Re: Questions about cosmology
- From: "Ahmed Ouahi, Architect" <ahmed.ouahi@xxxxxxxxx>
- Date: Thu, 3 Aug 2006 18:23:58 +0300
For the time being, along that matter, it would be a necessary to pay an
adequate attention and to consider anything cosmological along the
relativity.
Therefore, among a microcosm of a details, it would not be without to
remark, that generally the universe as it is already so constituted and
would have, along an appropriate respect to its gravitationnal field, not
even a center.
However, an appropriate decrease of a density along a spacial infinity would
a definitely not have, in any way, to be assumed, but however, both the mean
potential and the mean density would, therefore remain constant to infinity.
Therefore, along that a case specifically, would remains a primordial
conflict with a statistical mechanics, which also, could be remarked along
the Newtonian theory.
However, along a definite but extremely small density, along a matter in an
equilibrium, without any internal material form of any pressures, that being
required to maintain that equilibrium.
Therefore, to apply to the distribution for gas molecules to the stars,
along a comparing the stellar system as along a gas in a thermal
equilibrium, it would appear that the Newtonian stellar system would not be
able to exist at all, as even it would, first of all, seems hardly possible
to surmount these difficulties on the basis of the Newtonian theory.
However, along that matter, a question would remain, if the Newtonian theory
would not requires an appropriate modification!?
--
Ahmed Ouahi, Architect
Best Regards!
<denis.besak@xxxxxx> wrote in message
news:1154532826.462986.148110@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Hi!
I'm currently writing my diploma thesis for which I need the theory of
linear perturbations around a flat FRW-universe. I work together with a
Ph.D.-student who deals, as part of his doctoral thesis, with the same
topic. He uses synchronous gauge whereas I try to do the calculations
in longitudinal gauge. We both face the problem that the deeper we go
into the subject, the more questions and conceptual problems arise und
we obtain qualitatively different results which seem to contradict each
other. Our supervisor, unfortunately, is not experienced with this
formalism since in the past he only dealt with an exact FRW-universe.
He is not able to help us or tell us, what papers or books we should
read. This is why we want to ask you some of the questions here and we
hope, that someone will be able to answer them or at least to give a
hint where we can read something about it. No one is supposed to answer
all the questions at once; we know that it is quite a lot. The most
important questions for us are number 1, 3, 4, 6 and 7.
Here we go:
1.What is the precise meaning of the term "gauge-invariant"? I was
always convinced that it means that the equation is invariant under
general coordinate transformations and takes the same form in every
gauge. But in (1), the author writes on occasions that he is going to
give "the gauge-invariant equation of motion in this particular gauge".
To me, this seems like a contradiction-if it is gauge-invariant it is
the same in all gauges, so how can we say it is the equation in a
specific gauge? Might be that his sentence is just abuse of language,
but it confuses me.
2.As far as I understand it, the relative perturbation delta := delta
n/n_0 of the particle number density is not a gauge-invariant quantity,
right? If this is the case, how come the power spectrum P(k) computed
from
<delta(k) delta(k')> = (2pi)^3 P(k) delta^(3) (k - k')
is an observable and therefore gauge-invariant quantity? Is it because
we observe it only on subhorizon scales where the time development of
the perturbations is the same in all gauges?
3.A look at equation (3.16) in (2), however, leaves the impression that
delta computed in the longitudinal gauge coincides with the
gauge-invariant perturbation. Does this allow the conclusion that this
delta is the correct physical quantity we should look at and that delta
computed in synchronous gauge does not tell us practically anything?
4.If we deal with multicomponent-systems (in our case one massless and
one massive component) then, as I understand it, we are forced to
consider entropy perturbations as well. In principle, the authors of
(2) treat them but they claim that delta S/S is a constant and they
express all solutions as functions of this constant.
a) Why is it a constant? Is this always true or did they just assume it
for simplicity?
b) If constant or not, how can I actually calculate its value? I do not
know any book or review that explicitly calculates the entropy
perturbation delta S.
5.In (3), the authors say that the longitudinal gauge is nonlocal in
the sense that matter at an infinite distance influences the physical
quantities. This sound strange to me-where can I find more about that?
And does this have any relevance for practical calculations?
6.The time development of perturbations in longitudinal gauge and
synchronous gauge is not the same if we consider superhorizon scales
(which we are forced to do). In (4), this is explained in the following
way: It does not matter what you get on superhorizon scales since this
cannot be observed-the only important thing is, that the results
coincide on subhorizon scales. If this is correct, is it possible to
make any quantitative predictions on super-horizon scales which are not
gauge-dependent and which could be checked by observation?
7.The growing super-horizon modes in synchronous gauge are always said
to be t^+1 and t^+1/2. Which modes correspond to these in longitudinal
gauge? The constant mode should correspond to the t^+1, as far as I
understand it, but there are no more nondecaying modes in longitudinal
gauge, there is just one with t^(-3/2). And using the transformation
formulas from (2) to transform these solutions into synchronous gauge,
we get different results, not the two modes mentioned above. OK, I
should finally mention that we are talking about the relative energy
perturbation delta rho/rho_0, not the gravitational potential.
8.Is there any manifestly gauge-invariant form of the Boltzmann
equation and, if so, where can I find it?
9.If we want to calculate the left-hand side of the Boltzmann equation
using the Liouville-operator from (5), then it makes a difference
whether we consider energy and momentum, which are of course related by
E^2 = p^2 + m^2, as dependent or independent variables. Only if we
consider them as independent, the result is the same as given in the
literature. (Calculating it in the way proposed in (6), however, causes
no such problems.) Why do E and p have to be considered as independent
when using the Liouville operator?
10.Are the S-matrix elements influenced by gravity? Or, to put it in
another way, is there an (nonnegligible) influence of the nontrivial
metric on scattering cross sections?
Thx in advance,
Denis Besak + Alexander Kartavtsev
(1) Ali Malik, astro-ph/0101563 (Ph.D. thesis)
(2) Mukhanov, Feldman, Brandenberger, Phys.Rep. 215, 204 (1992)
(3) Bucher, Moodley, Turok, Phys.Rev. D62, 083508
(4) Lesgourgues, Pastor, Phys.Rep.429, 307 (2006)
(5) Kolb/Turner, The Early Universe
(6) S.Dodelson, Modern Cosmology
.
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