Exploring the Hubble Age Estimate

[yogi]

Following different lines of reasoning (most likely all faulty) - I can convince myself that the current estimate(s) of the Hubble age may be off by a factor or 2 (more or less) depending upon the physiology asssumed for space and the model used to describe the expansion rate - specifically:
If the cosmological redshift (CR) is attributed to stretching space (per Harrison's description as incorporated in Wiki) then the scale factor "now" divided by the scale factor "then" seems consistent with the present estimates 70+ and an estimated age of about 13.5 billion years. This description, however, implies a substantive property of space akin to what one might attribute to a medium - no one seems to have a convincing argument of why space can stretch so as to lengthen the wavelength if the void does not have medium-like properties.
On the other hand, if the CR is in reality a Doppler affect as originally thought (prior to Robertson's interpretation) - and as sometimes argued by some members of this Forum, then z is not representative of the present size of the Hubble Scale because the red shifted light has taken about 13 billion years to arrive from the most distant sources - during that 13 billion year travel time since the photon was launched, the universe continued to expand - perhaps doubling in size to 26 billion light years - or more if q is negative.

A third way of viewing the CR which does not require a stretching medium embraces the notion that the receding nebula are not moving wrt space as is the case with kinematical motion that relies upon mediums (such as sound in air) - but rather, the light sources are comoving with respect to local space, that is, the spatial coordinate system is expanding - In this model, light sources are wafted along by the local space - this would seem to explain the faster than c recessional velocity consistent with redshift data

But like the kinematical model, the data would "out dated" by the time it is received - the distant source and Earth having moved further apart (with their own local space) during the photon's travel time - the snapshot taken by the captured redshift data from the most distant galaxies would seem to be correct only in the stretching space scenareo - but not in the comoving space model. As in the kinematical formalism, The difference would seem to be further augmented if the universe is accelerating.

While the velocity distance law is well established - Does it really make sense to define the present age of the universe based thereon?

 

[yogi]

I am not sure I have expressed the issue very well - As I sit here playing with my Hoberman sphere, I can vizualize a photon emitted from a light source at one node (1) that is moving away from another nodes (2) [call node 2 earth] The space in the vicinity of the light source (1) is receding as is the source - so the photon initally is not moving toward Earth at c - it spends time like the red queen - going nowhere at the speed of light - and this it would seem will impact the calculation of the cosmological age - so where does it get taken into account?

 

[Chalnoth]

It doesn't matter how you look at it. As long as you use the proper relativistic equations derived from General Relativity, it works out correctly that the cosmological redshift exactly coincides with the expansion.

 

[Jorrie]

While the velocity distance law is well established - Does it really make sense to define the present age of the universe based thereon?

I'm not sure if this answers the question, but it is enlightening to look at how the various cosmological calculators perform the calculation of the age of the universe. It is surely not simply a Hubble time (=constant/H_0) calculation. It is normally obtained out of an integration of the Friedman equation for scale factor a=0 to a=1.

$$t_0 = \int_0^1{\frac{da}{aH_0\sqrt{(1-\Omega)/a^2 + \Omega_m/a^3 +\Omega_r/a^4 + \Omega_\Lambda}}}$$

I suppose one can say that it is based upon an integration of the inverse of the time varying Hubble parameter. The fact that it gives a result that is quite close to the the present Hubble time is probably just a coincidence.

 

[marcus]

Chalnoth's post says what needs to be said

It doesn't matter how you look at it. As long as you use the proper relativistic equations derived from General Relativity, it works out correctly that the cosmological redshift exactly coincides with the expansion.

However, in case it might help clarify, I will add my two-cents.

I think your basic fallacy is here:

... This description, however, implies a substantive property of space akin to what one might attribute to a medium - no one seems to have a convincing argument of why space can stretch so as to lengthen the wavelength if the void does not have medium-like properties.
...

It does not imply space is substance, just as the fact that Maxwell's equations work in space does not imply space has "a substantive property".

Maxwell's equations work because space has geometry. The shape of the wave as it approaches me from the West will determine the shape of the wave as it continues on to the East. If the geometry is static, and distances are not changing, then Maxwell predicts the wavelength will not change.

However if the geometry is dynamic then obviously the geometry of the Maxwell equations is affected. If distances are increasing then Maxwell equations must predict that wavelengths increase, as we observe they do.

Imagine a very low frequency radio wave where the distance between peaks is one light year, traveling in intergalactic space.
The peak-to-peak distance is not like one between gravitationally bound objects or one between the ends of a rod, fixed by crystal lattice bonds. This peak-to-peak distance will be subject to the Hubble Law, taken as purely geometric statement.

