Hubble Time

Accordingly to Wikipedia http://en.wikipedia.org/wiki/Age_of_...cal_parameters
the Hubble time is defined as:
" So a ROUGH estimate of the age of the universe comes from the Hubble time,
the inverse of the Hubble parameter, or 1/H0. "
In simpler wording: Age of the universe T = 1/H0 or H0 = 1 / T
Does this mean that 6.3 billion years from now when the age is
20 billion years that H0 = 1/20 ?

Nicolaas Vroom
http://users.pandora.be/nicvroom/

In article , Nicolaas Vroom
writes:

Accordingly to Wikipedia http://en.wikipedia.org/wiki/Age_of_...cal_parameters
the Hubble time is defined as:
" So a ROUGH estimate of the age of the universe comes from the Hubble time,
the inverse of the Hubble parameter, or 1/H0. "
In simpler wording: Age of the universe T = 1/H0 or H0 = 1 / T
Does this mean that 6.3 billion years from now when the age is
20 billion years that H0 = 1/20 ?

No. Several points: First, by what appears to be a coincidence, the
age of the universe NOW is very close to the Hubble time. (The age of
the universe is ALWAYS the Hubble time only in the case of linear
expansion.) This is because the early phase of deceleration and the
later phase of acceleration more or less balance. With time, since the
universe will always accelerate, the universe will be older than the
Hubble time. (Our universe will asymptotically approach the de Sitter
universe, in which the Hubble constant, and hence the Hubble time, no
longer changes with time, but of course the universe will continue to
age.) No-one has an explanation for this coincidence nor does anyone
know if it is important. Second, in general the Hubble constant changes
with time, but not in such a way that the Hubble time is always roughly
the age of the universe. Rather, what Wikipedia means is that for most
"sensible" values of the cosmological parameters, the age of the
universe is roughly (say, within a factor of 2 either way) equal to the
Hubble time during a large fraction of the history of the universe (at
least up until now). (For a universe with a positive cosmological
constant which will expand forever, as mentioned above the Hubble
constant approaches a constant value.)

(Note that the term Hubble "constant" does NOT mean "constant in time";
rather, it is a constant in the sense that m is a constant in the
equation for a line y = mx + b. At any given time, the Hubble constant
is constant, of course.)

In article
Nicolaas Vroom writes:
Accordingly to Wikipedia
the Hubble time is defined as:
" So a ROUGH estimate of the age of the universe comes from the Hubble
time, the inverse of the Hubble parameter, or 1/H0. "
In simpler wording: Age of the universe T = 1/H0 or H0 = 1 / T
Does this mean that 6.3 billion years from now when the age is
20 billion years that H0 = 1/20 ?
No. Several points:
First, by what appears to be a coincidence, the age of the universe NOW
is very close to the Hubble time.

I still have a problem.
The current accepted values for omega(m) and omega(Lambda) are 0.26 and 0.74
See for definition:
http://en.wikipedia.org/wiki/Friedma...#The_equations
Using my simulation program discussed at:
http://users.telenet.be/nicvroom/friedmann's%20equation.htm#Q6
you can calculate Lambda which is equal to 0.01129
This Lambda is a Universal constant.

Using that Lambda value and assuming that the age of the Universe
is 20 billion years the 1/H value at t=0 becomes 15.5
which value is not in agreement with the age of the Universe.

What that means is 6.3 billion years from now the age of Universe
is much larger than calculated value based on the measured value
of H0 valid at that moment.

That raises the question: Why is the present age of the Universe
not larger than 13.7 ?

Nicolaas Vroom
http://users.pandora.be/nicvroom/

In article , Nicolaas Vroom
writes:

" So a ROUGH estimate of the age of the universe comes from the Hubble
time, the inverse of the Hubble parameter, or 1/H0. "
In simpler wording: Age of the universe T = 1/H0 or H0 = 1 / T
Does this mean that 6.3 billion years from now when the age is
20 billion years that H0 = 1/20 ?
No. Several points:
First, by what appears to be a coincidence, the age of the universe NOW
is very close to the Hubble time.

I still have a problem.
The current accepted values for omega(m) and omega(Lambda) are 0.26 and 0.74

OK.

you can calculate Lambda which is equal to 0.01129
This Lambda is a Universal constant.

Lambda = lambda*3H^2 is the usual definition. Be aware that different
units are used; sometimes there is a factor of the square of the speed
of light.

Using that Lambda value and assuming that the age of the Universe
is 20 billion years the 1/H value at t=0 becomes 15.5
which value is not in agreement with the age of the Universe.

