[astroph/0506534] On cosmic acceleration without dark energy
Authors:  E.W. Kolb (Fermilab and University of Chicago), S. Matarrese (Physics Dept., Padova), A. Riotto (INFN, Padova) 
Abstract:  We elaborate on the proposal that the observed acceleration of the Universe is the result of the backreaction of cosmological perturbations, rather than the effect of a negativepressure darkenergy fluid or a modification of general relativity. Through the effective Friedmann equations describing an inhomogeneous Universe after smoothing, we demonstrate that acceleration in our local Hubble patch is possible even if fluid elements do not individually undergo accelerated expansion. This invalidates the nogo theorem that there can be no acceleration in our local Hubble patch if the Universe only contains irrotational dust. We then study perturbatively the time behavior of generalrelativistic cosmological perturbations, applying, where possible, the renormalization group to regularize the dynamics. We show that an instability occurs in the perturbative expansion involving subHubble modes, which indicates that acceleration in our Hubble patch may originate from the backreaction of cosmological perturbations on observable scales. 
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[astroph/0506534] On cosmic acceleration without dark energ
Oh, no, here they are again!
This has been extensivelly discussed here: http://www.cosmocoffee.info/viewtopic.php?t=218
Now they seem to claim that most arguments presented agains their model are wrong. Could someone more knowledged enlighten us on these issues?
I've talked to various people and a majority seems to think that doing stuff in Fourier space is wrong as you easily break causality and causality is the biggest problem here: so, conceptually, what is their main argument why naive causal counterarguments are wrong?
This has been extensivelly discussed here: http://www.cosmocoffee.info/viewtopic.php?t=218
Now they seem to claim that most arguments presented agains their model are wrong. Could someone more knowledged enlighten us on these issues?
I've talked to various people and a majority seems to think that doing stuff in Fourier space is wrong as you easily break causality and causality is the biggest problem here: so, conceptually, what is their main argument why naive causal counterarguments are wrong?

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[astroph/0506534] On cosmic acceleration without dark energ
In fact, in the new paper Kolb et al acknowledge that their model was wrong and that superhorizon perturbations in a (vorticityfree) dust universe cannot lead to acceleration.
They also discuss various issues related to subhorizon perturbations, with the bottom line that after density perturbations go nonlinear, linear theory breaks down and nonlinear methods are needed to evaluate backreaction effects.
I don't quite understand what you mean about Fourier space and causality.
The patch of space which has been in causal contact is (in inflationary settings) much bigger than the apparent horizon. Hui and Seljak argued that the effect of this is restricted to setting the initial conditions nonlocally. They then argued that regardless of the initial conditions, the expansion cannot accelerate if only superhorizon perturbations are present (in the case of rotationless dust). The validity of this conclusion seems to be now generally accepted. (Note that this does not mean that superhorizon perturbations cannot have a local effect in other situations, e.g. in scalar field driven inflation.)
Woodard and collaborators have studied the effects of superhorizon perturbations in the context of quantized gravity and QFT in curved spacetime for some time, and their explicit computations confim that at least in those settings superhorizon perturbations can have a physical effect which is not resricted to setting the parameters of a FRW background; see e.g. grqc/0408080 .
They also discuss various issues related to subhorizon perturbations, with the bottom line that after density perturbations go nonlinear, linear theory breaks down and nonlinear methods are needed to evaluate backreaction effects.
I don't quite understand what you mean about Fourier space and causality.
The patch of space which has been in causal contact is (in inflationary settings) much bigger than the apparent horizon. Hui and Seljak argued that the effect of this is restricted to setting the initial conditions nonlocally. They then argued that regardless of the initial conditions, the expansion cannot accelerate if only superhorizon perturbations are present (in the case of rotationless dust). The validity of this conclusion seems to be now generally accepted. (Note that this does not mean that superhorizon perturbations cannot have a local effect in other situations, e.g. in scalar field driven inflation.)
Woodard and collaborators have studied the effects of superhorizon perturbations in the context of quantized gravity and QFT in curved spacetime for some time, and their explicit computations confim that at least in those settings superhorizon perturbations can have a physical effect which is not resricted to setting the parameters of a FRW background; see e.g. grqc/0408080 .

