## [astro-ph/0410541] Cosmological influence of super-Hubble perturbations

 Authors: Edward W. Kolb, Sabino Matarrese, Alessio Notari, Antonio Riotto Abstract: The existence of cosmological perturbations of wavelength larger than the Hubble radius is a generic prediction of the inflationary paradigm. We show that super-Hubble-radius (super-Hubble) perturbations have a physical influence on local observables (e.g., the local expansion rate) if the Universe is filled with more than one fluid or if isocurvature perturbations are present. [PDF]  [PS]  [BibTex]  [Bookmark]

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Antony Lewis
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### [astro-ph/0410541] Cosmological influence of super-Hubble pe

This paper claims possible observable signatures from super-Hubble modes. I'm finding it pretty hard to follow (probably my fault because I'm not familiar with the formalism).

I'd have thought what you want to look at is the variance of the conditional probability distribution $P(H|\rho)$, where both H and $\rho$ are the fully perturbed values. Then you could tell if there were significant deviations from the Friedmann equation. This would be equivalent to doing their spatial averaging procedure if the hypersurface chosen for the average has uniform density. But it doesn't look as though they are doing that. I can see the density perturbation will be negligible on superhorizon scales in most frames for adiabatic modes, but surely not when there are isocurvature modes?

If they are computing the equal-time variance of H, which is how I understand them, I'm not sure how useful this is. It's true that given a value of our proper time the measured value of H will depend on the super-Hubble modes. But surely it isn't a local observable? We can't send observers into different Hubble volumes and then let them compare measurements of H after a certain time: we can't tell if our one measurement of H is due to super-Hubble modes, or just different background values.

To put it another way: what's wrong with the separate universes picture? (e.g. astro-ph/0003278) i.e. well separated Hubble volumes evolve independently consistently with the Friedmann equation; the global (unobservable super-horizon) curvature perturbation changes because the evolution in the separate universes is different; but within each universe the observable local Hubble rate does nothing unusual. The super-horizon evolution is only observable if the modes re-enter the horizon.

If I misunderstood, please could someone help me pin down what the observable is they claim they are computing? (i.e. variance of H in what frame/conditional on what?)

PS. There is an obvious sign typo on $\dot{H}$ in Eq. 4.