## [hep-th/0503117] Primordial inflation explains why the universe is accelerating today

 Authors: Edward W. Kolb, Sabino Matarrese, Alessio Notari, Antonio Riotto Abstract: We propose an explanation for the present accelerated expansion of the universe that does not invoke dark energy or a modification of gravity and is firmly rooted in inflationary cosmology. [PDF]  [PS]  [BibTex]  [Bookmark]

Discussion related to specific recent arXiv papers
Sarah Bridle
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### [hep-th/0503117] Primordial inflation explains why the unive

This paper says that the observed acceleration of the Universe can be explained by super-Hubble density perturbations, without the need for any dark energy!

Is it correct to think of this theory as proposing that there are some matter concentrations outside the Hubble radius that we are being stretched towards? If so, then surely it seems so simple that it is embarassing it wasn't thought of before?!
* Was it previously assumed that these perturbations were too small to make a difference?
* Do the authors need to assume an unconventional spectral index for perturbations? (I didn't spot anything odd..)
* It doesn't seem intuitive to me that the model would depend only on one parameter, , as I would have thought it would depend at least on the amount of power on different scales.
* Can anyone spot any flaws?

The paper shows the magnitude redshift relation that would be observed, compared to LCDM, which is nice.
* What is assumed about &#937;m for this plot?.
* The lines seem to be getting further and further apart at z=2.. am curious to know what happens at higher redshift.
* I would also like to know qualitatively why this is happening, since I got the impression that at early times this model would be indistinguishable from LCDM since the super-horizon perturbations would be very small early on and so have no effect.

On a practical level, if this theory is correct what would be the implications for all these upcoming experiments to measure dark energy?!
* Is it still as interesting to do these experiments?! I guess a lot of the mystery is gone! On the other hand does this paper imply that we would be able to measure the properties of the Universe beyond the "observable Universe"!
* Are there other observational implications that could be looked for?

Anze Slosar
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### [hep-th/0503117] Primordial inflation explains why the unive

I don't quite understand what happens to the spatial curvature here. They seem to claim that the accelerated expansion can be explained by the virtue us living in an underdense part of the supper-hubble universe and thus perceive an accelerated expansion: wouldn't this imply that the local spatial curvature follows that and hence we should see a locally open universe and thus peaks in the CMB at the wrong position? Dark Energy fills the gap between $\Omega_m=0.3$ and $\Omega_t=1$ (observed by CMB), but I don't see how this could arise from SH perturbations.
(In general Kolb et company know what they are talking about so I am probably wrong, but would like to understand this anyway)

Simon DeDeo
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### [hep-th/0503117] Primordial inflation explains why the unive

There's been a lot of discussion of this paper here – I won't try to summarize the ideas of those I've talked to (perhaps they will post!), but I also wonder what the spatial curvature is in these models – it seems the effect of perturbation evolution is to alter w for "curvature density" from −1/3? It's also been remarked that this alteration happens precisely *because* of spatial gradient terms in the potential (another way to to it is via isocurvature flucts according to another paper from [some] of the same authors), so it is another reason to worry about curvature.

Sean Carroll has some notes on his blog from a different angle. In general, there has been some sticking points re: causality: i.e., can a superhorizon mode do anything more than change the value of H0 and Omega_m? I am not a causality guru, but I still have to worry about the curvature question before getting involved in this second debate.

I've heard rumors that there will be an arXiv posting about the paper coming soon... or perhaps Kolb and other authors will post here!

Admin note: The Kolb isocurvature ref is astro-ph/0410541, the blog is at http://preposterousuniverse.blogspot.com/

Syksy Rasanen
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### Re: [hep-th/0503117] Primordial inflation explains why the u

Sarah Bridle wrote:Is it correct to think of this theory as proposing that there are some matter concentrations outside the Hubble radius that we are being stretched towards? If so, then surely it seems so simple that it is embarassing it wasn't thought of before?!
This line of work, usually known as backreaction (though these authors don't use the term) has been pursued in the past. Brandenberger and collaborators have looked at these things in the inflationary era, and there has also been work on the effect of perturbations today from the 1990s (the first papers on the effect are in fact from the 1960s).

