
Universe
Big
Bang Theory
CMBR (Cosmic
Microwave Background Radiation) Spectrum
CMBR
Fluctuations
CMBR
Polarization
CMBR Power
Spectrum
Wilkinson Microwave
Anisotropy Probe (WMAP)
Dark Energy, Dark
Matter
Parallel Universes,
Multiverse - the Unobservable Universe
Footnotes
References
Index

The Observable Universe
The observable
universe is the space around us bounded by the event horizon - the distance to
which light can have traveled since the universe originated. This space is huge
but finite with a radius of 1028 cm. There are definite total numbers
of everything: about 1011 galaxies, 1021 stars,
1078 atoms, 1088 photons. There is a hierarchy of
structure: Everything is

composed of smaller things and is a part of something
larger as shown in Figure 02-01a and Figure 15-01. The
character of structures with different scale changes according to the
interplay of various physical forces. Quantum phenomena control the small
scales, while gravity dominates on large scales, and both come into play
at the beginning of the universe. On each scale of size there is a
corresponding scale of time: processes

Figure 02-01a The Observable Universe [view large
image]

Figure 02-01b Inflationary Cosmology [view large
image]

tend to happen quickly on small scales and slowly on large
scales. See "Earth &
Universe" for a different perspective of this subject.

Note that according to inflationary cosmology, the
entire universe is much bigger than the observable one (see Figure 02-01b, not
to scale), and the confine of observable universe depends on the location.
Observers living in the Andromeda galaxy and beyond have their own observable
universes that are different from but overlap with ours.

[Top]

Big Bang Theory1,2

In 1922 Alexander
Friedmann predicted the Big Bang cosmology, which portrays the
universe as expanding space from a point where the matter-energy density
was extremely high. The expansion can be visualized by a two dimensional
analogy as shown in Figure 02-02. As the balloon expands, all the points
on the surface recede from each other, and the wavelength on the surface
is stretched. It is similar to the shift to longer wavelength when the
source and receiver are moving away from each other. This phenomenon is
called red
shift of the spectrum because in visible light the shift to longer
wavelength is toward the red colour. It plays a prominent role in
discovering the cosmic expansion through the detection of the spectral
line shift from distant galaxies.

Figure 02-02 Cosmic Expansion
[view large
image]

Note that contrary to the balloon analogy, it is the space
itself that is expanding. It needs neither a center to expand away from
nor empty space on the ouside to expand into.

This simple picture of expanding universe with all the galaxies flying away
from each other remained unchanged until the 1980s when the Inflation
Theory3 was introduced
to resolve a number of discrepancies. The rapid expansion occurred at the
interval between 10-35 sec and 10-32 sec. It predicts a
much smaller universe near the origin of the Big Bang such that the
matter-energy within can be mixed evenly as reflected in the CMBR mapping. It
also predicts that the geometry of the Universe is flata. Events
before the inflation is essentially unknown. It is subjected to a lot of
speculations. For example, it is suggested that space-time may be created from
vacuum fluctuation - the quantum foam; and that
the four fundamental forces may be unified to just one kind (as envisioned by
the grand unified theories). Baryongenesis (generation of quarks and anti-quarks
which has a baryon number of 1/3 or -1/3) happened in an epoch before inflation,
when a imbalance between matter and anti-matter was established by a quantum
process called CP
violation. Quarks and anti-quarks combined to form baryons and mesons at
10-5 sec. Nucleosynthesis started at about 3 min. During this epoch
the light chemical elements were produced from protons and neutrons. The
universe was still opaque up to 380,000 years when neutral atoms started to form
and the radiation was able to escape as shown by the CMBR. This epoch is called
decoupling to indicate that matter and radiation are separated. From then on
matter had a chance to condense into stars and galaxies and evolved to the
present-day universe. Figure 02-03a shows the history of the universe according
to the Big Bang Theory. Table 02-01 summarizes the major events during the
course of the cosmic history.

Supplement to the legend of Figure
02-03a:
The quark (q), electron (e), and neutrino (n) are the
fundamental particles. The corresponding anti-particle is labeled with a
bar on top. The gluon (g) is the boson mediating the strong interaction
between quarks. The vector bosons W and Z mediate the weak interaction
between electrons/neutrinos and the quarks. The photon (wavy line)
mediates the electromagnetic interaction between charged particles. One
quark and one anti-quark combine to form a meson. Three quarks combine to
form a baryon (proton, neutron, etc.). Protons and neutrons combine to
form nucleus (ion). Nucleus and electrons combine to form atom. The muon
(m) and tau (t) are the 2nd and 3rd generation of the lepton family, the
1st generation is the electron. (See more about elementary particles in Topic-15.)

Figure 02-03a History of the Universe [view large
image]

There are scales for the time t (in second), temperature T
(in oK) and energy
E (in Gev) of the photon gas at the
bottom of Figure 02-03a. These variables are related by the simple
mathematical formulas:

For the earlier relativistic matter
dominated era: E(Gev) = 2.76x10-3 / t1/2(sec) ---
(1) where the proportional constant is calibrated with the Planck scale of

E(Gev) = 1.2x1019 Gev at 5.4x10-44sec.

