The Observable Universe and Beyond

Contents

The Observable Universe

		composed of smaller things and is a part of something larger as shown in Figure 02-01a (See also "Map of the Universe" for a different perspective) 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
Figure 02-01a The Observable Universe [view large image]	Figure 02-01b Inflationary Cosmology [view large image]	scale of time: processes tend to happen quickly on small scales and slowly on large scales.

Big Bang Theory^1,2

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 flat^a. 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.

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 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. Figure 02-03e shows the sequence of nucleosynthesis during the first few hundred
  Figure 02-03e Nucleosynthe- sis, Pictorial [large image]	Figure 02-03f Nucleosynthesis, Graphical [view large image]	seconds after the Big Bang. Figure 02-03f is the same time development for nucleosynthesis in a more quantitative way.

  
  
  

  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 02-03g). 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". Measurements of lithium abundance in ancient stars in the early 2000's reveal some discrepancy between the theoretical prediction and observable amount. The observed Li-7 is only 1/3 of the amount predicted by theory; while there is a 1000 fold too much with the observed Li-6. The discrepancy can be resolved by adding supersymmetry into the theoretical calculation. However, the concept of supersymmetry has not been confirmed by

  Figure 02-03g Nucleosynthesis, Theoretical Fit [view large image]

  observation/experiment, even the soon to be activated LHC may not be able to detect the very weak interacting gravitinos or the super-heavy staus.

  
  
  
• 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 02-03h shows the scope of the survey including the Hubble Ultra Deep Field.

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

  
  
  
• Cosmic Microwave Background Radiation : See section on WMAP.

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]

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

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.

CMBR Power Spectrum^8,9

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]

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

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.

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]

		(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:

1. 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.
2. 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.
3. 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.

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. It is suggested that the mass of dark matter within the lunar orbit can be computed by subtracting the total mass (Earth + Dark Matter) within the lunar orbit from the mass of the Earth measured by a gravity-sensing satellite (Figure 02-10a). It turns out to be no more than 1.5x1015 kg or about one

Figure 02-10a Earth-Moon System [view large image]

billion times lower than the mass of the Earth. It means that the difference is too small to be measured by the 2008 technology. All that can be found is the upper bound, which is just another way of saying that there is no difference up to the current level of accuracy.

Figure 02-10b 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 02-10b 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 02-10c, 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 02-10c 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.

The nature of dark matter has been a mystery defying all attemps to explain as summarized below:


• 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 02-10d). 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 02-10e 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 02-10d MOND Theory [view large image]	Figure 02-10e MOND Prediction [view large image]

• See also "Hints of Dark Matter from Cosmic Rays".

Dark Energy

		there is some kind of repulsive "dark energy" to induce the acceleration. Figure 02-10g 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 02-10f Supernova Ia [view large image]	Figure 02-10g Energy-Matter in the Universe	New data in 2006 further refine the universe's contents to: 4% ordinary matter, 22% dark matter, and 74% dark energy.

Table 02-02 Composition of the Universe

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.

Another method to verify the cosmic acceleration is by detecting the bunching intervals of the clusters of galaxies. Whereas Type Ia supernovae behave like standard candles, the spacing between clusters of galaxies acts like a standard ruler. The bunching was generated by the cosmic sound wave, which compressed matter to higher density at its peaks. According to different scenarios of cosmic expansion, the amount of stretching is different as shown in Figure 02-10h. In the primordial gas, the incoherent acoustic oscillations

Figure 02-10h Dark Energy and Sound Wave

created peaks at intervals of 436000 light years, today the spacing should be about 500 million light years depending on the kind of cosmic model.

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 02-10i). Such idea has been confirmed in 2008 by NASA's Chandra X-ray Observatory. The X-ray results on the hot gas in dozens of

Figure 02-10i Galaxy Formation & Dark Energy

galaxy clusters some of which are relatively close and others are more than halfway across the universe reveal that accelerated expansion stifles the growth of galaxy clusters. It also tentatively identifies the cosmic constant as the dark energy.

The nature of "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 02-10j 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 02-10j 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 02-10k).

Figure 02-10k Dark Energy Illusion

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.

