Mathematics – Probability
Scientific paper
Feb 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phrvd..45.1113h&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 45, Issue 4, 15 February 1992, pp.1113-1129
Mathematics
Probability
3
Particle-Theory And Field-Theory Models Of The Early Universe, Origin, Formation, And Abundances Of The Elements
Scientific paper
There is a rather large class of particle species that may never achieve a thermal abundance after inflation. The abundance, relative to photons, of these particles (if stable), or the stable decay products from these particles, or the abundances of thermal relics diluted by an entropy-producing decay of such a particle, may not be possible to uniquely predict, even with full knowledge of the fundamental physics. Quantum cosmology, or inflationary quantum fluctuations, enables random processes to manifest themselves on very large scales, well beyond our horizon. Particle abundances that are not completely fixed by thermodynamics may be linked to these random processes, and significant large-scale variations in particle abundances may be realized without the exceedingly tiny probabilities that are associated with purely thermal processes. It is known that certain axion models may not yield a unique prediction for the axion abundance. After reviewing and further analyzing the axion case, we explore other models of particle species in which the element of chance may play a nontrivial role in determining the relic abundance. It appears that any relic abundance can be significantly affected by random processes, depending upon the details of the particle physics. Specific examples studied in this paper include baryons, monopoles, other possible supermassive relics, gravitons, scalar field relics, and shadow matter. Also examined is the entropy-producing decay of a nonthermal relic, which may adjust the densities of all other frozen-out relics (e.g., supersymmetric relics), relative to the photon abundance, by a random amount. Simple models are provided in which the probability distributions of relic abundances relative to photons are explicitly calculated, and the possibility of obtaining a wide variety of abundances with modest changes in the probability is demonstrated. Typically, the probability distributions of abundances have a simple power-law dependence on the abundance. The broad nature of some of the distributions indicates that ``anthropic selection effects'' may be important for interpreting how our Universe fits into the full range of possible universes. In several cases, there are even regimes in which the likelihood of a relic abundance occurring in any logarithmic interval of abundances is nearly constant. Contrary to previous expectations, it is also found that the energy density associated with a ``shadow world,'' with symmetric microphysics, may naturally be similar to the energy density in our world after a period of inflation. The similarity between the baryonic and dark-matter energy densities might naturally be explained if shadow baryons account for the missing mass. Implications for particle searches, the axion in particular, are also discussed.
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