IT seems fairly likely that there was a Big Bang. The obvious question that could be asked to challenge or define the boundaries between physics and metaphysics is: what came before the Big Bang?Physicists define the boundaries of physics by trying to describe them theoretically and then testing that description against observation. Our observed expanding Universe is very well described by flat space, with critical density supplied mainly by dark matter and a cosmological constant, that should expand forever.
If we follow this model backwards in time to when the Universe was very hot and dense, and dominated by radiation, then we have to understand the particle physics that happens at such high densities of energy. The experimental understanding of particle physics starts to poop out after the energy scale of electroweak unification, and theoretical physicists have to reach for models of particle physics beyond the Standard Model, to Grand Unified Theories, supersymmetry, string theory and quantum cosmology.
This exploration is guided by three outstanding problems with the Big Bang cosmological model:
1. The flatness problem
2. The horizon problem
3. The magnetic monopole problem
Flatness problem
The Universe as observed today seems to enough energy density in the form of matter and cosmological constant to provide critical density and hence zero spatial curvature. The Einstein equation predicts that any deviation from flatness in an expanding Universe filled with matter or radiation only gets bigger as the Universe expands. So any tiny deviation from flatness at a much earlier time would have grown very large by now. If the deviation from flatness is very small now, it must have been immeasurably small at the start of the part of Big Bang we understand.
So why did the Big Bang start off with the deviations from flat spatial geometry being immeasurably small? This is called theflatness problem of Big Bang cosmology.
Whatever physics preceded the Big Bang left the Universe in this state. So the physics description of whatever happened before the Big Bang has to address the flatness problem.
So why did the Big Bang start off with the deviations from flat spatial geometry being immeasurably small? This is called theflatness problem of Big Bang cosmology.
Whatever physics preceded the Big Bang left the Universe in this state. So the physics description of whatever happened before the Big Bang has to address the flatness problem.
Horizon problem
The cosmic microwave background is the cooled remains of the radiation density from the radiation-dominated phase of the Big Bang. Observations of the cosmic microwave background show that it is amazingly smooth in all directions, in other words, it is highlyisotropic thermal radiation. The temperature of this thermal radiation is 2.73° Kelvin. The variations observed in this temperature across the night sky are very tiny.
Radiation can only be so uniform if the photons have been mixed around a lot, or thermalized, through particle collisions. However, this presents a problem for the Big Bang model. Particle collisions cannot move information faster than the speed of light. But in the expanding Universe that we appear to live in, photons moving at the speed of light cannot get from one side of the Universe to the other in time to account for this observed isotropy in the thermal radiation. The horizon size represents the distance a photon can travel as the Universe expands.
The horizon size of our Universe today is too small for the isotropy in the cosmic microwave background to have evolved naturally by thermalization. So that's the horizon problem.
Radiation can only be so uniform if the photons have been mixed around a lot, or thermalized, through particle collisions. However, this presents a problem for the Big Bang model. Particle collisions cannot move information faster than the speed of light. But in the expanding Universe that we appear to live in, photons moving at the speed of light cannot get from one side of the Universe to the other in time to account for this observed isotropy in the thermal radiation. The horizon size represents the distance a photon can travel as the Universe expands.
The horizon size of our Universe today is too small for the isotropy in the cosmic microwave background to have evolved naturally by thermalization. So that's the horizon problem.
Magnetic monopole problem
Normally, as we observe on Earth, magnets only come with two poles, North and South. If one cuts a magnet in half, the result will not be one magnet with only a North pole and one magnet with only a South pole. The result will be two magnets, each of which has its own North and South poles. 
A magnetic monopole would be a magnet with only one pole. But magnetic monopoles have never been seen? Why not?
This is different from electric charge, where we can separate an arrangement of positive and negative electric charges so that only positive charge is in one collection and only negative charge is in another.
Particle theories like Grand Unified Theories and superstring theory predict magnetic monopoles should exist, and relativity tells us that the Big Bang should have produced a lot of them, enough to make one hundred billion times the observed energy density of our Universe.
But so far, physicists have been unable to find even one.
So that's a third motivation to go beyond the Big Bang model to look for an explanation of what could have happened when the Universe was very hot and very small.
A magnetic monopole would be a magnet with only one pole. But magnetic monopoles have never been seen? Why not?
This is different from electric charge, where we can separate an arrangement of positive and negative electric charges so that only positive charge is in one collection and only negative charge is in another.
Particle theories like Grand Unified Theories and superstring theory predict magnetic monopoles should exist, and relativity tells us that the Big Bang should have produced a lot of them, enough to make one hundred billion times the observed energy density of our Universe.