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[astroph/0506534] On cosmic acceleration without dark energ
Hi Sysky,
"In fact, in the new paper Kolb et al acknowledge that their model was wrong and that superhorizon perturbations in a (vorticityfree) dust universe cannot lead to acceleration. "
I am sorry, where they write this ?
Cheers
Ale
"In fact, in the new paper Kolb et al acknowledge that their model was wrong and that superhorizon perturbations in a (vorticityfree) dust universe cannot lead to acceleration. "
I am sorry, where they write this ?
Cheers
Ale

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[astroph/0506534] On cosmic acceleration without dark energ
In their p.6 they say:
"In Ref. [5] a deviation from the pure matterdominated evolution was obtained by a combination of suband superHubble modes generated by inflation, the latter being improperly used to amplify the backreaction."
In fact, I think this is as close as they get to retracting their original claim.
The rest of the paper pretends that there is a deeper truth to their original claim, although what they come up with (e.g., Eq. 78), is completely different: It is UV divergent not IR, and its net value is supposed to become significant and not its variance.
Also, the term that they end up suggesting as replacement for dark energy is just one in the gradient expansion (with six gradients). They also acknowledge that there is no reason for this term to dominate over others. I suspect that observations of large scale structure or at galactic scales can rule out such severe deviations from Newtonian gravity, as such corrections (with so many gradients) should be very clumpy.
To summarize:
1 The original claim is out.
2 The new suggestion is still highly speculative, and probably wrong, as it is severely constrained by the required smoothness of dark energy.
"In Ref. [5] a deviation from the pure matterdominated evolution was obtained by a combination of suband superHubble modes generated by inflation, the latter being improperly used to amplify the backreaction."
In fact, I think this is as close as they get to retracting their original claim.
The rest of the paper pretends that there is a deeper truth to their original claim, although what they come up with (e.g., Eq. 78), is completely different: It is UV divergent not IR, and its net value is supposed to become significant and not its variance.
Also, the term that they end up suggesting as replacement for dark energy is just one in the gradient expansion (with six gradients). They also acknowledge that there is no reason for this term to dominate over others. I suspect that observations of large scale structure or at galactic scales can rule out such severe deviations from Newtonian gravity, as such corrections (with so many gradients) should be very clumpy.
To summarize:
1 The original claim is out.
2 The new suggestion is still highly speculative, and probably wrong, as it is severely constrained by the required smoothness of dark energy.

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Re: [astroph/0506534] On cosmic acceleration without dark e
Page 6, end of the second full paragraph:Alessandro Melchiorri wrote:"In fact, in the new paper Kolb et al acknowledge that their model was wrong and that superhorizon perturbations in a (vorticityfree) dust universe cannot lead to acceleration. "
I am sorry, where they write this ?
"In this paper, we will show that the deviation from a matterdominated background is entirely due to the nonlinear evolution of subHubble modes which may cause a large backreaction (technically due to the disappearance of the filter modeling the volume average), while the superHubble modes play no dynamical role."
Page 14, end of the first paragraph of section A (which is dedicated to deriving this result):
"the effect of pure super Hubble perturbations is limited to generating a true local curvature term which may be important but can not accelerate the expansion of the Universe."
Page 19, beginning of the last paragraph of section A:
"if only longwavelength perturbations were present, at large times the lineelement would take the form of a curvature dominated Universe, with [tex]h_{ij} \sim t^2 C_{ij}(x)[/tex], where [tex]C_{ij}(x)[/tex] is a function of spatial coordinates only."
Page 27, beginning of the third paragraph of the section Conclusions:
"Through the renormalization group technique, we have then shown that superHubble modes can be resummed at any order in perturbation theory yielding a local curvature term $\sim a_D^{2}" at large times."

