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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

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
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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