But so far, physicists have been unable to find even one.
So that's a third motivation to go beyond the Big Bang model to look for an explanation of what could have happened when the Universe was very hot and very small.
Inflationary universe?
Matter and radiation are gravitationally attractive, so in a maximally symmetric spacetime filled with matter, the gravitational force will inevitably cause any lumpiness in the matter to grow and condense. That's how hydrogen gas turned into galaxies and stars. But vacuum energy comes with a high vacuum pressure, and that high vacuum pressure resists gravitational collapse as a kind of repulsive gravitational force. The pressure of the vacuum energy flattens out the lumpiness, and makes space get flatter, not lumpier, as it expands.
So one possible solution to the flatness problem would be if our Universe went through a phase where the only energy density present was a uniform vacuum energy. If this phase occurred before the radiation-dominated era, then the Universe could evolve to be extraordinarily flat when the radiation-dominated era began, so extraordinarily flat that the lumpy evolution of the radiation- and matter-dominated periods would be consistent with the high degree of remaining flatness that is observed today.
This type of solution to the flatness problem was proposed in the 1980s by cosmologist Alan Guth. The model is called theInflationary Universe. In the Inflation model, our Universe starts out as a rapidly expanding bubble of pure vacuum energy, with no matter or radiation. After a period of rapid expansion, or inflation, and rapid cooling, the potential energy in the vacuum is converted through particle physics processes into the kinetic energy of matter and radiation. The Universe heats up again and we get the standard Big Bang.
So an inflationary phase before the Big Bang could explainhow the Big Bang started with such extraordinary spatial flatness that it is still so close to being flat today.
Inflationary models also solve the horizon problem. The vacuum pressure accelerates the expansion of space in time so that a photon can traverse much more of space than it could in a spacetime filled with matter. To put it another way, the attractive force of matter on light in some sense slows the light down by slowing down the expansion of space itself. In an inflationary phase, the expansion of space is accelerated by vacuum pressure from the cosmological constant, and light gets farther faster because space is expanding faster.
If there were an inflationary phase of our Universe before the radiation-dominated era of the Big Bang, then by the end of the inflationary period, light could have crossed the whole Universe. And so the isotropy of the radiation from the Big Bang would no longer be inconsistent with the finiteness of the speed of light.
The inflationary model also solves the magnetic monopole problem, because in the particle physics that underlies the inflationary idea, there would only be one magnetic monopole per vacuum energy bubble. That means only one magnetic monopole per Universe.
That's why the inflationary universe theory is still the favored pre-Big Bang cosmology among cosmologists.
So one possible solution to the flatness problem would be if our Universe went through a phase where the only energy density present was a uniform vacuum energy. If this phase occurred before the radiation-dominated era, then the Universe could evolve to be extraordinarily flat when the radiation-dominated era began, so extraordinarily flat that the lumpy evolution of the radiation- and matter-dominated periods would be consistent with the high degree of remaining flatness that is observed today.
This type of solution to the flatness problem was proposed in the 1980s by cosmologist Alan Guth. The model is called theInflationary Universe. In the Inflation model, our Universe starts out as a rapidly expanding bubble of pure vacuum energy, with no matter or radiation. After a period of rapid expansion, or inflation, and rapid cooling, the potential energy in the vacuum is converted through particle physics processes into the kinetic energy of matter and radiation. The Universe heats up again and we get the standard Big Bang.
So an inflationary phase before the Big Bang could explainhow the Big Bang started with such extraordinary spatial flatness that it is still so close to being flat today.
Inflationary models also solve the horizon problem. The vacuum pressure accelerates the expansion of space in time so that a photon can traverse much more of space than it could in a spacetime filled with matter. To put it another way, the attractive force of matter on light in some sense slows the light down by slowing down the expansion of space itself. In an inflationary phase, the expansion of space is accelerated by vacuum pressure from the cosmological constant, and light gets farther faster because space is expanding faster.
If there were an inflationary phase of our Universe before the radiation-dominated era of the Big Bang, then by the end of the inflationary period, light could have crossed the whole Universe. And so the isotropy of the radiation from the Big Bang would no longer be inconsistent with the finiteness of the speed of light.
The inflationary model also solves the magnetic monopole problem, because in the particle physics that underlies the inflationary idea, there would only be one magnetic monopole per vacuum energy bubble. That means only one magnetic monopole per Universe.
That's why the inflationary universe theory is still the favored pre-Big Bang cosmology among cosmologists.
But how does Inflation work?
The vacuum energy that drives the rapid expansion in an inflationary cosmology comes from a scalar field that is part of the spontaneous symmetry breaking dynamics of some unified theory particle theory, say, a Grand Unified Theory or string theory.