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Re: [astroph/0506534] On cosmic acceleration without dark e
The terms with the highest number of derivatives (at each order in [tex]\Phi[/tex]) \emph{are} the Newtonian ones. The question is whether terms with a \emph{smaller} number of derivatives could important. (Though, as Kolb et al correctly note, a nonperturbative treatment would be needed to discuss the issue, so talking about orders of perturbation theory is probably not very meaningful.)Niayesh Afshordi wrote:Also, the term that they end up suggesting as replacement for dark energy is just one in the gradient expansion (with six gradients). They also acknowledge that there is no reason for this term to dominate over others. I suspect that observations of large scale structure or at galactic scales can rule out such severe deviations from Newtonian gravity, as such corrections (with so many gradients) should be very clumpy.
Of course, dark energy was introduced precisely because deviations from the FRW dust behaviour (which agrees with the Newtonian average result, for closed spatial sections; see astroph/9510056 ) are seen on large scales.
For a good new overview of the issues, I recommend grqc/0506106 , "The universe seen at different scales" by Elis and Buchert.
Could you elaborate on the constraints from smoothness?Niayesh Afshordi wrote:2 The new suggestion is still highly speculative, and probably wrong, as it is severely constrained by the required smoothness of dark energy.

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Re: [astroph/0506534] On cosmic acceleration without dark e
This should read: the page 19, the \emph{end} of the last paragraph of section A.Syksy Rasanen wrote:Page 19, beginning of the last paragraph of section A:

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Re: [astroph/0506534] On cosmic acceleration without dark e
Newtonian terms (at any order) cannot lead to any backreaction other than a boundary term. That's why they are hoping postNewtonian terms can do the trick.Syksy Rasanen wrote:
The terms with the highest number of derivatives (at each order in [tex]\Phi[/tex]) \emph{are} the Newtonian ones. The question is whether terms with a smaller number of derivatives could important. (Though, as Kolb et al correctly note, a nonperturbative treatment would be needed to discuss the issue, so talking about orders of perturbation theory is probably not very meaningful.)
I don't think this statement is correct. Newtonian and GR dymaincs (and backreaction) are different through postNewtonian terms. Q_D (as defined by Buchert et al.) is a total derivative in a flat space, but not necessarily in a curved one.Syksy Rasanen wrote: Of course, dark energy was introduced precisely because deviations from the FRW dust behaviour (which agrees with the Newtonian average result, for closed spatial sections; see astroph/9510056 ) are seen on large scales.
Dark Energy is supposed to be relatively smooth (at least observationally) as it only affects the cosmic dynamics through changing the background evolution. On the other hand, a term like \langle \delta^2 v^2 \rangle is probably very different within a galaxy cluster and within a void.Syksy Rasanen wrote:Could you elaborate on the constraints from smoothness?Niayesh Afshordi wrote:2 The new suggestion is still highly speculative, and probably wrong, as it is severely constrained by the required smoothness of dark energy.

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Re: [astroph/0506534] On cosmic acceleration without dark e
I don't see a contradiction between my statement and yours. Because the Newtonian backreaction term is a total derivative, it does not lead to any backreaction for closed spatial sections. Therefore the Newtonian average equations agree with the (spatially flat) FRW dust equations.Niayesh Afshordi wrote:I don't think this statement is correct. Newtonian and GR dymaincs (and backreaction) are different through postNewtonian terms. Q_D (as defined by Buchert et al.) is a total derivative in a flat space, but not necessarily in a curved one
Backreaction is the difference between the average behaviour of a given domain and the behaviour of a corresponding smooth and isotropic domain. So it doesn't make sense to talk about 'backreaction' within a single cluster. (Unless one is treating the cluster as homogeneous and isotropic in order to evaluate some average quantities, but that's presumably not what you mean?)Niayesh Afshordi wrote:Dark Energy is supposed to be relatively smooth (at least observationally) as it only affects the cosmic dynamics through changing the background evolution. On the other hand, a term like \langle \delta^2 v^2 \rangle is probably very different within a galaxy cluster and within a void.
On the other side, dark energy effects beyond the background level are not ruled out. For example, dark energy could have perturbations, and even affect the virialisation of collapsing structures (e.g. astroph/0401504,astroph/0505308).

