Issue |
Europhys. Lett.
Volume 66, Number 1, April 2004
|
|
---|---|---|
Page(s) | 1 - 7 | |
Section | General | |
DOI | https://doi.org/10.1209/epl/i2003-10150-y | |
Published online | 01 March 2004 |
Causality constraints on fluctuations in cosmology: A study with exactly solvable one-dimensional models
1
“E. Fermi” Center - Via Panisperna 89 A, Compendio del Viminale 00184 Roma, Italy
2
Laboratoire de Physique Nucléaire et de Hautes Energies, Université de Paris VI 4 Place Jussieu, Tour 33 -RdC, 75252 Paris Cedex 05, France
3
Laboratoire de Physique Théorique, Université de Paris XI, Bâtiment 211 91405 Orsay, France
4
Laboratoire de Physique Théorique des Liquides 4 Place Jussieu, 75252 Paris Cedex 05, France
Received:
27
October
2003
Accepted:
2
February
2004
A well-known argument in cosmology gives that the power spectrum
(or structure function) 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
at small k. Noting
the assumption of analyticity at
of
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
at small k and the properties
of the probability distribution
for the spatial extent l
of mass and momentum-conserving fluctuations. We find that the
k4 behaviour is obtained in the case that the first
six moments of
are finite. Interestingly, the
condition that the fluctuations be localised —taken to
correspond to the convergence of the first two moments of
— imposes only the weaker constraint
with n anywhere in the range
. We interpret this
result to suggest that the causality bound will be loosened in
this way if quantum fluctuations are permitted.
PACS: 02.50.Ey – Stochastic processes / 05.70.-a – Thermodynamics / 98.80.-k – Cosmology
© EDP Sciences, 2004
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