Accelerated expansion and its rate

In summary, Michael Turner found that the rate of acceleration of the expansion of the universe is measured by the dimensionless number q. This number is described by the second Friedmann equation, and is given by the equation \frac{R}{R H^2}. The increase in R tracks the expansion of the universe. Michael Turner also mentions an article by Lineweaver which is good for further understanding of the expansion parameter. Finally, to calculate the deceleration parameter q, you only need to know the dark energy fraction of total energy density, which is 0.73.
  • #1
kristobal hunta
7
0
I am graduate student working now at the project in cosmology. I would appreciate any links or references to the papers or publications casting a light on the problem of accelerated expansion of the universe.

Did they found the rate of accelerated expansion?
 
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  • #2
kristobal hunta said:
I am graduate student working now at the project in cosmology. I would appreciate any links or references to the papers or publications casting a light on the problem of accelerated expansion of the universe.

Did they found the rate of accelerated expansion?

please look at this easy survey paper
"Making Sense of the New Cosmology"
by Michael Turner

http://arxiv.org/astro-ph/0202008 [Broken]

he is at Chicago and is one of the most eminent of today's cosmologists
you can rely on what he says
it is representative of the main consensus
(but the numbers are sharper in more recent papers)

the acceleration of expansion is measured by the dimensionless number q

see the definition of q on page 7 near the bottom

see equation (1) on page 7
where you see the quantity R"/R which measures acceleration
is given by the second Friedmann equation

R is the scale factor in the RW metric (the standard metric used in cosmology),
R is usually normalized so it is equal to 1 at present time
and the increase in R tracks the expansion

R' is the increase rate (the time derivative) of R
R'' is the increase in the increase in R

to get rid of units and get a more pure number we can divide first by R

R''/R has dimension of reciprocal time2
that is it is a "per second per second" or a "per year per year" type of quantity

Now one can further normalize this if one divides by the square of the H parameter, because the H parameter is itself a reciprocal time!

therefore one can have a pure dimensionless number that expresses the amount of acceleration if one writes

[tex] \frac{R''}{R H^2}[/tex]

this is the q which he mentions

it would be good to know this number since it expresses how much acceleration there is

also he talks about why we know about this
(from the 1998 supernova observations)

also this article by Lineweaver is good
http://arxiv.org/astro-ph/0305179 [Broken]
 
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  • #3
Ok, marcus, but you forgot the signus minus in the formula for q :wink:
I have problems understanding the expansion parameter. The expansion parameter a is

[tex]
a= \frac {R} {R_0}
[/tex]
R is the scale factor at time t, and R0 the scale factor at time t0. What's the exact value of the expansion parameter at this moment?
 
  • #4
Ultimate Acceleration...


The Universe is far more dimentionally vast now at this instant in time than what is currently optically viewable through primordial radiation.

Integrating Hubble's Law into the average acceleration theorem yields the following solution:

WMAP Ho = 71 +/- 4 km/sec/Mpc

[tex]\Delta d_t = (d_f - d_i)[/tex] (31.5 BLy - 13.18 BLy)
[tex]a_u = 2 H_o^2 \left( \Delta d_t - \frac{nc}{H_o} \right)[/tex]

au = 4.679*10^-10 m*s^-2

n - fractional luminous galaxy velocity
au - Universe Expansion Acceleration Rate
Ho - Hubble 'Constant'

[tex]H_o = \frac{ (V_i + V_f)}{ 2(d_f - d_i)} = \frac{ c(n_i + n_f)}{ 2(d_f - d_i)}[/tex]

[tex]H_o = \frac{a}{(V_f - V_i)} = \frac{a}{c(n_f - n_i)}[/tex]

According to these solutions, Hubble's 'Constant' is not actually a constant, but a function of the Universe Expansion Acceleration Rate and the differential galaxy velocities which compose it.

Reference:
http://www.astro.ucla.edu/~wright/cosmolog.htm
http://www.sltrib.com/2004/mar/03022004/nation_w/144063.asp
https://www.physicsforums.com/showthread.php?t=14613&page=2&pp=15
 
  • #5
meteor said:
Ok, marcus, but you forgot the signus minus in the formula for q :wink:
I have problems understanding the expansion parameter. The expansion parameter a is

[tex]
a= \frac {R} {R_0}
[/tex]
R is the scale factor at time t, and R0 the scale factor at time t0. What's the exact value of the expansion parameter at this moment?

they usually use subscript zero to mean the present
so time t0 is the present
and H0 is the Hubble parameter at present

by your definition, a, at present is equal to 1.