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[astroph/0506534] On cosmic acceleration without dark energ
Hi all,
Just saw a nice talk by Sabino Matarrese last week in Paris.
Indeed the original claim is out, Matarrese was very clear on this.
However the points raised in the new article seems interesting to me.
BTW I hope we don't decide if a scientific theory is correct or not on the basis of a poll ! :)
cheers
alessandro
Just saw a nice talk by Sabino Matarrese last week in Paris.
Indeed the original claim is out, Matarrese was very clear on this.
However the points raised in the new article seems interesting to me.
BTW I hope we don't decide if a scientific theory is correct or not on the basis of a poll ! :)
cheers
alessandro

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[astroph/0506534] On cosmic acceleration without dark energ
Hi all,
In grqc/0509108, Ishibashi and Wald refute the claims of backreaction being the reason for the observed local acceleration. They have an example showing that averaging could show up an artificial acceleration. Just after reading this, I saw astroph/0510059. This is a "white paper" on the dark matter problem by Bean, Carrol and Trodden. They feel that the possibility of explaining "dark energy" by incorporating higherorder corrections is still possible. Is this the common feeling ?? The poll here certainly does not point that way :?
In grqc/0509108, Ishibashi and Wald refute the claims of backreaction being the reason for the observed local acceleration. They have an example showing that averaging could show up an artificial acceleration. Just after reading this, I saw astroph/0510059. This is a "white paper" on the dark matter problem by Bean, Carrol and Trodden. They feel that the possibility of explaining "dark energy" by incorporating higherorder corrections is still possible. Is this the common feeling ?? The poll here certainly does not point that way :?

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 Joined: November 26 2005
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[astroph/0506534] On cosmic acceleration without dark energ
Hi everybody,
I am joining now this forum, and I would like to say my opinion on the subject.
As I stressed in my paper astroph/0503715 I have shown that the perturbative series (that is, assuming the density contrast [tex]\delta[/tex] and the gravitational potential [tex]\phi[/tex] be much smaller than 1) breaks down at redshifts of order 1.
This is the series of the PostNewtonian terms.
It could be that this is just an artifact of the perturbative expansion, but so far we have no serious result.
The only serious criticism made to this is that in a Newtonian and PostNewtonian expansion, the leading term "could" be of the form (for dimensional arguments) :
[tex]<\phi \delta>[/tex] (where <> is the spatial average)
and this is typically [tex]10^{5}[/tex]
Note however that this is only a guess. It is very important to have the correct form of the correction. As Niayesh says it is true that in the newtonian approach [tex]\phi[/tex] is small.....but I believe it is not true the conclusion that the backreaction is necessarily small.
There is an additional quantity in fact which is [tex]\delta[/tex], and [tex]\delta>>1[/tex].
Suppose that the backreaction appears for example as:
[tex]\sqrt{< \phi^2 \delta^2>}[/tex]
Dimensional anlysis would say that this is of the same order of [tex]\delta\phi[/tex]...but it is not!
And in fact it is of order 1.
I am joining now this forum, and I would like to say my opinion on the subject.
As I stressed in my paper astroph/0503715 I have shown that the perturbative series (that is, assuming the density contrast [tex]\delta[/tex] and the gravitational potential [tex]\phi[/tex] be much smaller than 1) breaks down at redshifts of order 1.
This is the series of the PostNewtonian terms.
It could be that this is just an artifact of the perturbative expansion, but so far we have no serious result.
The only serious criticism made to this is that in a Newtonian and PostNewtonian expansion, the leading term "could" be of the form (for dimensional arguments) :
[tex]<\phi \delta>[/tex] (where <> is the spatial average)
and this is typically [tex]10^{5}[/tex]
Note however that this is only a guess. It is very important to have the correct form of the correction. As Niayesh says it is true that in the newtonian approach [tex]\phi[/tex] is small.....but I believe it is not true the conclusion that the backreaction is necessarily small.
There is an additional quantity in fact which is [tex]\delta[/tex], and [tex]\delta>>1[/tex].
Suppose that the backreaction appears for example as:
[tex]\sqrt{< \phi^2 \delta^2>}[/tex]
Dimensional anlysis would say that this is of the same order of [tex]\delta\phi[/tex]...but it is not!
And in fact it is of order 1.

