Clarification on Cosmic Expansion

[heliocentricprose]

I've read in books and seen on television programs that the universe is expanding, and not only is it expanding it is accelerating in its expansion. I was just reading "parallel worlds" by michio kaku, and I came across the Hubble constant, H. This number is the rate at which the universe is expanding.

My confusion comes from the contant number of expansion, and the claim of acceleration of expansion.

I've resolved the idea in my head, but wanted confirmation that it was correct.

Is the universe expanding at a constant rate, and is it only the matter inbetween space that is accelerating away from each other?

In which case, it would be incorrect to say the universe is accelerating. I don't know if I'm right, because I've read this phrase in many books.

 

[George Jones]

I've read in books and seen on television programs that the universe is expanding, and not only is it expanding it is accelerating in its expansion. I was just reading "parallel worlds" by michio kaku, and I came across the Hubble constant, H. This number is the rate at which the universe is expanding.

Accleration refers to rate of change of the scale factor of the universe as time increases, not the Hubble constant. The Hubble constant refers to the rate of increase of of recession speed with distance, with everything considered at one fixed time.

Just to confuse you further , current observation indicate that as time increases: the rate of expansion of the scale factor universe increases; the value of the Hubblle constant decreases.

 

[pervect]

I'm not sure whether this will help, but the way it works is:

a(t) is the scale factor of the universe. It appears, for instance, in the metric: ds^2 = c^2*dt^2 - a(t)^2 * (dx^2 + dy^2 + dz^2), which is the metric for a flat expanding universe.

The Hubble constant H, is (da/dt) / a

The acceleration of the expansion is usually measured by the deceleration parameter q, which is defined as

q = -(d^2 a / dt^2) / a * H^-2

http://scienceworld.wolfram.com/physics/DecelerationParameter.html

q is negative, which means that the expansion of the universe, is accelerating.

A negative value for q or an accelerating expansion implies the existence of "dark energy". Normal matter would cause q to be positive, i.e. gravity would slow the expansion of the universe down as time evlolved without dark energy.

Dark energy is something different than "dark matter". One form of "dark energy" is the cosmological constant.

 

[DrChinese]

The universe is indeed expanding, according to the latest data available:

The universe is 156 billion light years across

If you want to learn more: google Lineweaver and Davis, who have written several articles describing this in more detail. Amazing to me was the discovery of galaxies that are receding from us at over 3x the speed of light!

 

[pervect]

Are you in a position to tell where that 156 billion number comes from in detail? I can see the figure reported in the article you cite, but don't have enough information from that article to understand, in detail, where the number comes from.

I only get about 90 billion LY from Ned Wright's cosmology calculator for comoving radial diameter (i.e. about 45 billion LY comoving radius). That's with H=71 km/sec per MPC, .27 for omega-m, and .73 for omega-v (and a very large z, approaching infinity).

I don't see how to explain the 2:1 discrepancy, I suspect that possibly some non-comoving distance is being used - either that or there are some very large differences in H and/or omega.

Note that this is an outstanding issue in the Wikipedia
http://en.wikipedia.org/wiki/Observable_universe, which is one reason I'm asking. I haven't contributed to the wiki article because I don't know how to resolve this rather large discrepancy.

 

[yogi]

The notion that the expansion rate of the universe is increasing rests upon data which presumes that certain key factors have not changed since the early universe. If either G or the inertial magnitude of a given quantity of atoms changes with time, then the observed reduced intensity of distant 1a supernova data indicate something other than acceleration.

 

[Garth]

Indeed yogi, the interpretation of all cosmological observations is theory dependent. The robustness of such interpretation depends on how well the underlying theory is tested in laboratory experiments.

The fact that the standard $\Lambda$CDM model relies on inflation, non baryonic DM and DE, while these all remain undiscovered in laboratory science, requires us to retain an open mind on the question of its veracity.

Garth

 

[George Jones]

I can see the figure reported in the article you cite

I'm sure whether you mean the BBC article, or the Physical Review Letters article (http://www.arxiv.org/abs/astro-ph/0310233" ) to which the BBC article gives a link.

 

[heliocentricprose]

Accleration refers to rate of change of the scale factor of the universe as time increases, not the Hubble constant. The Hubble constant refers to the rate of increase of recession speed with distance, with everything considered at one fixed time.

Just to confuse you further , current observation indicate that as time increases: the rate of expansion of the scale factor universe increases; the value of the Hubblle constant decreases.

Wow, I simply can't wrap my head around that just yet.

I don't quite understand what you mean by scale factor in your first sentence. What is recession speed with distance?

Also, If the Hubble constant changes, why is it called a constant? How is it possible that the Hubble constant decreases and the rate of 'change of the scale factor' increases?