1/H at t=0 is 0 because H is infinite at t=0. This follows from the
fact that H:=(1/R)dR/dt and R=0 at t=0 (for big-bang models) while dR/dt
is not.

What that means is 6.3 billion years from now the age of Universe
is much larger than calculated value based on the measured value
of H0 valid at that moment.

That raises the question: Why is the present age of the Universe
not larger than 13.7 ?

It probably means that there is a mistake in your code or that you are
assuming the wrong system of units.

Nicolaas Vroom wrote:
The current accepted values for omega(m) and omega(Lambda) are 0.26 and 0.74
See for definition:
http://en.wikipedia.org/wiki/Friedma...#The_equations
Using my simulation program discussed at:
http://users.telenet.be/nicvroom/friedmann's%20equation.htm#Q6
you can calculate Lambda which is equal to 0.01129
This Lambda is a Universal constant.

I don't think we know whether Lambda is a universal constant or not.
That is, right now we have only rather weak observational constraints
on the time variation (or lack thereof) of Lambda over cosmological time.

There are various planned observations which should give us a better
idea of this in the next decade, but for right now taking Lambda=constant
is more of a reasonable Occam's-razor simplifying assumption than a
statement of observed fact.


Using that Lambda value and assuming that the age of the Universe
is 20 billion years the 1/H value at t=0 becomes 15.5
which value is not in agreement with the age of the Universe.

As Phillip Helbig already explained, there's no reason that 1/H should
agree with the age of the Universe.

To put this another way, let's define
S(t) := H * age_of_universe(t)
so that (by construction)
age_of_universe(t) = S(t) * 1/H

Then (as PH pointed out) for most (not all!) cosmological models at most
(not all!) times, S(t) is a number of order unity. That's all. There's
nothing amiss about finding that S = 20/15.5 = 1.29.


That raises the question: Why is the present age of the Universe
not larger than 13.7 ?

Why should it be? Or, if you prefer, why should the Hubble constant be
less than 72 km/sec/Mpc? To be more precise, could you explicate the
line of reasoning which suggests a larger age of the universe and/or
a smaller Hubble constant?



Here's an analogy which may be informative:

Consider the elevation profile of a country road, which for simplicity
let's say starts at the (an) ocean.
x := distance along the road, measured from 0 at sea level
and define
H(x) := height-above-sea-level of the road

If we know nothing more about the topography or road layout, then we
can't say much of anything about the relative values of x , H, and
dH/dx at my home. For example, we can't say whether dH/dx is positive
or negative at some randomly chosen point, nor can we say that dH/dx
is even approximately equal to H/x.)

However if I were to tell you that (moving away from the ocean, i.e.,
moving in the direction of increaing x) the road slopes upwards almost
everywhere, and that that slope doesn't vary *too* dramatically from
one place to another, then you could infer that at most places along
the road, dH/dx is at least vaguely similar to H/x (say, they're within
an order of magnitude of each other), or equivalently, x is at least
vaguely similar to H / (dH/dx).

But it shouldn't surprise you if I then tell you that at some particular
place, H / (dH/dx) is (say) a factor of 2 different from x. After all,
real roads do vary in their slope from one place to another.

ciao,

--
-- "Jonathan Thornburg [remove -animal to reply]"
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
on sabbatical in Canada starting August 2012
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam

In article , "Jonathan
Thornburg [remove -animal to reply]"
writes:

I don't think we know whether Lambda is a universal constant or not.
That is, right now we have only rather weak observational constraints
on the time variation (or lack thereof) of Lambda over cosmological time.

There are various planned observations which should give us a better
idea of this in the next decade, but for right now taking Lambda=constant
is more of a reasonable Occam's-razor simplifying assumption than a
statement of observed fact.

True. However, within the context of traditional cosmology, Lambda is
constant (which is why it is called the cosmological CONSTANT). Yes,
this might not be the case and it is important to look for it. However,
a non-varying Lambda does fit all the observations at the moment. So,
there is no evidence in favour of Lambda changing with time. In any
case, the OP's questions don't have anything to do with a time-varying
Lambda.

Op zondag 2 december 2012 14:36:01 UTC+1 schreef Phillip Helbig---undress to reply het volgende:
In article , Nicolaas Vroom

writes:
I still have a problem.
The current accepted values for omega(m) and omega(Lambda) are 0.26 and 0.74
OK.
you can calculate Lambda which is equal to 0.01129
This Lambda is a Universal constant.

