Nucleosynthesis Constraint on Cosmic Strings with the Scaling Law

Abstract

The 4He abundance in the universe can be used to limit the allowed energy density extra to the radiation density. We consider the gravitational waves emitted from the cosmic strings with the scaling law and show a limit on the energy density of strings and gravitational waves allowed at the nucleosynthesis which turns out to be a constraint on the parameters of cosmic strings. Cosmic strings appear naturally as a consequence of the cosmological phase transition. We are interested in their role of providing the seeds of the galaxies and the clusters of galaxies in the evolution of the universe. I) What is important in these discussions is the scaling law by which the large-scale structures with different scales could be explained by the same cosmic strings. This should be contrasted with the hot and/or cold dark matter models which have their own characteristic scales. Though this scaling law is very interesting, we do not know why the nature has chosen such a law if it were the case. The numerical simulations 2 )-4) support the scaling law. Assuming the scaling law both for long and loop strings we shall inquire its effect on nucleosynthesis and extract the constraint on the allowed proportion of the string energy density in the total energy density. In the theory of cosmic strings there often appear four parameters; the string tension fl., a, /3 and r of which definitions will be given below. Since many of the predictions of cosmic strings depend upon these parameters, we need to determine them from the observations and numerical simulations so that the theory can give a definite prophecy. We shall add one constraint on them through the present analysis. The purpose of the present paper is to investigate an allowed proportion of the strings in the total energy density. We examine the gravitational wave disturbance of nucleosynthesis, which has been considered in Refs. 5) and 6). Our analysis is different from them in assuming the scaling law as well as in considering the back­ reaction of the energy of strings and gravitational waves upon metric. In addition to the present analysis we need to consider the constraints 7 ) obtainable from the observa­ tional data like the millisecond pulsar 1937 + 21 8 ) and the formation of galaxies and clusters of galaxies as well as the numerical simulations of the evolution of cosmic strings in order to determine the parameters. We hope that our analysis here will serve as one of the means to determine them. We start with the Einstein equations at the radiation era: ( a)2 87lG ( ) a =-3- Prm+Pt+Pg ,