This field is sometimes called the inflaton. The average value of the inflaton at temperature T is the value at the minimum of its potential energy at that temperature. The location of this minimum changes with temperature, as is shown in the animation to the right.
For temperatures T above some critical temperature Tcrit, the minimum of the potential is at zero. But as the temperature cools, the potential changes and a second minimum develops in the potential at a nonzero value. This signals something called a phase transition, like when steam cools and condenses into water. For water the critical temperature Tcrit where this phase transition happens is 100°C, or 373°K.
The two minima in the potential represent the two possible phases of the inflaton field, and of the Universe, at the critical temperature. One phase has the minimum of the field f=0, and the other phase represents the vacuum energy if the ground state hasf=f0.
According to the inflationary model, at the critical temperature, spacetime starts to under go this phase transition from one minimum to the other. But it doesn't do it smoothly, it stays in the old "false" vacuum too long. This is called supercooling. This region of false vacuum expands exponentially fast, and the vacuum energy of this false vacuum is the cosmological constant for the expansion. It is this process that is called Inflation and solves the flatness, horizon and monopole problems.
This region of false vacuum expands until bubbles of the new broken symmetry phase with f=f0 form and collide, and eventually end the inflationary phase. The potential energy of the vacuum is converted through to kinetic energy of matter and radiation, and the Universe expands according to the Big Bang model already outlined.
This field is sometimes called the inflaton. The average value of the inflaton at temperature T is the value at the minimum of its potential energy at that temperature. The location of this minimum changes with temperature, as is shown in the animation to the right.
For temperatures T above some critical temperature Tcrit, the minimum of the potential is at zero. But as the temperature cools, the potential changes and a second minimum develops in the potential at a nonzero value. This signals something called a phase transition, like when steam cools and condenses into water. For water the critical temperature Tcrit where this phase transition happens is 100°C, or 373°K.
The two minima in the potential represent the two possible phases of the inflaton field, and of the Universe, at the critical temperature. One phase has the minimum of the field f=0, and the other phase represents the vacuum energy if the ground state hasf=f0.
According to the inflationary model, at the critical temperature, spacetime starts to under go this phase transition from one minimum to the other. But it doesn't do it smoothly, it stays in the old "false" vacuum too long. This is called supercooling. This region of false vacuum expands exponentially fast, and the vacuum energy of this false vacuum is the cosmological constant for the expansion. It is this process that is called Inflation and solves the flatness, horizon and monopole problems.
This region of false vacuum expands until bubbles of the new broken symmetry phase with f=f0 form and collide, and eventually end the inflationary phase. The potential energy of the vacuum is converted through to kinetic energy of matter and radiation, and the Universe expands according to the Big Bang model already outlined.
A testable prediction?
It's always good to have testable predictions from a theory of physics, and the inflation theory has a distinct prediction about the density variations in the cosmic microwave background. A bubble of inflation consists of accelerating vacuum. In this accelerating vacuum, a scalar field will have very small thermal fluctuations that are nearly the same at every scale, and the fluctuations will be have a Gaussian distribution. This prediction fits current observations and will be tested with greater precision by future measurements of the cosmic microwave background.
So are all the problems solved?
Despite the prediction above, inflation as described above is far from an ideal theory. It's too hard to stop the inflationary phase, and the monopole problem has other ways of resurfacing in the physics. Many of the assumptions that go into the model, such as an initial high temperature phase and a single inflating bubble have been questioned and alternative models have been developed.
Today's inflation models have evolved beyond the original assumption of a single inflation event giving birth to a single Universe, and feature scenarios where universes nucleate and inflate out of other universes in the process called eternal inflation.
There is also another attempt to solve the problems of Big Bang cosmology using a scalar field that never goes through an inflationary period at all, but evolves so slowly so that we observe it as being constant during our own era. This model is calledquintessence, after the ancient spiritual belief in the Quinta Essentia, the spiritual matter from which the four forms of physical matter are made.
So where does string theory fit in all of this? That's the next topic.
Today's inflation models have evolved beyond the original assumption of a single inflation event giving birth to a single Universe, and feature scenarios where universes nucleate and inflate out of other universes in the process called eternal inflation.
There is also another attempt to solve the problems of Big Bang cosmology using a scalar field that never goes through an inflationary period at all, but evolves so slowly so that we observe it as being constant during our own era. This model is calledquintessence, after the ancient spiritual belief in the Quinta Essentia, the spiritual matter from which the four forms of physical matter are made.
So where does string theory fit in all of this? That's the next topic.
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