Figure 02-03b Cosmic Expansion [view large
image]

For the non-relativistic matter dominated era: E(Gev) =
156x10-3 / t2/3(sec) --- (2)
where the
proportional constant is calibrated with the CMBR temperature of
2.73oK at the present age of 13.7x109years.

According to Eqs.(1) and (2), the energy of radiation
and matter became equal at about 1000 years after the Big Bang.

The
energy and temperature are related by the formula:    E(Gev) =
10-13 x T(oK) ----- (3)

There is no such simple
formula for the size R of the early universe and time until 10-32 sec
at the end of the inflation. Their relationship during the earlier epoch can be
obtained from a graph (Figure 02-03b, the numerical values are not reliable as
the precise numbers are highly uncerain according to the unknow details of the
Grand Unified Theories). For the later period, a mathematical formula for the
size and time can be found from the standard model curve on the same graph:

log[R(cm)] = 0.5036 x log[t(sec)] + 19.12 -----
(4)

where the constants are estimated by fitting two points on the
straight line - one with the size of 1000 cm for the end of the inflation at
10-32sec, the other with the size of about 1028cm for the
present age of 13.7x109years. Eq.(4) implies a relativistic matter
dominated cosmological model with R ~ 1019x t1/2; because
in the logarithmic scale, more than 90% of the graph is related to the
relativistic matter dominated era. It also equates the distance to the cosmic
horizon (in the present) to be the size of the universe, which in general are
not equal.

Table 02-01 depicts the sequence of events
after the Big Bang in time order. The relics and observables are physical facts,
while the interpretations of the events are mostly theories or
conjectures.

Era

Time

Size

Energy or
Temperature

Relics & Observables

Events

Planck era

< 10-43 sec

< 10-50 cm

> 1019 Gev

4-dimensional spacetime;
cosmic
expansion

Smallest unit of
space-time started to expand; all forces united into
one

GUT era

< 10-35 sec

< 10-47 cm

> 1014 Gev

Super-heavy
particles; fundamental
interactions

Separation of spacetime
and matter; gravitational, strong,
and electroweak forces

Inflation

< 10-32 sec

< 1000 cm

> 1013 Gev

Observable
universe;
large scale
structures

Unstable vacuum;

quantum
fluctuations

Electro-weak era

< 10-10 sec

< 1014 cm

> 100 Gev

Radiation; excess of matter
over antimatter; separation of force and matter fields

Radiation released in reheating; baryon-antibaryon
asymmetry; separation of weak and electromagnetic forces, origin of
mass

Strong era

< 10-4 sec

< 1017 cm

> 200 Mev

Exotic forms of dark matter

Formation of hadrons from quarks including neutrons and
protons

Weak decoupling

< 1 sec

< 1019 cm

> 3 Mev

Hydrogen nuclei domination

Neutrinos decouple, neutron/proton ratio fixed

e-e+ Annihilation

< 5 sec

< 3x1019 cm

> 1 Mev

Photons hotter than neutrinos today

Electron heat dumped into photons

Nucleo-synthesis

< 100 sec

< 1020 cm

> 200 Kev

Light element abendances: D, He, Li

Nuclear reactions freeze out, stable nuclei form

Spectral decoupling

< 106 sec

< 1022 cm

> 3 Kev

Blackbody background radiation

End of efficient photon production

Matter ~ radiation

< 104 yrs

< 8x1024 cm

> 3 ev

Mass density fluctuations

Matter density ~ radiation density

Recom-bination

< 0.3 My

< 4x1025 cm

> 3500oK

CMBR

e- and p+ recombine into H atoms,
universe transparent
to light

Dark ages

< 1 Gy

< 3x1027 cm

> 15oK

First stars,
heavy
elements

mass fluctuations grow, first small objects coalesce, reionization

Galaxy
formation

< 2 Gy

< 4x1027 cm

> 10oK

Stars, quasars, galaxies

Collapse to galactic systems

Bright ages

< 13 Gy

< 9.7x1027 cm

> 2.8oK

Milky Way and
Solar
System

Gas consumed into stars, remnants, planets

Present era

~ 13.7 Gy

~ 1028 cm

~ 2.73oK

Supercluster

Large scale gravitational instability

Table 02-01 A History of Cosmic Expansion

In an effect to learn more about the processes occurred in the early
universe, which was associated with very high energy as shown in Table 02-01.
Particle Physicists have been simulating the condition in the laboratory with
high energy particle accelerators (see the entries in top left of Figure
02-03a). In collaborating with the theory of elementary particles, experiments
are developed to investigate the creation of fundamental particles, and their
properties. A list of the major accelerators in the world is shown in Table
15-01.

The following is a summary of the evidences which support the validity of
the Big Bang Theory.

The Night Sky : It is referred to as the Olber's
Paradox. He posed the question way back in 1823. According to his
calculation, the night sky would glow brightly from all the stars if the
universe is infinite both in space and in time. The arguement is
illustrated by Figure 02-03c, which shows the night sky receiving light
from stars in successive spherical shells r. The total amount of
light reaching the earth is equal to the sum of nLr from all the shells,
where n is the density and L is the intrinsic luminosity of the stars.
Since it was believed that the universe is infinite, and so we would
expect the night sky to be about as brilliant as a star's surface.
Obviously, this is not true. The paradox is resolved by the Big Bang
Theory which limits the observable horizon to about 1028 cm.
and an age of about 14 billion years. In addition, the light from remote
objects is also diminished by the red shift of the spectrum.