Void - If the Earth is located in a vast cosmic void (with less matter than the average) of the size between 300 million to 3 billion light years, then object outside the void would be further away (than envisioned from a homogeneous universe) because the void would expand faster with less gravitational retardation (see Figure 02-10l). The problem with this explanation is the requirement that the Earth has to be in the middle of the void (in violation of the Copernican Principle); otherwise it would be inconsistent with the WMAP data, which is isotropic. Measurement of the rate of cosmic expansion

Figure 02-10l Earth in a Void [view large image]

over time can be used to check against this hypothesis. The observational sensitivity required to record the tiny changes is currently beyond astronomers' capabilities. But it should become feasible with a new generation of ultra-sensitive telescopes.

Citing some seemingly inexplicable anomalies in astronomical observations, it is suggested that the "Void Theory" would remain viable even the Earth is slightly off center (up to 50 million light years). It has been shown that the CMBR is a bit lopsided - hotter in one direction than in the other. This asymmetry is usually attributed to the motion of the Solar system through space but could also be a sign of a lumpy universe. Furthermore, small fluctuations in the CMBR appear to align in the specific direction (the "axis of evil"). This alignment picks out a preferred direction in the sky, which, though hard to imagine in a Copernican universe, might be explained in terms of displacement of the Earth from the center of a void.

A preferred direction would also have other effects, such as large-scale coherent motions of galaxies and galaxy clusters. Several observations have claimed detection of such "dark flow", but it remains controversial. And then there is the argument that the "Void Theory" would not violate the Copernican principle (that the Earth is not special) if the region under consideration is very large and containing many more voids such as the inhomogeneous universe shown in Figure 02-10m, which also depicts the different explanations with dark energy and void.

Figure 02-10m Inhomogeneous Universe [view large image]

	Figure 02-10n Future of the Universe

		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 envisioned by Einstein. Figure 02-10o shows the sequence of events according to an artist's rendition.
Figure 02-10o Future of the	Milkyway [large image 1, 2]

scale, a model has been constructed with no other interactions between each other or with ordinary matter. It fits the observational 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 interactions — 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

Figure 02-10p Insignificance [view large image]

grand scheme of the universe as portrayed in a 1985 movie called "Insignificance" in which Einstein and Monroe explores relativity and our place in the universe (Figure 02-10p).

Parallel Universes, Multiverse - the Unobservable Universes¹²

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.

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.

Quantum Cosmology and Pre-Big Bang Theories

	According to the classical cosmology, the universe starts from a singularity state. It is obvious that the size of the universe would be very small during the initial expansion, and thus quantum effect must be taken into consideration. Unfortunately, a theory of quantum gravity is not available now. However, it
Figure 02-17 Quantum Cosmology [view large image]	does not stop physicists from adding quantum effects into this early phase of the universe in an ad hoc fashion, some examples are listed in Table 02-03:

Table 02-03 Quantum Cosmology

	answer to such open-end interrogation. Figure 02-17 shows the progression of our understanding about the Big Bang. Figure 02-17(a) portrays our ignorance in classical cosmology. There is no further explanation when we encounter the singularity. Gradually, quantum standard cosmology suggests that the seed of the universe was tunneling through a high energy and high curvature region without
Figure 02-18 String Cosmology [view large image]	specifying from what as shown in Figure 02-17(b). In quantum string cosmology (Figure 02-17(c)), the pre-big bang is identified with the string perturbative vacuum in the Superstring Theory as sketched qualitatively in Figure 02-18.

The models are constructed with a framework where the universe can be represented as a wave (the Wheeler-DeWitt wave function) propagating in an abstract, multidimensional space dubbed superspace (no connection with super-symmetry). The string perturbative vacuum is characterized by a nearly flat space-time geometry and the vanishingly small coupling of all interactions. Figure 02-19 shows the evolution of the curvature (represented by the Hubble parameter H) and the gravitational constant G (determined by the dilaton).

Figure 02-19 Evolution of H and G [view large image]

links now represent units of area, and the nodes become quantized units of volume. A crucial difference in such formulation is that the lattice is not fixed, it evolves according to some rules. Thus, space-time is not a background scaffold anymore. Its application to cosmology reveals that the universe evolved from a pre-existing state toward very high density in a very small volume but then bounced back because repulsion is generated at such high density in LQG. It led to a "super-inflation" era, then the "inflation" era and the classical space-time afterward (Figure 02-20). It has been shown that super-inflation can produce the kind of quantum fluctuations in the fabric of space-time for the formation of galaxies and clusters of galaxies later. The period of inflation is still required to resolve the horizon and flatness problems. Since the

Figure 02-20 LQG Cosmology [view large image]

repulsive dark energy has not been taken into consideration in the computation, it is not known if the pre-existing universe will really collapse as suggested in this model.