 

[Mechanic]

Universal acceleration rate

We've heard that the universe is expanding - and that the rate of expansion is increasing, or accelerating. Does anybody know the measured rate of universal accleration? E.g., the Hubble expansion rate is 50-100 km/sec per megaparsec - what is the corresponding universal expansion rate?

Thanks

 

[Ich]

I don't see how to explain the 2:1 discrepancy, I suspect that possibly some non-comoving distance is being used - either that or there are some very large differences in H and/or omega.

Note that this is an outstanding issue in the Wikipedia
http://en.wikipedia.org/wiki/Observable_universe, which is one reason I'm asking.

Following George's link the explanation given in Wikipedia seems quite reasonable.

what is the corresponding universal expansion rate?

I get ~0.57 for omega lambda = 0.7 and ~0.61 for omega lambda = 0.73.

 

[Mechanic]

Ich – Thanks. A couple additional questions:
Firstly, what are the units of the values you provide – km/sec^2 per megaparsec or percent increase or ?? Hopefully there is some km/sec^2 type unit.

Also - Are those calculated values? I’m looking for measured – or derived with the least amount of calculation – values. Maybe some calcs are required – like getting velocity form Hubble measure redshifts?

Thanks much,
Mechanic

 

[marcus]

Ich – Thanks. A couple additional questions:
Firstly, what are the units of the values you provide – km/sec^2 per megaparsec or percent increase or ?? Hopefully there is some km/sec^2 type unit.

Also - Are those calculated values? I’m looking for measured – or derived with the least amount of calculation – values. Maybe some calcs are required – like getting velocity form Hubble measure redshifts?

Thanks much,
Mechanic

q is dimensionless. It is a pure number without units

if you go back to Pervect's post #3 you will see the definition is that -q
is equal to a"/(a H²)

this is a unit-less number because if you think of the scalefactor as having units of distance the units in the numerator (L/T²) are canceled by the units in the denominator
(which are also L/T²)

if you think of the scalefactor as itself being dimensionless then it is even simpler. the units in both numerator and denominator are then simply one over time-squared (1/T²)

if you have any trouble at all understanding what I just said, please ask. I don't want to explain unless you need it.

q is called the "deceleration parameter", so the negative, -q, is a measure of acceleration

=================
Most likely you are well-aware that the units of the Hubble parameter (km/s per Megaparsec) boil down to the riciprocal of time (1/T) so that the square of of the Hubble is in units of (1/T²)

 

[Ich]

Also - Are those calculated values?

Even worse, they are calculated with an Excel-Sheet I made myself, so hopefully some of the gurus here may want to check.

I’m looking for measured – or derived with the least amount of calculation – values.

They are not even absolutely certain about the value of H - the mainstream has some sidebranches here - which means that there is no way of measuring q directly or deriving it with few assumptions from measurements. It's rather that they fit in with the whole picture. If some aspects of the standard cosmology would have to be changed, q could change drastically.

 

[Mechanic]

Ok – so there is no way to measure q directly. Now…Hubble used shifted spectra to show that the velocities of the galaxies he observed followed a pattern in which the farther away a galaxy was the higher its recessional velocity. He described the behavior of the galaxies as a group at a certain instant in time. Now I am curious about the behavior of a single galaxy of a long period of time. To adhere to Hubble’s law a given galaxy would be increasing it’s distance from us and since velocity increases as distance increases the velocity of that galaxy would be increasing – it would be accelerating relative to us. Is there any evidence (measurements) that single galaxies are accelerating relative to us? Has anybody compared the spectrum shifts of the galaxies obtained by Hubble years ago to the current spectrum shifts of the same galaxies to see if the shifts have changed to indicate a change in velocity over time?

BTW – the info you all have provided is greatly appreciated.

 

[Ich]

Has anybody compared the spectrum shifts of the galaxies obtained by Hubble years ago to the current spectrum shifts of the same galaxies to see if the shifts have changed to indicate a change in velocity over time?

Well, ask yourself how much this velocity (redshift) would change in, say, 50 years. Compare that figure with an assumed optimistic measurement accuracy of 0.01%.
No chance.

 

[marcus]

... To adhere to Hubble’s law a given galaxy would be increasing it’s distance from us and since velocity increases as distance increases the velocity of that galaxy would be increasing – it would be accelerating relative to us...

that is correct, it is a different sort of acceleration but it should be observable in principle, it has even been proposed that in the future, with more accurate instruments and longer timespans it could be observed

distances currently increase at a rate of 1/140 of one percent every million years.

so recession speeds of individual objects are increasing at a rate of 1/140 percent every million years

this is obviously too slow an acceleration to measure with current technology over the short timespans we have covered to date which are less than 100 years!
when you count the poor accuracy of early measurments the timespace is almost nothing so far. but give us time

=============
Oh, I see Ich beat me to it by a minute. Ich is right.