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[astroph/0506534] On cosmic acceleration without dark energ
I've been trying to understand these papers, but I have some naive questions that I was hoping someone could help me with:
 On p.21 of astroph/0506534, they repeat an argument that the Newtonian terms at order [tex]n[/tex], of the form [tex](\partial^2 \phi)^n[/tex], are total derivatives. This seems obvious to everyone who is knowledgeable about such matters, but I'm having trouble understanding why it should be the case. Such terms aren't total derivatives in the usual sense, and indeed the later argument relies on terms like [tex]\langle (\partial^2 \phi)^2 \rangle[/tex] (with at least four gradient operators  but at order [tex]2n > 4[/tex] in the expansion) being arbitrarily large. I assume there is a subtlety with the averaging that I am missing?
 On p. 22, they claim that [tex]\langle (\partial^2 \phi)^2 \rangle[/tex] diverges like [tex]\ln \Lambda[/tex], for some ultraviolet cutoff [tex]\Lambda[/tex]. Although the argument isn't written out, it seems to be that for a term with [tex]p+q = N[/tex] gradient operators,
[tex]
\frac{1}{a_0^N H_0^N}
\overline{\langle \partial^p \phi
\partial^q \phi \rangle} \simeq \frac{1}{H_0^N} \int
\frac{d^3 k}{(2\pi)^3} \; k^N \overline{\phi(k)^2} T^2(k)
[/tex]
(up to factors of [tex]i[/tex] and minus signs), where [tex]T(k)[/tex] is the CDM transfer function, [tex]T(k) \sim (k_{eq}/k)^2[/tex] for large [tex]k[/tex] (and [tex]2\pi/k_{eq}[/tex] is the comoving size of the horizon at matterradiation equality), an overline is the ensemble average, and angle brackets are the spatial average. Then it follows that
[tex]
\frac{1}{a_0^N H_0^N}
\overline{\langle \partial^p \phi \partial^q \phi \rangle} \sim
(2\pi)^3 \frac{k_{eq}^4}{H_0^N} \int^\Lambda
\frac{d k}{k} \; \frac{k^N}{k^4} \delta^2_{rms} .
[/tex]
if the integral is dominated by its upper limit, assuming a scale invariant spectrum (as they do), and [tex]\delta_{rms} \simeq 10^{5}[/tex] is the amplitude of perturbations. Thus for [tex]N=4[/tex] this diverges like [tex]\ln \Lambda[/tex]. My understanding was that [tex]\phi[/tex] was the gravitational potential after inflation (cf. the discussion on p.15) and was the initial condition for their "renormalization" procedure. Is there an easy way to see why the CDM transfer function should enter here?
 Assuming that [tex]T(k)[/tex] ought to be present, the point of the lengthy calculations in Sec. III.A & III.B seems to be that for sufficiently highorder terms in the gradient expansion ([tex]n \geq 3[/tex]), the averages can become arbitrarily large. This conclusion appears to rely on the scaleinvariant spectrum extending to arbitrarily large wavenumbers. However, I would naively have expected that the spectrum is really cut off at a scale corresponding to the horizon size at the end of inflation. If this is done, then
[tex]
\frac{1}{a_0^4 H_0^4} \overline{\langle \partial^2 \phi \partial^2 \phi
\rangle} \sim (2\pi)^3 \left( \frac{k_{eq}}{k_0} \right)^4 \delta_{rms}^2
\ln k_0
[/tex]
where a subscript [tex]0[/tex] indicates the end of inflation. Since [tex]k_{eq}[/tex] is less than [tex]k_0[/tex] this quantity is presumably tiny?
 It's claimed (on p.24) that for large [tex]a[/tex], the socalled "renormalized" gravitational potential [tex]\Psi[/tex] behaves as in Eq. (71), Eq. (75) when truncated to 2 gradients or 4 gradients (respectively), and in particular grows like [tex](\ln a)^n[/tex] when truncated to [tex]2n[/tex] gradients. However, since they seem to assume [tex]\partial^2 \phi \ll (\partial \phi)^2[/tex], in (eg.) Eq. (71), the argument of the logarithm goes to zero for
[tex]
a = 9 a_0 \left( \frac{a_0 H_0}{2} \right)^2 \exp(10 \phi/3) \frac{1}{\partial^2 \phi  5(\partial \phi)^2/6}
[/tex]
Presumably this is like the Landau pole in QED, and would seem to indicate that their "renormalized" perturbation theory breaks down at a finite value of [tex]a[/tex]?

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[astroph/0506534] On cosmic acceleration without dark energ
Just caught sight of this: "Toward a NoGo Theorem for an Accelerating Universe through a Nonlinear Backreaction"
astroph/0602506
astroph/0602506
Although our work does not give a complete proof, it strongly suggests the following nogo theorem: No cosmic acceleration occurs as a result of the nonlinear backreaction via averaging.