Figure 02-03c Olber's Paradox [view large image]

The Red Shift : It was discovered in the 1920s that Andromeda and
other similar smears of light were akin to our own Milky Way.
Subsequently, it was noticed that more distant galaxies are receding
faster than those nearby - an observation that could be explained if the
universe were expanding. The speed of recession§ is
measured by red shift of the spectral lines. The distance is measured by
standard candle
such as the class of stars known as Cepheid Variable which, possesses an
unique relationship between the period (of brightness variation) and its
intrinsic luminosity. The speed-distance relation is known as the Hubble's law. It is

Figure 02-03d Red Shift
[view large
image]

an empirical formula equating the speed v to the
distance d, i.e., v = Ho x d, where Ho is the Hubble's constant. It has a value of 71
(km/sec)/Mpc according to the latest measurement by WMAP
(see Figure 02-03d).

§ The
speed of recession v is related to the red shift z by the formula: v/c = [(1 +
z)2 - 1] / [(1 + z)2 + 1].

Nucleosynthesis : The universe's
light-element abundance is another important criterion by which the Big
Bang Theory is verified. It is now known that the elements observed in
the Universe were created in either of two ways. Light elements (namely
hydrogen, deuterium, helium, and lithium) were produced in the first few
minutes of the Big Bang, while elements heavier than lithium are thought
to have their origins in the interiors of stars which formed much later
in the history of the universe. The relative abundances of the light
atomic nuclei has been calculated as a function of the average density
of the universe based on the Big Bang model. There is a convincing
coincidences between the observed and calculated values at a density of
3x10-31 g/cm3 (Figure 02-03e). This density
implies an open universe, which will keep on expanding forever. Such
conclusion seems to be in contradiction with the Inflation Theory which
predicts a flat universe at the critical density of 10-29
gm/cm3. This problem could be resolved by the presence of
"dark matter".

Figure 02-03e Nucleosynthesis
[view large
image]

Hubble's Deep Field Survey : The Hubble Space Telescope
(HST) was launched on April 24, 1990. Since then it has collected photographs
of various celestial objects in astonishing details. One of the photos called Hubble Deep Fields
has captured astronomical objects from nearby star to some immature galaxies
near the beginning of the Big Bang. We

are able to sample different epochs in the photo because
light from the nearer objects reaches us sooner than from those further
out (because light propagates with a finite speed of 3x1010
cm/sec). The objects in the photo can be separated by redshift into a series of
images corresponding to different epochs. It unveils a universe that
is steadily changing over time, just as the Big Bang predicts. Figaure
02-03f shows the scope of the survey including the Hubble Ultra Deep
Field.

Figure 02-03f Hubble Deep Field
[view large image]

Cosmic Microwave Background Radiation : See section on WMAP.

[Top]

CMBR (Cosmic Microwave Background Radiation)
Spectrum4

It was discovered in 1965 that there is a feeble microwave
radiation emanating uniformly from all directions in the sky. It
contributes about one percent to the static on a television screen that is
not tuned to a local channel. This is the cosmic microwave background
radiation (CMBR). The CMBR spectrum is identical to a blackbody
radiation of 2.726oK as shown in Figure 02-04. The
solid line represents the blackbody radiation spectrum that has been
computed from theory. The data being represented by various symbols are
collected from various measurements. The agreement between observation and
theory is remarkable.

Figure 02-04 CMBR Spectrum [view large
image]

[Top]

CMBR Fluctuations5

The all sky maps in Figure 02-05 shows the three views of CMBR (in
false colours) with increasing sensitivity (in temperature variation). To
a first approximation the sky is uniform (top). At a sensitivity level of
1 part in 1000, it reveals a shift in wavelength to blue and red (middle)
. The pattern is caused by the motion of the earth relative to the frame
of the CMBR. When this shift is subtracted off, fluctuations are visible
at a sensitivity level of 1 part in 100000 (bottom). The red band in the
middle is the emission from the Milky
Way.

Figure 02-06 shows the final view after all the corrections have been
applied. The slight variation in temperature then takes on a blotchy
appearance with each patch a little above or below the average temperature
of 2.726oK.

All the above-mentioned observations can be interpreted in a consistent
way by the Big Bang
Theory. According to this theory the CMBR was emitted about 380000 yr.
after the Big Bang when neutral atoms (such as the hydrogen atoms) started
to form. As the neutral atoms interact much less to the radiation, they
became free and escaped the fireball at a blackbody temperature of about
4000 oK. It takes about 14 billion years to reach us and has
since been cooled down to 2.726 oK by the cosmic expansion.

Figure 02-05 The Three Views of CMBR

The patchy features in Figure 02-06 are related to the
fluctuations occurred close to the beginning of the universe. The CMBR is
the furthest astronomical phenomenon that can be witnessed by any beings
because the universe was opaque before this event. It is like looking up
in a cloudy day when nothing can be seen beyond the cloud
ceiling.