A mini-list of relevant references is given in my talk "Backreaction of linear perturbations and dark energy" astro-ph/0407317, and an exhaustingly more comprehensive one is in "Dark energy from backreaction" astro-ph/0311257.
Sarah Bridle wrote:* Was it previously assumed that these perturbations were too small to make a difference?
* Do the authors need to assume an unconventional spectral index for perturbations? (I didn't spot anything odd..)
* It doesn't seem intuitive to me that the model would depend only on one parameter, , as I would have thought it would depend at least on the amount of power on different scales.
* Can anyone spot any flaws?
In order of appearance:

* Possibly. There has also been skepticism whether super-Hubble perturbations can have an effect on local physics. I think the answer (supported by explicit calculations by for example Woodard and his collaborators in a different setting) is clearly "yes".

*No, they just need n<1. (The numbers needed are discussed in their previous papers, of which this is essentially a summary.)

*They mean one extra parameter in addition to the usual inflationary parameters.

*One point is that the calculations are only to second order, but the variance of a second order variable should be consistently calculated at fourth order. The authors have noted that the result should be qualitatively the same, which may be true.

Syksy Rasanen
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### Re: [hep-th/0503117] Primordial inflation explains why the u

Simon DeDeo wrote:I also wonder what the spatial curvature is in these models – it seems the effect of perturbation evolution is to alter w for "curvature density" from −1/3?
The essence of these backreaction calculations is that the relation between the average geometry and sources cannot be expressed in terms of the FRW equation and its parameters. So the right question is not "what is the value of the curvature parameter?" but "what is the right equation and what are its parameters?". See for example gr-qc/9906015 and gr-qc/0102049 by Buchert for details.

As for causality, there is no problem, for the same reason that it's no problem that the CMB temperature is the same in causally disconnected regions. The correlations between different regions were set up during inflation when they were in causal contact. A perhaps helpful analogy is creation of particle and antiparticle pairs in a constant electric field: even when the pairs disappear far away, the electric field between them remains.

Simon DeDeo
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### [hep-th/0503117] Primordial inflation explains why the unive

Dear Sysky – thanks!

I've also been passed an e-mail which says that the question of the curvature is not as simple as it first appears – I'm digesting it now and will post when I have a better idea of what is going on.

Exciting stuff.

Alessandro Melchiorri
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### [hep-th/0503117] Primordial inflation explains why the unive

Hi,

I think we have to see if the model can explain also other observables like large scale structure data, the position and amplitude of the CMB peaks, the age of the universe (too small for Omega_m=1) etc etc. before being really competitive with dark energy and lambda.

Another point (perhaps Syksy could answer on this) why there is no anisotropic expansion ? If there are super horizon perturbations with
a large variance I would expect that a non-isotropic universe is possible.

Anyway intersting subject !

Cheers
Alessandro

Syksy Rasanen
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### Re: [hep-th/0503117] Primordial inflation explains why the u

If backreaction gives accelerated expansion, the age problem is solved in the same way as in LCDM. But you're right, Alessandro, that more work needs to be done (both on observational implications and on theoretical issues) before these ideas are on the same footing with LCDM.

Some things I don't understand about the work by Kolb et al include the treatment of ultraviolet modes (esp. in their paper astro-ph/0501152, where I cannot understand how they neglect their effect on the average).
One aspect of this is that they seem to decompose the modes in a Fourier series as usual, which implies using periodic boundary conditions. This is important because the averages involve terms which are total derivatives and therefore vanish when integrated over the whole space. But if the box you are using is super-Hubble sized, and you take the average only over the local Hubble volume, then clearly these modes should not average to zero in general.

The issue of anisotropy is not clear to me. But it seems to me that in the case when the effect comes from super-Hubble modes, the anisotrpy over a single Hubble patch would be expected to be small.

As for curvature, one observation to make is that (as explained in the papers by Buchert I mentioned) a backreaction effect (for the average quantities) mimicking dark energy would imply a non-zero spatial curvature. (In which case the mode decomposition of course has to be more involved.) However, in the case of Kolb et al, the effect does not come from the average but from the variance, so the issue is not clear (to me at least).

