Re: Dark Energy

Me:
>> 8 pi G rho + gamma + -3H^2 = 0
>>
>> ( gamma = cosmological constant, a form of dark energy.
>> rho = average matter density
>> G = Newton's constant
>> H = Hubble's expansion factor. )
>>
>> The question is: how do we interpret this equation?
>>
>> Since the first two terms are proportional to energy density then
>> it is a reasonable inference that we have an expression of energy
>> conservation if the last term is also proportional to energy density;
>> in this case the energy of the dynamic geometry.
>>
[.......]
Philip:
> Let me rephrase my criticism. You say that there is a conservation
> equation, and say that the energy of the cosmological constant "comes
> from" the expansion and also that the equation is valid if there is no
> cosmological constant. So, my question is, if there is no cosmological
> constant, then, in the case of no cosmological constant, where does the
> energy go which, in the case of a cosmological constant, is transformed
> into the cosmological constant?

Let me answer it this way: the cosmological constant currently dominates
the expansion of the universe. The matter and photons are just being
carried along for the ride. (This wasn't always the case. Earlier the
matter dominated, and before that the photons.) The dominant flow of
energy, today, is from the Hubble expansion to the cosmological constant,
each one growing in magnitude although of opposite sign. Without a
cosmological constant the presently insignificant flow from the photons
(via the red shift) to the Hubble factor would dominate, as it did in the
early universe. i.e. the direction of the energy flow would be reversed.

> Imagine the Einstein static universe. There is no expansion. Yet there
> is an energy density due to the cosmological constant. How does it
> "come from" the (non-existent) expansion in this case? What about a
> negative cosmological constant?

Indeed, as you point out, in Einstein's original static universe the
cosmological constant was negative and its now negative energy offset
the energy in the matter and photons. With no expansion there was no
energy transfer to/from the cosmological constant.
>
> I'll reply in more detail later.
>
> Perhaps we are merely using completely different terminology. However,
> I think that what you are saying is misleading, or at least confusingly
> phrased. You seem to be saying "no mystery where the dark energy comes
> from, it comes from expansion". Of course if there is an equation which
> holds while the universe expands, then something is conserved; the
> question is how this relates to commonly used usages of the term.

True.

> I think Edward Harrison has explained rather well what is meant by
> "energy is not conserved in the expanding universe". Do you disagree
> with his analysis?

Yes. If I understand Harrison's argument it is that pressure and pressure
gradients mediate the transfer of energy in the thermodynamic dE = -P dV
equation (which has a cosmological equivalent), which describes the
expansion of, say, a pressurised gas against its environment. But in the
universe there is no exterior system to push against and hence no transfer
of energy. Instead he concludes the red-shift energy is lost and not
transferred. I think he is being lead astray by the thermodynamic
analogy with pressure. Pressure is the result of particles (including
photons) with momenta, which have de Broglie wavelengths. It is the
stretching of the wavelengths by the Hubble expansion which causes the
loss of momenta and the red-shift. The loss of radiation pressure is a
consequence of this stretching and not a mediating mechanism; no
pressure gradient or exterior system is required.

I agree with your point about definitions and the Doppler effect.

Cheers,
Michael C Price
----------------------------------------
http://mcp.longevity-report.com
http://www.hedweb.com/manworld.htm

.

Relevant Pages

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