Figure 02-06 Cosmic Microwave Background
Radiation

[Top]

CMBR Polarization6

Recently in 2002, the Degree Angular Scale Interferometer (DASI) has
detected partial polarization
of the CMBR at the sensitivity level of one part in a million. In Figure
02-07 the temperature fluctuations are represented by yellow for hotter,
red for colder regions. Superimposed is the polarization measured by
DASI7. The
polari-zation at each point is represented by a black line, whose
orientation and length correspond to the direction and amount of
polarization, respectively. The magnitude of the polarization on small
angular scales depends on the anisotropy being in place at recombination
but on large angular scales, the polarization patterns were formed at the
beginning of the reionization era, when the first starlight began ionizing
the cold hydrogen that filled the universe after the Big Bang cooled.
Measurement by WMAP indicates that the first stars were born about 100 to
400

Figure 02-07 CMBR Polarization
[view large
image]

million years after the Big Bang. New polarization data
(white bars in Figure 02-09a) from WMAP in 2006 provide further evidence
that the first stars formed some 400 million years after the Big Bang,
which was followed by a period of inflation.

[Top]

CMBR Power Spectrum8,9

Theoretical physicists use the power
spectrum plot to determine the cosmological parameters by the
observational data. Essentially, the power spectrum is a plot of the
amount of fluctuation against the angular (or linear) size. The
fluctuation is the difference in the two measurements at the corresponding
points. It can be the fluctuation of temperature or density or any other
kind of measurable quantity. Figure 02-08 shows just one example with the
WMAP observational data superimposed on a theoretical curve. The
theoretical curve varies with several parameters such as the total cosmic
density, the baryon density (luminous matter) and the Hubble's constant.
The best fit model is the lambda cold dark matter model with an initial
inflation, a period of galaxies formation induced by cold dark matter, and
then the speedup of the cosmic expansion. However, none of the theoretical
models based on inflation can account for the anomalous data in Figure
02-08 at large angular size. Double checking the instruments and analysing
procedures also fails to explain the anomalies. More observations are
needed to resolve the puzzle.

Figure 02-08 Power Specturm
[view large
image]

[Top]

Wilkinson Microwave Anisotropy Probe
(WMAP)10

The Wilkinson Microwave Anisotropy Probe (WMAP) team has
released the first detailed full-sky map of the oldest light in the
universe on February 11, 2003. Figure 02-09a shows the measurements with
red indicates "warmer" and blue indicates "cooler" spots. The patterns in
the map are tiny temperature differences within an extraordinarily evenly
dispersed microwave radiation bathing the Universe, which now averages a
frigid 2.73 degrees above absolute zero temperature. WMAP resolves the
slight temperature fluctuations, which vary by only millionths of a
degree. Analyses of this microwave radiation emitted only 380,000 years
after the Big Bang

Figure 02-09a High Resolution CMBR
[view large image]

appear to define our universe more precisely than ever
before. Measurements
from WMAP resolve several

long-standing disagreements
in cosmology rooted in less precise data. Specifically, present analyses of the
WMAP all-sky image indicate that the universe is 13.7 billion years old
(accurate to 1 percent), composed of 73 percent dark energy, 23 percent cold
dark matter, and only 4 percent atoms, is currently expanding at the rate of 71
km/sec/Mpc (accurate to 5 percent), underwent episodes of rapid expansion called
inflation, the geometry
of the Universe is flat1, and will
expand forever. The Wilkinson Microwave Anisotropy
Probe was launched on June 30, 2001. It is designed to operate for four
years.

Further analysis of the WMAP data in 2007 reveals two oddities:

1. It has been deduced from the absence of radio sources
that there is a big hole in the sky devoid of both normal and dark matter
in the direction of the constellation Eridanus. Its size is nearly a
billion light years across at a distance 6 - 10 billion light years away
(40 times larger in volume than the previous record holder). The void
coincides with an extra large cold spot in the WMAP map covering a few
degrees of the sky (many times more than the full moon). The temperature
of the void is

Figure 02-09b WMAP Oddities
[view large
image]

between 20 and 45 % lower than the average. It is
suggested that the discovery of the void ties in neatly with the WMAP cold
spot and the existence of dark energy as the photons would lose energy
passing through an empty space.

2. WMAP's temperature
variations can be decomposed into set of patterns called multipoles. The lowest
multipoles are the largest-area, continent- and ocean-size undulations on the
temperature map. Higher multipoles are like successively smaller-area plateaus,
mountains and hills (and trenches and valleys) inserted on top of the larger
features. As shown in Figure 02-09b both the quadrupole and the octupole are
aligned along an "axis" which standard cosmology cannot explain. This could
happen by chance only about 0.1% of the time. Critics have considered a variety
of possibilities. One explanation involves some kind of imperfection in WMAP's
detector that introduces the patterns, but there is no evidence for
this.

A theory based on the multiverse
aspect of the string theory claims that the dynamic effect of matter
and gravity would have weeded out the majority of string vacuums, leaving
only our patch and close neighbours in the string landscape. A calculation
shows that interaction between neighbouring patches in early epoch would
leave the universes in an entangled
state linking them together even when their separation is space-like
(meaning they cannot interact with each other in the usual way). It
predicts that pushing and squeezing between the patches will produce voids
on the scales of about 1/2 billion light year. The alignment in the lower
multipoles is the byproduct of such interaction, which squeezes our
universe on one side, perhaps shaped it like a pancake. This theory may
point us to the first glance of another universe after all kinds of
speculation in science fictions (Figure 02-09c).

