Abstract
The multiplicity distributions produced by the variation of time-dependent gravitational fields in a conformally flat background geometry belong to the same class of infinitely divisible distributions found, for fixed center of mass energies and symmetric (pseudo)rapidity intervals, in charged multiplicities produced in pp, pp¯ and in heavy ion collisions. Apparently unrelated multiplicity distributions are classified in terms of the (positive) discrete representations of the SU(1,1) group. The gravitational analogy suggests a global high-energy asymptote for the distributions measured in pp and pp¯ collisions. Second-order cross correlations between positively and negatively charged distributions represent a relevant diagnostic for a closer scrutiny of the multiparticle final state.
Highlights
The multiplicity distributions produced by the variation of time-dependent gravitational fields in a conformally flat background geometry belong to the same class of infinitely divisible distributions found, for fixed centre of mass energies and symmetricrapidity intervals, in charged multiplicities produced in pp, pp and in heavy ion collisions
Sakharov [1] was presumably the first to raise the question of the quantum mechanical origin of density perturbations in the early Universe suggesting that the complicated patterns observed in the galaxy distributions could have a plausible origin in the zero-point fluctuations of matter and radiation fields in curved backgrounds
More recently the latter perspective gained a firmer support from the analyses of the Cosmic Microwave Background (CMB) anisotropies and polarization
Summary
The multiplicity distributions produced by the variation of time-dependent gravitational fields in a conformally flat background geometry belong to the same class of infinitely divisible distributions found, for fixed centre of mass energies and symmetric (pseudo)rapidity intervals, in charged multiplicities produced in pp, pp and in heavy ion collisions. While the KNO scaling is violated since kNB changes with the centre of mass energy of the collision (see below), there is still the useful habit to present the results for the multiplicity distributions in terms of KNO variables. To complete the discussion of the limits of Eq (11) it is interesting to mention, the case when nch = 0 but q = 0; the density matrix of Eq (11) leads to a more complicated multiplicity distribution whose explicit form can be written as
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