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keepitmoving
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what was the value of the Hubble parameter when the universe was decelerating?
Hmmm, that's not something that's usually computed. And, unfortunately, the precise value of the Hubble parameter when the universe stopped decelerating and started accelerating is not known to much precision (it's a rather noisy measurement). It is also worth mentioning that our universe was decelerating for most of its history, from the end of inflation to relatively recently (when dark energy took over). This covers an incredibly wide range of Hubble parameters.keepitmoving said:what was the value of the Hubble parameter when the universe was decelerating?
Well, larger. It varied dramatically with time. The smallest would have been roughly twice the current value, as I calculated above. The largest would have been whatever it was at the end of inflation, which we don't know precisely yet. A rough ballpark would be somewhere around [tex]10^{22}[/tex] to [tex]10^{25}[/tex] km/sec/Mpc.keepitmoving said:thank you Chalmoth. The math was above me but i did expect the Hubble parameter to be more at the end of deceleration than now.
By the way, i`m not a real physicist but i did have dinner at a Holiday Inn last year (a joke that was on TV).
Anyway, but what would the Hubble parameter be when the universe was actually decelerating? If it was still expanding during deceleration wouldn`t a given object be moving faster relative to a reference point than it was the previous Myr? It`s hard for me to picture expanding without a given object moving away from a reference point at a speed that is less than it was moving away during the previous Myr.
keepitmoving said:what was the value of the Hubble parameter when the universe was decelerating?
The acceleration is the acceleration of the scale factor.keepitmoving said:maybe i`m on the wrong track. Is the acceleration really the acceleration of acceleeration?
keepitmoving said:maybe i`m on the wrong track. Is the acceleration really the acceleration of acceleeration?
The Hubble parameter is given by the Friedman equation:keepitmoving said:Marcus, thanks. Just to confirm that i understand - during the deceleration phase the scale factor was increasing at a decreasing rate? Would the Hubble parameter go up or down as you go from, say, 5 Byr`s ago to 10 Byrs ago?
Yes, that's a nice shortcut for the calculation of H at the end of deceleration:The Hubble parameter is given by the Friedman equation
Eh, you're right. My mistake.Ich said:Yes, that's a nice shortcut for the calculation of H at the end of deceleration:
[tex]H_{then}=H_{now} \sqrt{\frac{\Omega_{\Lambda now}}{\Omega_{\Lambda then}}}=H_{now} \sqrt{3\Omega_{\Lambda}}[/tex]
It seems that you forgot the sqrt in your derivation, the factor being 1.5 rather than 2.22?
marcus said:...
Chalnoth, thanks for estimating when deceleration stopped! I see your estimate of the H parameter is 2.22 times presentday. If I take the presentday value of 74 (which Adam Riess et al just came out with) that means that H was about 164 when the switch from decel to accel occurred. (I'll save rounding off for later.)
Again using Riess et al numbers, that would mean the switch occurred around z = 1.5. Does that seem about right to you?
This puts the age of expansion when the changeover occurred at 4.3 billion years, or 9 billion years ago. Again, does that seem right? I had the impression that changeover was more recent, not 9 billion years ago.
keepitmoving said:Marcus, thanks. Just to confirm that i understand - during the deceleration phase the scale factor was increasing at a decreasing rate? Would the Hubble parameter go up or down as you go from, say, 5 Byr`s ago to 10 Byrs ago?
keepitmoving said:what was the value of the Hubble parameter when the universe was decelerating?
Indeed. Wouldn't do it otherwise :)marcus said:You are welcome! Everybody appreciates getting questions like that. I believe that Chalnoth and Ich would say the same. It's fun responding.
Well, nearly constant. Basically the proposal of inflation is that during that time, the universe was dominated by some sort of field which had a large energy density that varied very slowly with time. By the Friedman equation, then, the Hubble parameter would have also been nearly constant.zeebo17 said:Could someone explain why the Hubble parameter was constant during inflation?
The only way in which the Hubble parameter is model dependent is that it depends upon the description of our universe as being approximately homogeneous and isotropic on large scales being accurate. Other than that, it is completely model independent.Hal King said:Thank you.
As I thought model dependent when using the term 'hubble parameter' -- General Relativity.
I suspected earlier posters were confused by that.
Chalnoth said:Well, nearly constant. Basically the proposal of inflation is that during that time, the universe was dominated by some sort of field which had a large energy density that varied very slowly with time. By the Friedman equation, then, the Hubble parameter would have also been nearly constant.
No. It would have had to have been vastly, vastly higher. We'll know more about precisely what the energy density during inflation was if we can get a positive detection of what is known as the B-mode polarization of the CMB (which is expected to be a very small, difficult to extract signal in the most optimistic scenarios...so far nobody has yet confirmed a detection, though, so we don't know at what level this sort of polarization actually is).zeebo17 said:Is this energy density that of dark energy?
Bear in mind that the density of the inflaton field right as inflation ended would have been identically equal to the total energy density of the particles it decayed into immediately afterwards. And we know the energy density of the very early universe had to be obscenely high to produce dark matter and the asymmetry between matter and anti-matter (as we haven't seen the physics for either of these in particle accelerators yet).zeebo17 said:I know that after inflation matter and radiation dominated the total energy density and then the universe transitioned into a state where dark energy is now dominating the total energy density. But what were these densities like before and during inflation?
Not easily. Basically you'd have to go back to evaluate the integrals numerically (they can't be solved by hand).zeebo17 said:During inflation the scale factor behaves as [tex]a \propto e^{Ht}[/tex] and during a radiation dominated era it behaves as [tex]a \propto t^{1/2}[/tex] and then during a matter dominated era behaves as [tex]a \propto t^{2/3}[/tex].
So then is it correct to say that during inflation: [tex]H= \dot{a}/a \propto constant[/tex]
radiation dominated era: [tex]H= \dot{a}/a \propto 1/t[/tex]
matter dominated era: [tex]H= \dot{a}/a \propto 1/t[/tex]
from simply taking the derivative and dividing by a?
Does the Hubble parameter behave as 1/t during these eras? How would you find how it behaves during an era with mixed conditions, such as the present?
Thanks!
The Hubble parameter, denoted as H0, is a measure of the rate at which the universe is expanding. It is named after Edwin Hubble, who first discovered the expansion of the universe. The Hubble parameter is related to the expansion of the universe through the Hubble's law, which states that the velocity of recession of a galaxy is directly proportional to its distance from us.
The Hubble parameter is calculated by dividing the velocity of recession of a galaxy by its distance. It is usually expressed in units of kilometers per second per megaparsec (km/s/Mpc). This means that for every megaparsec (3.26 million light years) of distance, the velocity of recession increases by a certain amount.
In a decelerating universe, the Hubble parameter is used to measure the rate at which the expansion of the universe is slowing down. This is because the Hubble parameter is inversely proportional to the age of the universe. In a decelerating universe, the Hubble parameter decreases as the universe ages, indicating a slower expansion rate.
The current accepted value of the Hubble parameter is approximately 70 km/s/Mpc. However, this value has been a subject of debate and has changed over time as new measurements and observations are made. In the past, the value of the Hubble parameter was thought to be higher, indicating a faster expansion rate. However, recent observations have shown that the expansion rate of the universe is actually slowing down.
The value of the Hubble parameter is crucial in understanding the past, present, and future of the universe. It helps us determine the age of the universe, the rate at which it is expanding, and the composition of the universe. By studying the changes in the value of the Hubble parameter, scientists can gain insights into the evolution and fate of the universe.