Lambda = lambda*3H^2 is the usual definition. Be aware that different
units are used; sometimes there is a factor of the square of the speed
of light.

When you perform the following calculation:
0.73743 * 3 /(14 * 14) you get 0.011287
(with lambda = 0.73743 and H = 1/14)
This means that my program which calculates omaga(Lambda) as a function
of Lambda is correct.
The program does not use the equation Lambda = omega(Lambda) * 3H^2

Using that Lambda value and assuming that the age of the Universe
is 20 billion years the 1/H value at t=0 becomes 15.5
which value is not in agreement with the age of the Universe.

1/H at t=0 is 0 because H is infinite at t=0. This follows from the
fact that H:=(1/R)dR/dt and R=0 at t=0 (for big-bang models) while dR/dt
is not.

1/H at t=0 should be read as: 1/(H at t=0) = 1/H0
1/H0 at present is 13.7 (13.7 billion years after BB)
1/H0 20 billion years after BB should be 20 (?)

What that means is 6.3 billion years from now the age of Universe
is much larger than calculated value based on the measured value
of H0 valid at that moment.

That raises the question: Why is the present age of the Universe
not larger than 13.7 ?

It probably means that there is a mistake in your code or that you are
assuming the wrong system of units.

At least for now: I do not think so.

For a copy of the program select:
http://users.pandora.be/nicvroom/friedmann%20new3.xls

Nicolaas Vroom

On 12/2/2012 11:25 PM, Nicolaas Vroom wrote:
Op zondag 2 december 2012 14:36:01 UTC+1 schreef Phillip Helbig---undress to reply het volgende:
In article , Nicolaas Vroom
..
...
That raises the question: Why is the present age of the Universe
not larger than 13.7 ?

It probably means that there is a mistake in your code or that you are
assuming the wrong system of units.

At least for now: I do not think so.

For a copy of the program select:
http://users.pandora.be/nicvroom/friedmann%20new3.xls

I can only see a list of numbers and a plotted
graph there, no copy of the program!

Where can we read this program?

--
Jos

Op maandag 3 december 2012 09:39:57 UTC+1 schreef Jos Bergervoet het volgende:
On 12/2/2012 11:25 PM, Nicolaas Vroom wrote:

Op zondag 2 december 2012 14:36:01 UTC+1 schreef Phillip Helbig---undress to reply het volgende:
In article , Nicolaas Vroom


It probably means that there is a mistake in your code or that you are
assuming the wrong system of units.

At least for now: I do not think so.

For a copy of the program select:
http://users.pandora.be/nicvroom/friedmann%20new3.xls

I can only see a list of numbers and a plotted
graph there, no copy of the program!

Where can we read this program?

For a quick description go to:
http://users.telenet.be/nicvroom/fri...0operation.htm

For comments about this description please mail me.

Nicolaas Vroom

In article , Nicolaas Vroom
writes:

Lambda = lambda*3H^2 is the usual definition. Be aware that different
units are used; sometimes there is a factor of the square of the speed
of light.

When you perform the following calculation:
0.73743 * 3 /(14 * 14) you get 0.011287
(with lambda = 0.73743 and H = 1/14)
This means that my program which calculates omaga(Lambda) as a function
of Lambda is correct.
The program does not use the equation Lambda = omega(Lambda) * 3H^2

Unless you are using something equivalent, you are defining it
differently than everyone else does.

1/H at t=0 is 0 because H is infinite at t=0. This follows from the
fact that H:=(1/R)dR/dt and R=0 at t=0 (for big-bang models) while dR/dt
is not.

1/H at t=0 should be read as: 1/(H at t=0) = 1/H0

OK, confusion. I was thinking of t=0 as the time of the big bang.
There is another convention to set t=0 now.

1/H0 at present is 13.7 (13.7 billion years after BB)

Yes, this is measured.

1/H0 20 billion years after BB should be 20 (?)

Why?

Note that, as far as we know, it is a COINCIDENCE that 1/H0 now is very
close to the age of the universe. There are some special models in
which this relation always holds, but it doesn't hold in our model. In
the future, the age of the universe will be more than 1/H0. In fact, H0
(and hence 1/H0) will converge on a constant value, while of course the
age will always increase.

What that means is 6.3 billion years from now the age of Universe
is much larger than calculated value based on the measured value
of H0 valid at that moment.

In order to do such a calculation, you also have to specify Omega and
lambda. The age of the universe is a function of Omega and lambda; H0
is essentially a scaling factor.