Figure 02-09c The Void
[view large
image]

The NASA/WMAP Science Team
presents the cosmic microwave temperature fluctuations from the 5-year WMAP data

(Figure 02-09d) on March, 2008. The composition of the
early universe has been measured from the data as shown in Fiugre 02-09e.
It is obvious by comparing with the composition in the current epoch that
it varies as the universe expands. It appears that the dark energy density
does not decrease at all, so

Figure 02-09d WMAP 5-Year Data [large
image]

Figure 02-09e Early Universe
[view large
image]

it now dominates the universe even though it was a tiny
fraction 13.7 billion years ago. Other major findings
include:

New evidence that a sea of cosmic neutrinos permeates the universe. Cosmic
neutrinos existed in such huge numbers they affected the universe’s early
development. That, in turn, influenced the microwaves that WMAP observes.

The first stars took more than a half-billion years to create a cosmic
fog. The data provide crucial new insights into the end of the "dark ages,"
when the first generation of stars began to shine. The glow from these stars
created a thin fog of electrons in the surrounding gas that scatters
microwaves.

The new WMAP data places tight constraints on the theory of inflation.
Some versions of the inflation theory now are eliminated. Others have picked
up new support.

[Top]

Dark Energy, Dark Matter11

It seems that the Big Bang Theory has been validated conclusively with all
these supporting evidences. However, recent observations in the last few years
reveal that there is something amiss. It is noticed that even though there is
not enough mass to hold the stars, galaxies and galaxy clusters in place, they
are still moving around and would not disperse. It looks as if there is some
kind of invisible force (gravity from the dark matter) to hold them together.
The situation is similar to a puppet show, where the audience can safely assume
that someone behind is manipulating the movements.

The second problem is related to the use of the
Type Ia supernovae as "standard candles" to measure the distance of
remote objects. The measurements imply that the cosmic expansion is
accelerating. It is proposed that there is some kind of repulsive "dark
energy" to induce the acceleration. Figure 02-10a shows the proportion of
the various matter-energy components in the Universe. Most of the
matter-energy content is in the form of "dark energy". The composition of the Universe is listed in Table 02-02
below.

Figure 02-10a Energy-Matter in the Universe
[view large
image]

New data in 2006 further refine the universe's contents
to: 4% ordinary matter, 22% dark matter, and 74% dark energy.

Acceleration of the cosmic expansion is placed on a firmer footing when it is
observed in 2003 that the CMBR becomes slightly hotter after going through a
galaxy, which forms a gravitational (potential) well. Dark energy, being
gravitationally repulsive, makes a gravitational well shallower as a photon
passes through, so the photon exits with slightly more energy than it had when
it entered.

Gradually, it dawns on some astronomers that dark energy
could be responsible for turning off galaxy and star formation in the
latter half of the cosmic history at redshift
z ~
0.75 (~ 6.5 billion years since the Big Bang). The central piece of
evidence is the rough coincidence in timing between the end of most galaxy
and cluster formation and the onset of the domination of dark energy. Both
happened when the universe was about half its present age. The influence
of dark energy include stopping the merger of galaxies, sorting out the
types of galaxies, lowering the rate of star formation, and preventing the
growth of galaxy clusters (Figure 02-10b).

Figure 02-10b Galaxy Formation & Dark Energy [large image]

Material

Representative Particles

Particle Mass or Energy (ev)

No. of Particles in Observed Universe

Probable Contribution to Mass of Universe

Sample Evidence

Ordinary matter

Protons, electrons

106 to 109

1078

5%

Direct observation, inference from element
abundances

Radiation

photons

10-4

1087

0.005%

Microwave telescope observations

Hot dark matter

Neutrinos

< 1

1087

0.3%

Neutrino measurements, cosmic structure

Cold dark matter

Supersymmetric particles?

1011

1077

25%

Inference from galaxy dynamics

Dark energy

Scalar particles?

10-33

10118

70%

Supernova observations of accellerated cosmic
expansion

Table 02-02 Composition of the Universe

The nature of both the "dark matter" and "dark energy" is still the
subject of intense research observationally and theoretically. Some of the
suggestions are listed below:

Cosmological constant - Eistein had introduced a term with the
cosmological constant in the gravitational field equation to keep a
static universe from collapsing. This additional repulsive force is no
longer necessary when the cosmic expansion became apparent. It has
become fashionable again with the new discovery of cosmic acceleration.
It is very tempting to identify the cosmological constant with the
vacuum energy of the various quantum fields. However, the simplest
versions of quantum theory predict far too much energy -
10120 higher than the observed value by one estimate. One
explanation involves the cancellation between the boson positive
contributions and the fermion negative contributions to almost zero,
leaving only a residual trace corresponding to the observed dark energy.

Figure 02-10c Dark Energy & Fates of the Universe [view large
image]

Quintessence - This hypothetical form of dark energy permeates all space.
Like inflation, quintessence is thought to have somehow originated when the
universe was just 10-35 sec old. It is driven by a scalar field
whose energy varies gradually. The difference is the energy and time scale:
inflation occurred quickly at very high energies, whereas the scalar field
responsible for quintessence operates at much lower energies over a much
longer time frame. One of its key differences from the cosmological constant
is that it can vary depending on time and place. Figure 02-10c portrays the
fates of the universe according to different scenarios of dark energy.
Research in 2006 found that the dark energy's influence on the universe in the
current epoch is the same as 9 billion years ago. The discovery rules out
quintessence models that change too rapidly.

