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Inflation leads to Ω=1. But we also have Ωmatter+Ωdark matter+Ωdark energy = 1. So if there were no dark energy and dark matter present in the universe, would Ω have eventually deviated away from 1?
Could you please elaborate on why that is so?mathman said:Without dark matter and dark energy the universe would be completely different. [tex]\Omega[/tex] would have not started at 1 after inflation. Also, inflation might not have happened.
I am assuming the standard ∧CDM model. I am trying to clarify something I read in Alan Guth's book The Inflationary Universe, and I quote two passages, first about a universe without the cosmological constant (p.p.177) and the second with the cosmological constant (p.p. 178, footnote).JMz said:The OP asks about something that is counter-factual. No problem, but in that case, what are you assuming is the same as reality? Are you still assuming general relativity; or if not, which theory of gravity? Are you assuming some specifics about the physics of inflation, like whether DE (or Λ) is a tiny residual of the inflation field? Which specifics?
It is assumed that the inflaton field (not the cosmological constant which is tiny) drives the universe to spatial flatness.Ranku said:What I am trying to clarify, however, is does the presence of cosmological constant alone make any difference at all about eventual deviation away from Ω = 1, such as maybe the deviation would have happened somewhat later than it would have if the cosmological constant had not been present.
The ##\Omega## parameters are defined as density fractions. Their sum is always equal to one. The fact that ##\Omega = 1## has no physical significance, it's just a statement about how the numbers are defined.Ranku said:Inflation leads to Ω=1. But we also have Ωmatter+Ωdark matter+Ωdark energy = 1. So if there were no dark energy and dark matter present in the universe, would Ω have eventually deviated away from 1?
Omega is the curvature of space and is not necessarily equal to one.kimbyd said:The ##\Omega## parameters are defined as density fractions. Their sum is always equal to one. The fact that ##\Omega = 1## has no physical significance, it's just a statement about how the numbers are defined.
Eh, you're right. I mixed up my notations. I was thinking of it as including ##\Omega_k##, which isn't the case.mathman said:Omega is the curvature of space and is not necessarily equal to one.
https://en.wikipedia.org/wiki/Shape_of_the_universe
FWIW, I seem to recall that -- before inflation became accepted -- either Bekenstein or Shimon Malin (or maybe both?) posited that there were in fact several cosmological symmetries that are laws of nature, not merely accidents of nature. They were on exactly the same footing as the equivalence principle, but in addition to them: isotropy, homogeneity, flatness. This lent itself to a group-theory formulation of gravity, one that is somewhat different from GR. I don't know the status of those ideas now, though it's my impression that inflation is simpler.kimbyd said:Unless there was some symmetry that fixed k=0 exactly...
I would believe it. One of the interesting discussions I had with a theorist some years ago involved him flatly and loudly proclaiming that it was just not possible for the cosmological constant to be non-zero, asserting that the numerical value of the constant was just too small to be possible.JMz said:FWIW, I seem to recall that -- before inflation became accepted -- either Bekenstein or Shimon Malin (or maybe both?) posited that there were in fact several cosmological symmetries that are laws of nature, not merely accidents of nature. They were on exactly the same footing as the equivalence principle, but in addition to them: isotropy, homogeneity, flatness. This lent itself to a group-theory formulation of gravity, one that is somewhat different from GR. I don't know the status of those ideas now, though it's my impression that inflation is simpler.
Apropos of that, I vaguely recall that someone showed that such a group-theoretic model obeyed Mach's principle (as Einstein called it): An empty universe would leave particles with no inertial at all. Something that GR does not, even though Einstein thought it should, and supposedly expected it to as he was developing the theory.kimbyd said:a symmetry that sets these things to zero
I suppose I have to admit that, even if inflation seems simpler (now, to me), the quantum folks have shown how valuable group theory can be, when it does apply. So it's easy to see why someone would look in that direction and put some work into it.kimbyd said:strong belief can be useful for a theorist
Inflation refers to the rapid expansion of the universe in the first few moments after the Big Bang. During this period, the universe expanded at a rate faster than the speed of light, leading to the smooth and homogeneous distribution of matter that we observe today.
Inflation explains the flatness and homogeneity of the universe by stretching out any irregularities or curvature that may have existed before the expansion. This explains why the universe appears to be the same in all directions and why the overall geometry of the universe is flat.
Dark matter is a type of matter that does not interact with light and thus cannot be observed directly. It is thought to make up about 27% of the universe and its gravitational pull helps to slow down the expansion of the universe.
Dark energy is a mysterious force that makes up about 68% of the universe. It is believed to be responsible for the accelerating expansion of the universe. Its exact nature is still unknown, but it is thought to be a property of space itself.
Scientists study the impact of dark matter and energy on the universe through a variety of methods, including observations of the cosmic microwave background radiation, measurements of the large-scale structure of the universe, and simulations using supercomputers. These methods allow scientists to better understand the role of dark matter and energy in the evolution of the universe.