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Alan Guth and Stephen Hawking on "Eternal Inflation"
It is an interesting topic and Alan Guth had two papers discussing it in 2003, also Hawking had one I found in 2003. might be interesting to check out their recent words on the subject
Hawking defined it as follows and then proceded to critique the idea:
"... In the case of inflation, the idea is that the exponential expansion, obliterates the dependence on the initial conditions, so we wouldn't need to know exactly how the universe began, just that it was inflating. To lose all memory of the initial state, would require an infinite amount of exponential expansion.
This leads to the notion of ever lasting or eternal inflation. The original argument for eternal inflation, went as follows. Consider a massive scalar field in a spatially infinite expanding universe. Suppose the field is nearly constant over several horizon regions, on a space like surface. In an infinite universe, there will always be such regions. The scalar field will have quantum fluctuations. In half the region, the fluctuations will increase the field, and in half, they will decrease it. In the half where the field jumps up, the extra energy density will cause the universe to expand faster, than in the half where the field jumps down. After a certain proper time, more than half the region will have the higher value of the field, because the high field regions will expand faster than the low. Thus the volume averaged value of the field will rise. There will always be regions of the universe in which the scalar field is high, so inflation is eternal. The regions in which the scalar field fluctuates downwards, will branch off from the eternally inflating region, and will exit inflation.
Because there will be an infinite number of such exiting regions, advocates of eternalinflation get themselves tied in knots, on what a typical observer would see. So even if eternal inflation worked, it would not explain why the universe is the way it is. But in fact, the argument for eternal inflation that I have outlined, has serious flaws.
First, it is not gauge invariant. If one takes the time surfaces to be surfaces of constant volume increase, rather than surfaces of constant proper time, the volume averaged scalar field does not increase.
Second, it is not consistent. The equation relating the expansion rate to the energy density, is an integral of motion. Neither side of the equation can fluctuate, because energy is conserved.
Third, it is not covariant. It is based on a 3+1 split. From a four-dimensional view, eternal inflation can only be de Sitter space with bubbles. The energy momentum tensor of the fluctuations of a single scalar field, is not large enough to support a de Sitter space, except possibly at the Planck scale, where everything breaks down.
For these reasons, not gauge invariant, not consistent, and not covariant, I do not believe the usual argument for eternal inflation..."
Hawking "Cosmology from the Top Down"
http://arxiv.org/astro-ph/0305562
(if that doesn't work there's a longer link)
http://www.arxiv.org/ftp/astro-ph/papers/0305/0305562.pdf
Alan Guth's couple of recent ones (2003):
"Time since the beginning"
http://arxiv.org/astro-ph/0301199
(quote: "'eternal' inflation...proposes that our universe evolved
from an infinite tree of inflationary spacetime")
"Inflation and cosmological perturbations"
http://arxiv.org/astro-ph/0306275
It is an interesting topic and Alan Guth had two papers discussing it in 2003, also Hawking had one I found in 2003. might be interesting to check out their recent words on the subject
Hawking defined it as follows and then proceded to critique the idea:
"... In the case of inflation, the idea is that the exponential expansion, obliterates the dependence on the initial conditions, so we wouldn't need to know exactly how the universe began, just that it was inflating. To lose all memory of the initial state, would require an infinite amount of exponential expansion.
This leads to the notion of ever lasting or eternal inflation. The original argument for eternal inflation, went as follows. Consider a massive scalar field in a spatially infinite expanding universe. Suppose the field is nearly constant over several horizon regions, on a space like surface. In an infinite universe, there will always be such regions. The scalar field will have quantum fluctuations. In half the region, the fluctuations will increase the field, and in half, they will decrease it. In the half where the field jumps up, the extra energy density will cause the universe to expand faster, than in the half where the field jumps down. After a certain proper time, more than half the region will have the higher value of the field, because the high field regions will expand faster than the low. Thus the volume averaged value of the field will rise. There will always be regions of the universe in which the scalar field is high, so inflation is eternal. The regions in which the scalar field fluctuates downwards, will branch off from the eternally inflating region, and will exit inflation.
Because there will be an infinite number of such exiting regions, advocates of eternalinflation get themselves tied in knots, on what a typical observer would see. So even if eternal inflation worked, it would not explain why the universe is the way it is. But in fact, the argument for eternal inflation that I have outlined, has serious flaws.
First, it is not gauge invariant. If one takes the time surfaces to be surfaces of constant volume increase, rather than surfaces of constant proper time, the volume averaged scalar field does not increase.
Second, it is not consistent. The equation relating the expansion rate to the energy density, is an integral of motion. Neither side of the equation can fluctuate, because energy is conserved.
Third, it is not covariant. It is based on a 3+1 split. From a four-dimensional view, eternal inflation can only be de Sitter space with bubbles. The energy momentum tensor of the fluctuations of a single scalar field, is not large enough to support a de Sitter space, except possibly at the Planck scale, where everything breaks down.
For these reasons, not gauge invariant, not consistent, and not covariant, I do not believe the usual argument for eternal inflation..."
Hawking "Cosmology from the Top Down"
http://arxiv.org/astro-ph/0305562
(if that doesn't work there's a longer link)
http://www.arxiv.org/ftp/astro-ph/papers/0305/0305562.pdf
Alan Guth's couple of recent ones (2003):
"Time since the beginning"
http://arxiv.org/astro-ph/0301199
(quote: "'eternal' inflation...proposes that our universe evolved
from an infinite tree of inflationary spacetime")
"Inflation and cosmological perturbations"
http://arxiv.org/astro-ph/0306275
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