Illusion - This explanation asserts that the apparent acceleration
is just an illusion. Sky
survey reveals that matter is distributed unevenly on large scales
with gigantic super-clusters and huge voids in between. Because we live
in a gravitationally bound system (the Milkyway), our clocks run more
slowly than they would in a void. In addition, space is negatively
curved in the void, so the volume for a given radius is larger than in
the relatively flat space. In effect, our estimate of volume is too
small and the estimate of time is too slow giving the wrong impression
of acceleration (see Figure 02-10d).

Figure 02-10d Dark Energy Illusion [view large
image]

However, slight increase of the WMAP
temperature associated with intervening regions of superclusters shows
that the dark energy is real. Since the CMBR photons gained a small
amount of additional energy as they re-emerge from a gravitational well
while the cosmic expansion is accelerating.

Neutrino - It
is a reasonable candidate for dark matter because of its unreactive nature.
Theoretical calculations indicate that there should be as many as 100 million
neutrinos for every atom in the universe. However, the recent estimates of
neutrino mass is so slight that it could account for only about 0.1 - 7 per
cent of the mass of the universe.

WIMP - Many new particles with heavy mass appear in the supersymmetry
formulation. These are referred to as weakly interacting massive particles, or
WIMPs. For example, the photino (the fermionic partner of photon) has a mass
about 10 to 100 times that of the proton. Most of these electrically neutral
particles would, like neutrino, go straight through Earth. On rare occasion,
however, one might interact with an atom in the material they pass through. So
far, the only claimed detection of a dark matter particle (by an Italian team
in 2000) has been strongly disputed.

Nonluminous matter - Ordinary hidden matter consists of atoms that emit
little or no light. It includes a host of celestial objects such as planets,
dark gas clouds, brown dwarfs, neutron stars, and black holes. The Massive
Compact Halo Objects Project (MACHO) has been looking for them in the halo of
the Milky Way. A search for microlensing has turned up four candidates toward
the Large Magellanic Cloud and 45 toward the Galactic Bulge.

MOND - It is proposed that instead of looking for the
dark matter, slight altering of Newton's second law will account for the
discrepancy. The formula F = ma is amended in such a way that smaller
gravitational force or mass can impart a given acceleration in a certain range
(see Figure 02-10e). According to MOND (Modified Newtonian Dynamics), a test
particle at a distance r from a large mass M is subject to the acceleration a
by the following formula:

(a/a0) a = G M /
r2

where G is the gravitational constant, a0 ~
cH0 ~ 10-8 cm/sec2 is the MOND parameter,
H0 is the Hubble constant, and (a/a0) is a function
of a/a0 such that (a/a0) ~
a/a0 for a/a0 << 1, and (a/a0) ~ 1 for
(a/a0) >> 1.

Figure 02-10f shows the MOND prediction
on mass discrepancy for many astronomical objects. Its main failure

occurs in the cores of large galaxy clusters. Since its
proposal in 1983, MOND has become a controversial subject among
astronomers. It is considered as a rather ad hoc invention to fit this
special problem of dark matter. Even if it is correct, the new formula
should be derived from a more fundamental theory.

Figure 02-10e MOND Theory [view large
image]

Figure 02-10f MOND Prediction
[view large
image]

Since we
don't feel the effect of dark energy and dark matter around us except through
the gravitational influence on large scale, a model has been constructed with no
other interactions between each other or with ordinary matter. It fits the
observa-tional data such as the high-redshift supernovae, the microwave
background radiation, the distribution of large-scale structure, and the dynamic
of celestial objects very well. But if 96% of the Universe is in the form of
unseen substances, does this not mean that there is the possibility of hidden
structure? Might the dark sector be a fascinating place, with its own intricate
inter-actions — perhaps even a kind of intelligent life? Is there a 'dark light'
that we do not see, radiating and absorbing in the dark Universe? Such
possibility suggests that human beings are extremely unimportant in the grand
scheme of the universe as port-rayed in a 1985 movie called "Insignificance" in
which Einstein
and Monroe explores relativity and our place in the universe.

It seems that the effect of dark energy became dominant only
recently about 8 x 109 years after the Big Bang. If the acceleration
presists in the future, it will impose a horizon surrounding a galaxy like the
Milkyway - a distance beyond which light cannot reach us. Figure 02-10g depicts
the sequence of events for the future of the universe with
cosmic acceleration according to a computer simulation (click image to obtain
larger view). The model assumes that the dark energy permeating the vacuum has a
positive, constant value - similar to the cosmological constant, as Einstein
once posited.

Figure 02-10g Future of the Universe

A study on the consequence of cosmic
acceleration concludes that while most of the galaxies move away beyond the
cosmic

horizon, the local group of galaxies will collapse into a
supergalaxy by gravitational attraction. Eventually, the universe goes
black when the last stars burn out. Future civilizations (if there is any
left) will have a very different perspective of the universe. Our
descendants will observe an island of stars (the supergalaxy) embedded in
a vast emptiness. It will resemble the de Sitter
universe originally

Figure 02-10h Future of the

Milkyway [large image 1, 2]

envisioned by Einstein. Figure 02-10h shows the sequence
of events in an artist's rendition.