The theory of superstring admits up to seven extra spatial dimensions. The cyclic universe model represents our universe as a 3-dimensional brane moving in a 4-dimensional space. It interacts with another 3-dimensional brane via a spring-like force, which is identified with the dark energy. These two branes execute periodic motion as shown in Figure 02-21. The moment of collision is perceived by us as the Big Bang. We can never reach out to the extra dimension, only gravity and the dark energy can reside there. Figure 02-21 depicts the sequence of events during one cycle of the endless oscillations with a more detailed description in the followings:

Figure 02-21 Cyclic Universe [view large image]

1. According to the cyclic universe model, the Big Bang is not the beginning of space or time. Instead, it is the moment when gravitational and other forms of energy are transformed into new matter and radiation and a new period of expansion and cooling begins.
2. Hot, dense matter and radiation fills the universe immediately after the bang. The cosmic temperature reaches about 10^{27 o}K. At this temperature, matter exists only in its elementary forms such as quarks, electrons, photons, and the like. However, the temperature remains modest compared to the 10^{32 o}K or higher in the scenario for the usual Big Bang.
3. During the following 9 billion years, the cosmos expands and cools. The elementary constituents clump into protons and neutrons, and eventually atoms, molecules, planet, stars, galaxies, clusters of galaxies, and superclusters. The blueprint had been laid down as tiny density variations (ripples) nearly the end of the previous cycle.
4. Dark energy becomes dominant at this point. The repulsive nature of this substance causes the cosmic expansion to speed up as witnessed by present day astronomers.
5. During the next trillion years, the accelerating expansion will continue and rapidly dilute the universe of the matter content and lumpy structures.
6. The universe is restored to a simple, uniform, and pristine state, which is essentially similar to the prediction by the usual Big Bang theory.
7. However in the cyclic universe model, dark energy is unstable. It will decay near the cycle's end into a form of extremely high-pressure energy that causes the universe to contract slowly.
8. Space becomes increasingly smooth and flat as the contraction proceeds, while quantum effect produces random fluctuations seeding density variations over all the regions.

This model provides answers to two annoying inquiries in cosmology:
1. What went before the pre-big bang, before the pre-pre-big bang, ... ad infinitum -- There could be no beginning or end in a cyclic universe, which may exist forever.
2. What is the 3 dimensional space expands into -- The usual explanation asserts that cosmic expansion is special, it doesn't expand into anything. Since the cyclic universe is a 3-D brane immersing in a 4-D space, the cosmic expansion in this model naturally expands into this 4-D bulk without invoking anything special.

The first image of a strip of the millimeter wavelength sky (Figure 02-22, from Planck in September 2009) shows that all systems are working well. Routine operations will continue for at least 15 months without a break. In this time, Planck will be able to gather data (at 9 different wavelengths) for two full independent all-sky maps. To fully exploit the high sensitivity of Planck, the data will require a great deal of delicate calibrations and careful analysis. It will keep cosmologists and astrophysicists busy for decades to come.

Figure 02-22 First Image from the Planck Satellite

Footnotes

References:

1. Big Bang Tour (animation) -- http://superstringtheory.com/cosmo/cosmo3.html
2. Cosmology (lecture notes) -- http://blueox.uoregon.edu/~jimbrau/astr123
3. Inflation -- http://www.ucolick.org/~patrik/ay5/notes/lecture15.pdf
4. CMBR Spectrum -- http://archive.ncsa.uiuc.edu/Cyberia/Cosmos/Footprints.html
5. CMBR Fluctuations -- http://pancake.uchicago.edu/~carroll/ourpreposterous/img19.htm
6. CMBR Polarization -- http://www-news.uchicago.edu/releases/02/020918.carlstrom.shtml
7. CMBR Polarization, DASI home page -- http://astro.uchicago.edu/dasi/
8. CMBR Power Spectrum -- http://www.livingreviews.org/Articles/Volume1/1998-11jones/node2.html
9. CMBR Power Spectrum (animation) -- http://background.uchicago.edu/~whu/intermediate/gravity.html
10. Wilkinson Microwave Anisotropy Probe (WMAP), Home Page -- http://map.gsfc.nasa.gov/
11. Dark Energy, Dark Matter -- http://hitoshi.berkeley.edu/290E/
12. Parallel Universes, Multiverse -- http://www.hep.upenn.edu/~max/multiverse.html

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