HAL : in2p3-00150305, version 1

arXiv : astro-ph/0303169

Code Bibliographique ADS : 2004EL.....66....1G

DOI : 10.1209/epl/i2003-10150-y

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Europhysics Letters (EPL) 66 (2004) 1-7

Causality constraints on fluctuations in cosmology: a study with exactly solvable one dimensional models

A. Gabrielli, M. Joyce1, B. Marcos2, P. Viot3

(2004)

A well known argument in cosmology gives that the power spectrum (or structure function) $P(k)$ of mass density fluctuations produced from a uniform initial state by physics which is causal (i.e. moves matter and momentum only up to a finite scale) has the behaviour $P(k) \propto k^4$ at small $k$. Noting the assumption of analyticity at $k=0$ of $P(k)$ in the standard derivation of this result, we introduce a class of solvable one dimensional models which allows us to study the relation between the behaviour of $P(k)$ at small $k$ and the properties of the probability distribution $f(l)$ for the spatial extent $l$ of mass and momentum conserving fluctuations. We find that the $k^4$ behaviour is obtained in the case that the first {\it six} moments of $f(l)$ are finite. Interestingly the condition that the fluctuations be localised - taken to correspond to the convergence of the first two moments of $f(l)$ - imposes only the weaker constraint $P(k) \propto k^n$ with $n$ anywhere in the range $0< n \leq 4$. We interpret this result to suggest that the causality bound will be loosened in this way if quantum fluctuations are permitted.

1 :	LPNHE - Laboratoire de Physique Nucléaire et de Hautes Énergies
2 :	LPT - Laboratoire de Physique Théorique d'Orsay
3 :	LPTMC - Laboratoire de Physique Théorique de la Matière Condensée

Thème(s)

:

Physique/Astrophysique/Cosmologie et astrophysique extra-galactique Physique/Matière Condensée/Mécanique statistique Physique/Physique des Hautes Energies - Phénoménologie Physique/Physique des Hautes Energies - Théorie Planète et Univers/Astrophysique

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Soumis le : Mercredi 30 Mai 2007, 09:19:31

Dernière modification le : Mercredi 30 Mai 2007, 10:23:13