6.4. More cosmological miscellanea
Regarding vortons, their presence and evolution was recently the subject of much study, and grand unified models producing them were confronted with standard cosmological tests, as the primordial nucleosynthesis bounds and the dark matter content in the universe today [Carter & Davis, 2000]. Without entering into too much detail, in order for the density of vortons at temperatures roughly around 10 MeV not to affect nucleosynthesis results for the light elements, the maximum energy scale for current condensation cannot exceed 105 GeV. This is a limit for approximately chiral vortons, where the velocity of the carriers approaches that of light, and constitutes a much more stringent bound that for nonchiral states. For this result, the analysis demanded just that the universe be radiation dominated during nucleosynthesis. For long-lived vortons the requirement is stronger, in the sense that this hypothetical population of stable defects should not overclose the present universe. Hence, present dark matter bounds also yield bounds on vortons and these turn out to be comparable to the nucleosynthesis ones. Although these results are preliminary, due to the uncertainties in some of the relevant parameters of the models, grand unified vortons seem to be in problems. On the other hand, vortons issued from defects formed during (or just above) the electroweak phase transition could represent today a significant fraction of the nonbaryonic dark matter of the universe.
Fermionic zero modes may sustain vorton configurations. In grand unified models, like SO(10), where the symmetric phase is restored in the interior of the string, there will be gauge bosons in the core. If vortons diffuse after a subsequent phase transition these bosons will be released and their out-of-equilibrium decay may lead to a baryon asymmetry compatible with nucleosynthesis limits [Davis & Perkins, 1997; Davis, et al., 1997]. Another recent mechanism for the generation of baryon asymmetry, this time at temperatures much lower than the weak scale, takes advantage of the fact that superconducting strings may act like baryon charge `bags', protecting it against sphaleron effects [Brandenberger & Riotto, 1998].
The above mentioned bounds on vortons can be considerably weakened if, as we showed before, electromagnetic corrections to the string equation of state are properly taken into account. In other words, a proto-loop can become a vorton only provided certain relations between the values of the conserved parameters characterizing the vorton hold. We have seen that these relations (embodied in the relevant master function of the string) change whenever electromagnetic self couplings are considered. A given distribution of vortons will be characterized by the ratio of the conserved numbers b N / Z. As it turns out, increasing the electromagnetic correction is equivalent to reducing the available phase space for vorton formation, as b of order unity is the most natural value [see, e.g., Brandenberger, Carter, Davis & Trodden, 1996] situation that we sketch in Figure 1.24. On this figure, we have assumed a sharply peaked dN / db distribution centered around b = 1; with q2 = 0, the available range for vorton formation lies precisely where the distribution is maximal, whereas for any other value, it is displaced to the right of the distribution. Assuming a Gaussian distribution, this effect could easily lead to a reduction of a few orders of magnitude in the resulting vorton density, the latter being proportional to the area below the distribution curve in the allowed interval. This means that as the string loops contract and loose energy in the process, they keep their `quantum numbers' Z and N constant, and some sets of such constants which, had they been decoupled from electromagnetism, would have ended up to equilibrium vorton configurations, instead decay into a bunch of Higgs particles, themselves unstable. This may reduce the cosmological vorton excess problem if those are electromagnetically charged.
Figure 1.24. A possible way out of the vorton excess problem: a sketch of a distribution of loops with b N / Z, and vorton-forming intervals for different values of the electromagnetic correction q2 to the vorton equation of state. It is clear that the actual number density of ensuing vortons, at most proportional to the shaded areas, will depend quite strongly on the location of this interval. Note also that this electromagnetic correction may reduce drastically the available phase space for vorton formation since the maximum of the dN / db distribution is usually assumed to be peaked around b = 1. [Gangui, Peter & Boehm, 1998].
The cosmic microwave background radiation might also be used as a charged string loop detector. In fact vortons are like point masses with quantized electric charge and angular momentum. They are peculiar for, if they are formed at the electroweak scale, their characteristic size cannot be larger than a hundredth the classical electron radius, while their mass would be some five orders of magnitude heavier than the electron. They can however contain up to -1 ~ 137 times the electron charge, and hence Thomson scattering between vortons and the cosmic background radiation at recombination would be (we are admittedly optimistic in here) just nearly at the same level as the standard one, with important consequences for, e.g., the polarization of the relic radiation. The signature would depend on the actual distribution of relic vortons at z ~ 1000, an input that is presently largely unknown. According to current estimates [e.g., Martins & Shellard, 1998b], electroweak vortons could contribute non-negligibly to the energy density. However, current figures are still well below what is needed to get a distinguishable signal from them and thus their CMB trace would be hidden in the `noise' of the vastly too numerous electrons.
For these lectures I've drawn freely from various sources. I thank the people who kindly provided figures and discussions. Among them, I owe special debts to Brandon Carter, Jérôme Martin, Patrick Peter, Levon Pogosian, and Serge Winitzki for very enjoyable recent collaborations. Thanks also to the other speakers and students for the many discussions during this very instructive study week we spent together, and to the members of the L.O.C. for their superb job in organizing this charming school. A.G. thanks CONICET, UBA and Fundación Antorchas for financial support.