Syksy Rasanen
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### Re: [hep-th/0503117] Primordial inflation explains why the u

Syksy Rasanen wrote:As for curvature, one observation to make is that (as explained in the papers by Buchert I mentioned) a backreaction effect (for the average quantities) mimicking dark energy would imply a non-zero spatial curvature. (In which case the mode decomposition of course has to be more involved.) However, in the case of Kolb et al, the effect does not come from the average but from the variance, so the issue is not clear (to me at least).
On second thought, this is a rather stupid comment. Of course they are still talking about the average behaviour over the horizon volume, so the observation that the average spatial curvature should be non-zero applies.

Niayesh Afshordi
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### [hep-th/0503117] Primordial inflation explains why the unive

It was so hard to hold my tongue till this moment, but now that our paper is out on the arXiv, without any fear from my collaborators, I can say that I believe, as Anze and Simon had guessed, the effect claimed by Kolb et al. is nothing more than a curvature effect. We show this in astro-ph/0503553.

In our communications with some of the authors of Kolb et al. papers, it appears that they think there will be some non-trivial effect from higher order gradient terms. We try to refute this in our paper as well.

Alessandro Melchiorri
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### [hep-th/0503117] Primordial inflation explains why the unive

Hi Niayesh,

Good point! certainly curvature should be investigated, but how you can use the CMB constraint on curvature ? this has been obtained under
the assumption of L-CDM. Anyway I think it would be difficult to reproduce
the CMB peaks positions in the SHCDM model.

Ale

p.s. For Syksy, I guess the age should be different in the SHCDM because they assume Omega_m=1.

Syksy Rasanen
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### Re: [hep-th/0503117] Primordial inflation explains why the u

Alessandro Melchiorri wrote:Anyway I think it would be difficult to reproduce
the CMB peaks positions in the SHCDM model.
How so? Models with Omega_m=1 are perfectly compatible with the CMB data (see for example astro-ph/0304237). From the point of view of the CMB, the case with super-Hubble perturbations is a mixture of Omega_m=1 and LCDM (the ratio of baryons and CDM is as in Omega_m=1 models, but the angular diameter distance is as in LCDM). Perhaps it doesn't work, but I don't see any a priori reason to conclude so.
Alessandro Melchiorri wrote:p.s. For Syksy, I guess the age should be different in the SHCDM because they assume Omega_m=1.
Why? The age problem arises because in a model with Omega_m=1 and the behaviour of the universe given by the FRW equations the Hubble parameter falls off too rapidly. So in order for the universe to be 13 billion years old, the Hubble parameter would have to have fallen to around h=0.45−0.50. If backreaction boosts the expansion rate so that the Hubble parameter does not fall, is the situation not the same as in LCDM?

Alessandro Melchiorri
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### [hep-th/0503117] Primordial inflation explains why the unive

Hi Sysky!

Yes CMB is compatible (at 2-sigma) with Omega_m=1 if h=0.45 and if you add [perhaps too many] massive neutrinos and with bumps in the primordial spectrum. In the paper by Rocky it seems from Eq. 9 (but I am not sure) that current aestimates of the Hubble parameter at z<0.1 should be slightly affected by super horizon perturbations. So we still have h around 0.7 from the HST and problems with the CMB and perhaps age.
I am correct ?

Anyway, someone should do the correct computations (not me, too busy in
posting on cosmocoffee :-)) !

cheers
Ale

Syksy Rasanen
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### Re: [hep-th/0503117] Primordial inflation explains why the u

Alessandro Melchiorri wrote:So we still have h around 0.7 from the HST and problems with the CMB and perhaps age. I am correct ?
The idea is that the super-Hubble perturbations would give accelerated expansion, so that you get h=0.7, thus no problems with age. As you say, the CMB calculation would have to be done, the issue is open. (An alternative take by some of the same authors is due to the affects of perturbations on the luminosity distance, in which case the HST observations would have to be reinterpreted.)

Alessandro Melchiorri
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### [hep-th/0503117] Primordial inflation explains why the unive

Ok but in the standard model, to get age=13.5 Gyrs with Omega_m=1
and h=0.7 you need Omega_Lambda=1.8. I guess structure formation would be rather different in this model !

ciao
Alessandro