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properman
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As the title suggests, I am wondering if there is an alternate way to describe the expansion of the universe outside of the Friedmann Equation. Specifically, can the expansion of the universe be modeled on time alone?
What do you mean, modeled on time alone?properman said:As the title suggests, I am wondering if there is an alternate way to describe the expansion of the universe outside of the Friedmann Equation. Specifically, can the expansion of the universe be modeled on time alone?
BillSaltLake said:The expansion factor "a" can be written as a function of time (although not in closed form). After the period of inflation, a~t1/2 until about 10,000 yr. Then a~t2/3. Now a is increasing a little faster, and since around t = 1 billion yr, a has increased about 1.2x what it would have been if it were at the t2/3 rate alone. At present a~t1, or more precisely, (1/a)(da/dt)~1/t now. (It was [1/2]/t and [2/3]/t at the earlier eras.)
Chalnoth said:What do you mean, modeled on time alone?
Sure, a(t) is a smooth function. It is continuous because a discontinuity in a(t) would mean a discontinuity in distances, which would mean infinite velocities. That isn't happening.properman said:Oh well. Thank you anyway.
I meant was looking for a single variable function of expansion over time, ie. a(t). But apparently from the post above, that does not exist as a smooth function.
I don't understand what you're asking here.properman said:Right. Didn't really think that through... So then would there be such a function that is not the piece-wise function mentioned above? Would it be to solution to one of the Friedmann equations?
Thanks for putting up with my random questions, I just was stricken by an idea earlier, and in order for it to work I would need a function for the expansion of the universe with regard to time.
BillSaltLake said:The expansion factor "a" can be written as a function of time (although not in closed form). After the period of inflation, a~t1/2 until about 10,000 yr. Then a~t2/3. Now a is increasing a little faster, and since around t = 1 billion yr, a has increased about 1.2x what it would have been if it were at the t2/3 rate alone. At present a~t1, or more precisely, (1/a)(da/dt)~1/t now. (It was [1/2]/t and [2/3]/t at the earlier eras.)
Chalnoth said:I don't understand what you're asking here.
Oh, well, the matter content of the universe changes with time, and the matter content determines how the expansion changes over time. So if you want to have one equation that models the whole expansion, it's going to have to take into account the matter content and how it's changed.properman said:Those above equations require the use of different equations for different times in the expansion of the universe. What I am looking for is one equation that can model the expansion for the entirety of the expansion.
Chalnoth said:Oh, well, the matter content of the universe changes with time, and the matter content determines how the expansion changes over time. So if you want to have one equation that models the whole expansion, it's going to have to take into account the matter content and how it's changed.
Pretty much, yes :)properman said:Ok, so you are telling me that in order to get a perfect model it would need to be a differential equation, which of course is what the Friedmann equations are. well there goes that idea.
The current understanding is that the universe is expanding at an accelerating rate due to the presence of dark energy. This was discovered through observations of distant supernovae and is supported by other measurements such as the cosmic microwave background radiation.
There have been several proposed alternative theories, such as the steady-state theory or the oscillating universe theory, but these have been largely discredited by observations. The current understanding of an expanding universe is supported by a large body of evidence and is widely accepted in the scientific community.
Yes, the expansion of the universe can be described using the theory of general relativity, which relates the expansion to the curvature of spacetime. It can also be described using the concept of cosmic inflation, which describes a period of rapid expansion in the early universe.
Yes, there are many ongoing studies and experiments aimed at further understanding the expansion of the universe. These include observations of distant galaxies and supernovae, mapping the cosmic microwave background radiation, and experiments such as the Large Hadron Collider to study the fundamental laws of physics that govern the expansion.
While it is always possible for new evidence or theories to emerge, the current understanding of the expansion of the universe is supported by a vast amount of evidence and is consistent with our understanding of physics. Any alternative explanation would need to account for all of the existing evidence and make testable predictions in order to be considered a viable alternative.