Figure 02-10i shows the large-scale distribution of dark
matter mapped by the Hubble's
Cosmic Evolution Survey in early 2007. Since light will follow the
deformed path created by massive object, the quantity and location of the
dark matter can be estimated by the amount of the bending. However, it
should be cautioned that such image represents only a small facet of the
whole picture. Just like representing the distortion of space-time
as a piece of stretched rubber sheet, or the probability density of an electron (in
the atom) by some foggy orbital, the dark matter distribution map does not
include the other interesting properties such as its lack of interaction
with other matter except via gravity.

Figure 02-10i Dark Matter Distribution [large
image]

Note the increasing clumpiness from distant past to more
recent epoch in the picture.

The map of dark matter forms a filamentous 'skeleton' upon
which visible matter congregates, eventually producing stars and galaxies.
Baryonic structures are expected to form only inside the dark-matter
scaffold. But as shown in Figure 02-10j, the concentrations of dark matter
(mapped in contours) usually - but not always - match up with normal
matter (coloured). The discrepancies could be a simple error resulting
from the way the observations were made. Alternatively it is suggested
that dark matter, if the clump is small enough, could have any
accumulating visible matter blown out of it by a high-energy phenomenon
such as

Figure 02-10j Dark Matter and Baryonic Matter [view large
image]

a quasar or a supernova, for example. The collision of two
galaxies could also blow an amount of visible matter out as a faint
satellite galaxy that has no associated dark matter.

[Top]

Parallel Universes, Multiverse - the
Unobservable Universes12
The
subject of parallel universes used to belong to the realm of science fictions.
The idea is familiar on some TV shows such as "Star Trek", which portrays
other worlds that are almost like our own, except ... there is a slight
difference. Then some cosmologists propose that our Universe might be just one
of many in an ever-multiplying network of parallel universes, which they call
the multiverse.
Recent observational data open up the possibility that it is conceivable
scientifically with some creative imagination.

Figure 02-11 shows recent astronomical observations, which
tend to support the hypothesis. The diagram on the left illustrates the
WMAP measurementb of the
fluctuations in the CMBR temperature. The strongest fluctuations are just
over half a degree across, which indicates that space is very large or
infinite. In addition, the diagram on the right illustrates the
measurements of matter density from WMAP and 2dF Galaxy Redshift
Surveyc. They are
consistent with uniform distribution of matter on large scales.

Figure 02-11 Universe, Flat & Uniform [view large
image]

These observational data support the inflation theory,
which suggests that the universe underwent an exponential expansion at
10-35 sec after the Big Bang. The universe became so large that
it looks flat within our event horizon, and in addition, the contents in
the universe were mixed uniformly as witnessed by the CMBR.

Our universe with a size of about 1026 meters (as limited by
the event horizon) is just a speck in comparison to this vast expand. The
number of ways to arrange matter in the space outside our universe is
enormous and each one would have its own event horizon (size); these are
the parallel universes. Statistically, an arrangement similar to ours is
bound to happen given enough space. Thus there would be universes
identical to ours somewhere. However, we cannot communicate with any of
these parallel universes because the speed of light is finite.

This conclusion is derived from elementary probability and does not
assume speculative modern physics, merely that space is infinite (or at
least sufficiently large)

Figure 02-12 Parallel Universes [view large
image]

in size and almost uniformly filled with matter, as
observations indicate. In infinite space, even the most unlikely events
must take place somewhere.

Followings is a more elaborated deduction with simple mathematics:

The radius of the observable universe is taken to be 4x1026 m.
It is assumed that the matter in the universe consists of nucleons, which has
a radius of about 2x10-13 m.

Therefore, the universe has roughly 10118 partitions for the
nucleons.

These partitions can be filled or unfilled according to the configuration
of the universe. The total number of different arrangements is
210118.

A box with a radius of 210118x1026 m ~
210118 m would exhausts all the possibilities. It
contains possibly all kinds of parallel universes.

Beyond that box, universes - including ours - must repeat. The identical
parallel universe would be about 210118 m away as shown
in Figure 02-12.

There are even more exotic scenarios about multiverse:

According to Superstring
theory, there can be 100500 different vacua each one
corresponds to a different universe. Our universe and contiguous regions
of space is a bubble embedded in an even vaster but mostly empty volume.
Other bubbles exist out there, disconnected from ours. They nucleate
like raindrops in a cloud. During nucleation, each one may acquire
different strength of the forces, and may emerge with different spatial
and temporal dimensions. It all depends on the outcome of symmetry
breaking. The anthropic principle dictates that we
see the universe the way it is because if it

Figure 02-13 Anthropic Principle
[view large
image]

were different we would not be here to observe it (see
more in Topic
15).

Figure 02-13 shows the consequence
of the variation in the strength of strong and electromagnetic interactions,
and the numbers of spatial and temporal dimensions. It is reported in 2006
that habitable universe is possible without weak interaction. Nuclear burning
can somehow be maintained inside stars albeit in a much reduced rate; while
heavy elements can still be dispersed into interstellar space via the process
of type Ia
supernova. Another possibility is the cold big bang (low number of
photons/baryon ~ 107) universe where the cosmological constant was
1017 times that of our universe. In such universe, the stars form
so quickly that they are in place before the cosmological repulsion takes
hold.