 

[Mechanic]

Ok – so the change in velocity is (currently) too small to be measured. Dang…that’s the problem with all this stuff…all the tiny-tiney numbers and gigantic-humongous numbers. Well, at least the acceleration per Hubble can be calculated - H^2*R. So...how does that relate to q? If anybody has the process whereby the equation describing the relationship between q and H (given by Pervect's post #3 above) is derived that would help greatly.

Thanks.

 

[Jorrie]

Oops!

that is correct, it is a different sort of acceleration but it should be observable in principle, it has even been proposed that in the future, with more accurate instruments and longer timespans it could be observed

The actual dark energy driven acceleration of expansion might have been observable if we could have somehow observed the CMB region where it is now, some 46 Gly away, receding at around 3.3c. According to my calculations, that recession speed is increasing at ~0.1% per annum. So in a 100 years...

Obviously, we can't!

Edit: Oops, I had a slip-up between seconds and years, so make that ~0.1% per annum equal to ~1% per billion years! Undetectable, drat!

 

[NEW4M]

Hi

Now I am curious about the behavior of a single galaxy of a long period of time. To adhere to Hubble’s law a given galaxy would be increasing it’s distance from us and since velocity increases as distance increases the velocity of that galaxy would be increasing – it would be accelerating relative to us. Is there any evidence (measurements) that single galaxies are accelerating relative to us? Has anybody compared the spectrum shifts of the galaxies obtained by Hubble years ago to the current spectrum shifts of the same galaxies to see if the shifts have changed to indicate a change in velocity over time?

BTW – the info you all have provided is greatly appreciated.

Continuing the question, has observation (comparison) made evidence that galaxies to disapear when their recession speed reach c and greater because their distance is greater today (here) compared to the visible horizon ?

 

[Amp1]

that is correct, it is a different sort of acceleration but it should be observable in principle, it has even been proposed that in the future, with more accurate instruments and longer timespans it could be observed

Marcus. What do you mean by different or sort of? Does it involve dimensions or dimensionality in some way? Does time having a direction create impossibilities or untenable results? It was said on a PBS program called “The Race for Absolute Zero” heat flowed in one direction; I surmise that’s entropy increasing over time. Well, I just thought it curious that they both have direction. Anyway why is it said that eventually there will be a ‘Big Rip’ due to the expansion?

 

[yogi]

Ok – so there is no way to measure q directly. Now…Hubble used shifted spectra to show that the velocities of the galaxies he observed followed a pattern in which the farther away a galaxy was the higher its recessional velocity. He described the behavior of the galaxies as a group at a certain instant in time. Now I am curious about the behavior of a single galaxy of a long period of time. To adhere to Hubble’s law a given galaxy would be increasing it’s distance from us and since velocity increases as distance increases the velocity of that galaxy would be increasing – it would be accelerating relative to us.

The velocity of a given galaxy should not increase in a finite spherical universe - expansion increases the distance, but the Hubble parameter is proportionately decreased, i.e, v = Hr ...when r doubles, H is halved

 

[Jorrie]

The velocity of a given galaxy should not increase in a finite spherical universe - expansion increases the distance, but the Hubble parameter is proportionately decreased, i.e, v = Hr ...when r doubles, H is halved

With $\Omega_{\Lambda,0}=0.73$ and $H_0=71$ km/s/Mpc, H(t) will eventually drop to around $60$ km/s/Mpc and remain practically constant for eternity (in the totally dark energy dominated future universe).

 

[marcus]

With $\Omega_{\Lambda,0}=0.73$ and $H_0=71$ km/s/Mpc, H(t) will eventually drop to around $60$ km/s/Mpc and remain practically constant for eternity (in the totally dark energy dominated future universe).

I did that calculation one time! I vaguely remember getting something like 56 or 57,

anyway around 60, like you said. Could you show us the calculation?

 

[Jorrie]

I vaguely remember getting something like 56 or 57, anyway around 60, like you said. Could you show us the calculation?

From

$$H(t) = \frac{\dot{a}}{a} = H_0 \sqrt{\Omega_m/a^3+\Omega_r/a^4 + \Omega_\Lambda}$$

for a flat universe. When $a \gg 1$, this approaches the constant:

$H(t) = H_0 \sqrt{\Omega_\Lambda} \approx 61$ km/s/Mpc for $\Omega_{\Lambda,0} =0.73$ and Ho=71 km/s/Mpc.

 

[yogi]

With $\Omega_{\Lambda,0}=0.73$ and $H_0=71$ km/s/Mpc, H(t) will eventually drop to around $60$ km/s/Mpc and remain practically constant for eternity (in the totally dark energy dominated future universe).

It is not known whether the expansion rate is determined by matter density - the cosmos appears to have critical density for some reason - but if expansion is not regulated by the amount of matter, then ...