You know the common estimate is that the universe is flat.
the energy density (all forms) is estimated to be about equal to one times the critical density. Actually they estimate 1.04 plus or minus some error bar.
But let's assume it is simply flat, to make things easy.

Then the "deceleration" parameter q (with the minus sign you mentioned)
comes out to be about -0.6
or maybe we should be focusing on -q, the "acceleration" parameter, which comes out to be about 0.6

expansion is accelerating so this dimensionless number 0.6 is positive.

I actually got 0.595, when I calculated it. But that is close to 0.6.

Assuming flat, which although not sure is within the uncertainty range, then to calculate this thing all you need is the 0.73 dark energy fraction of total energy density.

The formula is

[tex]-q = \frac{a''}{a H^2} = \frac{a'' a}{a'^2} = - \frac{1}{2}(1 - 3 (0.73))[/tex]

the formula comes from the two Friedmann equations
 
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  • #6
marcus said:
...

The formula is

[tex]-q = \frac{a''}{a H^2} = \frac{a'' a}{a'^2} = - \frac{1}{2}(1 - 3 (0.73))[/tex]

the formula comes from the two Friedmann equations

for me, this is the first time that I have calculated the acceleration parameter (or minus the deceleration)
anyone want to confirm or point out mistakes?

Meteor does this seem OK?

by definition H = a'/a
so dividing by H^2 is the same as dividing by (a'/a)^2
which is why the two alternative forms of writing -q

then one looks at the two friedmann equations and one equation
gives a''/a
and the other equation gives (a'/a)^2
and one divides first equation by second equation
I think it is not very hard or complicated to see
if you want friedmann equantions written out, please tell me
(or maybe someone else will)
 
  • #7
marcus, I don't see how the expansion parameter can be 1. That means that R and R0 have the same value. But aren't they the value of the scale factor at different stages of the evolution?
 
  • #8
meteor said:
Ok, marcus, but you forgot the signus minus in the formula for q :wink:
I have problems understanding the expansion parameter. The expansion parameter a is

[tex]
a= \frac {R} {R_0}
[/tex]
R is the scale factor at time t, and R0 the scale factor at time t0. What's the exact value of the expansion parameter at this moment?

you asked how it is at this moment
this moment is t = t0
(they often use this subscript zero for the present)

at this moment R = R(t) = R(t0) = R0 by definition

(the cosmologists often use the subscript zero to indicate the current value of some parameter, at this moment)

so dividing R by R0 is a way of normalizing the scale parameter so that it will be forced to equal 1 at the present moment

at present R/R0 = 1

they really have a bit too much redundant notation---and some cosmologists are using R instead of a, or a instead of R---they don't have completely consistent conventions
as a general rule either a or R will stand for a scale parameter that is very often normalized to be equal to one at the present moment.

then the Hubble parameter H(t) is defined to be a'/a
or equivalently R'/R

and the Hubble parameter at the present moment H0 is defined to be H(t0 ) = present value of a'/a
or equivalently R'/R

it is like having to learn French, or some even less efficient language, where they have many ways to say the same thing---or perhaps this is good?
 

1. What is accelerated expansion and its rate?

Accelerated expansion refers to the phenomenon where the universe is expanding at an increasing rate. This means that the distance between galaxies is increasing at a faster rate than in the past. The rate of accelerated expansion is measured by the Hubble constant, which describes the rate at which the universe is expanding.

2. What is causing the accelerated expansion of the universe?

The cause of accelerated expansion is still a topic of ongoing research and debate. One theory is that there is a mysterious force called dark energy that is pushing galaxies apart. Another theory is that our current understanding of gravity is incomplete and needs to be modified to account for the observed expansion.

3. How is the rate of accelerated expansion measured?

The rate of accelerated expansion is measured using various techniques, such as observing the brightness of distant supernovae, mapping the distribution of galaxies in the universe, and studying the cosmic microwave background radiation. These measurements allow scientists to calculate the Hubble constant and track how the expansion rate has changed over time.

4. Can the rate of accelerated expansion change over time?

Yes, the rate of accelerated expansion can change over time. In fact, it is believed that the expansion rate has varied throughout the history of the universe. Currently, the rate of accelerated expansion is increasing, but it is possible that it may slow down or even reverse in the future.

5. What are the implications of accelerated expansion for the future of the universe?

The implications of accelerated expansion are still being studied and debated. Some theories suggest that the universe will continue to expand at an increasing rate, eventually leading to a "big rip" where all matter is torn apart. Other theories suggest that the expansion rate will eventually slow down and stabilize, leading to a "big freeze" where the universe becomes cold and dark. Further research is needed to determine the ultimate fate of the universe.

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