Actually I would go further than the statement that space has geometry. There is no thing or material called space. There are only the geometric relations between events. There is only geometry. GR is the current prevailing theory of how this geometry evolves.
Geometry is primal to physics and all physical law, e.g. Maxwell equations, must be seen and formulated in that context in order to have meaning.

EDIT: I also agree with what Wallace says in the next post.

 

[Wallace]

When someone says 'space expands' they are describing a useful way of thinking about the FRW solution to general relativity. However, the theory itself does not contain any such concept. As others have said, if you just use the mechanics of the theory, you get a single unambiguous answer. The whole 'expanding space' thing is just one way of thinking about the theory in simple terms, but you can't actually do any calculations starting from this kind of idea, you have to use the actual theory itself (i.e. general relativity).

 

[yogi]

Thanks for the responses - I know I am thinking about things incorrectly - but I would like to explore the point one more time Using the model of an exponentially expanding universe such as in de Sitter cosmology - when the algebra is applied, don't we wind up with a finite Hubble period, a fixed Hubble radius, a fixed Hubble constant but an infinite age universe (or at least an undefined beginning)? Its my understanding that the redshift at the Hubble limit would be infinite in a de Sitter universe - but that is also the limiting value in a big bang universe - so back to my question - is it presumptious to make conclusions about the age of the universe based upon redshift or Hubble velocity distance data?

 

[Jorrie]

Using the model of an exponentially expanding universe such as in de Sitter cosmology - when the algebra is applied, don't we wind up with a finite Hubble period, a fixed Hubble radius, a fixed Hubble constant but an infinite age universe (or at least an undefined beginning)?

Integration of the Friedman equation with $\Omega = \Omega_\Lambda = 1$ gives a fixed Hubble constant and with H_0=70 km/s/Mpc, the age comes out as t_0 = 18.8 Gy.

I think it is only when the constant H_0 is set to (close to) zero that age approaches infinity, but then we are approaching a static model with no beginning.

 

[Chalnoth]

Its my understanding that the redshift at the Hubble limit would be infinite in a de Sitter universe

True. But this breaks down when you recognize that no universe is going to be perfectly de Sitter. There's going to be some stuff sitting around, and as you go back in time, eventually that stuff, whatever it is, will become more dense than the cosmological constant, causing the universe to stop acting like a de Sitter universe.

 

[yogi]

Jorrie: "Integration of the Friedman equation with gives a fixed Hubble constant and with H_0=70 km/s/Mpc, the age comes out as t_0 = 18.8 Gy."

That is closer to what I had arrived at using a q = zero model taken together with an intrinsic acceleration that follows from the geometry of a constant rate Hubble sphere
Thanks.

Chalnoth: "True. But this breaks down when you recognize that no universe is going to be perfectly de Sitter. There's going to be some stuff sitting around, and as you go back in time, eventually that stuff, whatever it is, will become more dense than the cosmological constant, causing the universe to stop acting like a de Sitter universe."

Actually, if you assume the universe is in tension with negative pressure = to 1/3 the energy density - the density term and the pressure term cancel - so you can have a perfectly well behaved de Sitter expansion with lots of energy in the form of cosmic stress and some chunks of mass here and there so long as the total equals 1/3 the negative pressure term - - so de Sitter's cosmology may be closer to reality that originally thought. But I appreciate the Input.

 

[Chalnoth]

Actually, if you assume the universe is in tension with negative pressure = to 1/3 the energy density - the density term and the pressure term cancel - so you can have a perfectly well behaved de Sitter expansion with lots of energy in the form of cosmic stress and some chunks of mass here and there so long as the total equals 1/3 the negative pressure term - - so de Sitter's cosmology may be closer to reality that originally thought. But I appreciate the Input.

It's no problem to have eternal expansion into the future: a nearly de Sitter universe just becomes more de Sitter with time. The problem is the past, as the opposite is true backward in time.

 

[yogi]

It's no problem to have eternal expansion into the future: a nearly de Sitter universe just becomes more de Sitter with time. The problem is the past, as the opposite is true backward in time.

Quite right - although I am getting a bit off my own original inquiry - You got me wondering if it makes sense to incorporate the notion of a zero energy universe in combination with a de Sitter expansion - i think it was Ed Tyron's that first came up with the idea of balancing the negative gravitational potential against the field energy - this would seem to be consistent with an early universe with less energy as you wound the clock backwards - I am curious if it can be made to fit a "no temporal beginning" universe

Of course, all so called steady state models have to contend with the CBR - there seems to be no event in de Sitter cosmology that would explain its presence unless one is introduced by fiat.