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The Observable Universe and Beyond

Quantum Cosmology and Pre-Big Bang Theories

Quantum Cosmology According to the classical cosmology, the universe starts from a state of singularity. It is assumed by most cosmic models 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 does not stop

Figure 02-17 Quantum Cosmology
[view large image]

physicists from adding quantum effects into this early phase of the universe in an ad hoc fashion, some examples are listed in Table 02-05:

Ad Hoc Add On Quantum Effect Epoch To Explain Status
A Period of Inflation Quantum fluctuation 10-35-10-32 sec after Big Bang Large structures in universe Healthy
Density fluctuations Uncertainty Principle When the universe is smaller than the size of an atom CMBR and large galactic structures Healthy
History of the universes Path integral From Big Bang to present Geometry of our universe Unknown
Probability of universes Schrodinger equation From Big Bang and beyond Our universe is most probable Dubious
Origin of Big Bang Interactions of branes At the moment of Big Bang Cosmic Expansion Obsolete
Pre-Big Bang Processes
(see below)
Wave propagation in theory of superstring Before the Big Bang Creation of our universe Obsolete
LQG universe (see below) Loop quantum gravity Big Bang and beyond Creation of our universe Lingering
Cyclic universe (see below) Theory of superstring Before the Big Bang, endless cycles Beginning of our universe Obsolete
Eternal inflation Quantum fluctuation Before the Big Bang, endless bubbles Beginning of our universe Dubious
Cosmic origin Qunatization of the Friedmann equation At the moment of Big Bang Beginning of our universe Unknown
Vacuum energy density Virtual particles Over cosmic time Dark energy Dubious

Table 02-05 Quantum Cosmology

Some cosmological models :

*** Quantum Model
When talking about Big Bang, the inevitable question would be: "what went before it?" The common expectation is that the scientists will disguise their ignorance with some sort of excuses. Physicists in the 21th century is fast coming up with an answer to such open-end
String Cosmology 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 specifying from what as shown in Figure 02-17(b). In quantum string cosmology (Figure 02-17(c)), the pre-big bang

Figure 02-18 String Cosmology
[view large image]

is identified with the string perturbative vacuum in the Superstring Theory as sketched qualitatively in Figure 02-18.
Evolution of H and G 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]

Figure 02-18(a) is a schematic diagram to portray the transition as a quantum mechanical reflection of the wave function in a mini-superspace whose coordinates correspond to the dilation and to the spatial radius of the universe. The dilaton is a neutral scalar force field (or particle) associated with the duality transformation for the spatial radius (of the universe) R 1/R. The incident wave describes the initial evolution of the universe from the string perturbative vacuum towards the high curvature regime. Part of this incoming wave is not stopped by the barrier and is classically transmitted to the region of ever increasing dilaton, running towards the singularity. Another part is reflected to the region of decreasing dilaton and standard post-big bang evolution. This process is not very efficient as shown in Figure 02-17(c). The more efficient one is the "anti-tunneling" effect of the wave function, i.e., as the creation of pairs of universes from the string perturbative vacuum. The wave function is amplified during this process as shown in Figure 02-18(b).

See a "Toy Model" by Quantization of the Friedmann Equation.

*** Loop Quantum Model
The theory of "loop quantum gravity (LQG)" incorporates quantum effect into gravity by latticizing general relativity (GR) in a way similar to the "lattice theory in QFT" with the spacing between nodes replaced by the Planck area (~10-66cm2), i.e., the links now represent units of area,
LQG Cosmology 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 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.

Figure 02-20 LQG Cosmology
[view large image]

*** Brane Model
Cyclic Universe 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 1027 oK. 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 1032 oK 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.
  9. The collision of the two branes produces another moment of Big Bang and starts another cycle.
    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.
See also "Pre-Big Bang Universe".

Big-Bang Models *** Multiverse (See "Multiverse, Eternal Inflation ").

Figure 02-22 summarizes the various cosmic theories into four classes with some examples.

Although the cyclic and inflationary theories explain equally well all the astronomical data, there are two tests that can distinguish them. Firstly, inflation in the usual Big Bang theory produces detectable gravitational waves. These wrinkle in space propagate through the universe and should produce a measurable polarization pattern in the CMBR. The gravitational waves in the cyclic model are far too weak to induce any change in the CMBR. Secondly, the inflationary picture predicts that the statistical distribution of temperature variations in CMBR should follow a bell curve, while the distribution has measurable deviation (from a bell curve) in the cyclic model. Observations in the next decade will be able to decide which one is correct. The first test may come very soon by ESA's Planck mission, scheduled for launch in 2009.

Figure 02-22 Big-Bang Models [view large image]

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