In quantum mechanics the superposition of
quantum states suddenly "collapsed" into a definite quantum state when
we make a measurement. For example, measurement of the spin state for a
spinning
particle would yield either 1 or 0; it would not be any value in
between. Generalization of this concept to the macroscopic world
suggests that one classical reality would gradually split into
superpostions of many as shown in Figure 02-14. Observation experiences
one of the splittings by a decoherent process, which mimics wavefunction
collapse. The classical states (no weird happening such as being in two
different places at once) are observed because they are in the most
robust states.

Figure 02-14 Quantum Worlds
[view large
image]

The correspondence between mathematics and physics has been a source
of debate that goes as far back as Aristotle and Plato.
According to the Aristotelian paradigm, physical reality is fundamental
and mathematical language is merely a useful tool. The Platonic argument
considers the mathematical structure to be the true reality and
observers only perceive it imperfectly. Thus a fundamental asymmetry
appears to be built into the very heart of reality - why is only one of
the many mathematical structures singled out to describe our universe?
It is suggested that complete mathematical symmetry holds: that all
mathematical structures exist physically as well. Every mathematical
structure

Figure 02-15 Aristotele and Plato [view large
image]

corresponds to a parallel universe. As a consequence, each
universe is governed by its own fundamental laws of physics (see more in
Topic
15). In Figure 02-15 Aristotle points down to the reality on earth
while Plato points up to multiverse.

By 2006, the confluence of events has pushed many leading physicists
toward the notion of a multiverse. These include: measurements that indicate the
universe's
expansion is accelerating; empirical tests that bolster the inflationary universe
scenario; theories of eternal inflation (see below) that suggest an endless
number of Big Bang; and developments in string theory
that show how to design universes with widely different properties.

The theory of eternal inflation posits that the entire
eternally inflating spacetime (false vacuum) originated as a minuscule
closed multiverse. It tunneled, quantum-mechanically, out of nothing and
immediately plunged into the never-ending inflation. Thus, the multiverse
is eternal, but it did have a beginning. Inflation rapidly blows the
universe up to an enormous size. It stopped where we are, producing our
own island universe, and many others. But due to the peculiar structure of
inflationary spacetime, it continues in other areas of the multiverse at
large. The multiverse contains an unlimited number of island universes. We
live in one of them, and our observable region is one of the infinite
numbers of observable regions (at different locations) that it contains
(see Figure 02-16). We may be able to travel to the other observable
regions, but we are forever confined to our own island universe. Constants
of nature that shape the character of our world take different values in
other island universes. Most of these universes are drastically

Figure 02-16 Multiverse, Eternal Inflation [view large
image]

different from ours, and only a tiny fraction of them are
hospitable to life.

[Top]

Footnotes
aSince the inflation has generated a much bigger universe
than we can see, the visible universe becomes flat to our perception just like
the flat Earth in local view. This implies parallel lines will never meet no
matter how far they are extended, and the familiar scenery of galaxies and
galaxy clusters would extend infinitely far beyond our cosmic horizon.

bThe first peak (the whole curve) of the power spectrum
moves from left to right with increasing radius of space.

cThe 2dF redshift
survey uses the two-degree field spectroscopic facility on the
Anglo-Australian Telescope to measure the redshifts of 250,000 galaxies.

[Top]

References:

Big Bang Tour (animation) -- http://superstringtheory.com/cosmo/cosmo3.html

Cosmology (lecture notes) -- http://blueox.uoregon.edu/~jimbrau/astr123

Inflation -- http://www.ucolick.org/~patrik/ay5/notes/lecture15.pdf

CMBR Spectrum -- http://archive.ncsa.uiuc.edu/Cyberia/Cosmos/Footprints.html

CMBR Fluctuations -- http://pancake.uchicago.edu/~carroll/ourpreposterous/img19.htm

CMBR Polarization -- http://www-news.uchicago.edu/releases/02/020918.carlstrom.shtml

CMBR Polarization, DASI home page -- http://astro.uchicago.edu/dasi/

CMBR Power Spectrum -- http://www.livingreviews.org/Articles/Volume1/1998-11jones/node2.html

CMBR Power Spectrum (animation) -- http://background.uchicago.edu/~whu/intermediate/gravity.html

Wilkinson Microwave Anisotropy Probe (WMAP), Home Page --
http://map.gsfc.nasa.gov/

Dark Energy, Dark Matter -- http://hitoshi.berkeley.edu/290E/

Parallel Universes, Multiverse -- http://www.hep.upenn.edu/~max/multiverse.html

[Top]

Index

Anthropic
Principle
Aristotle and
Plato
Big Bang
Theory
Black-body
radiation
CMBR
fluctuations
CMBR
polarization
CMBR power
spectrum
CMBR
spectrum
Composition
of the Universe
Dark energy, dark
matter
Decoupling
epoch
Future of the
Universe
History of the
Universe
Hubble's
law
Hubble's
constant
Hubble deep
fields

Hubble's space
telescope
Inflation
Theory
Loop quantum
gravity
Milky
Way
Multiverse
Nucleosynthesis
Observable
universe
Olber's
paradox
Parallel
Universes
Polarization
Quantum
Foam
Quantum
worlds
Red
shift
Standard
Candle
Supernova type
Ia
Wilkinson Microwave
Anisotropy Probe (WMAP)

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