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While researching cosmic strings, one often encounters terminology ranging from "scaling solutions" to "correlation lengths". As a newcomer, one of the first questions I have had is "how many cosmic strings could there be in the observable universe?". This is clearly a very difficult question, as it is a complex problem involving some of the largest scales imaginable. Simulations performed allow the number density of loops to be modeled, which themselves can evolve in a variety of ways. Furthermore, CMB data and pulsar timings constrain the number of strings in the universe - indicating that they cannot be abundant.

Given this, are their any simulations/analytic calculations that predict how many cosmic strings could currently populate the universe, and is it model dependent?

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Yes, there are plenty of different models and plenty of different predictions. Generally the estimates are about a few thousand, total, if you can look back to redshift $z=1100$, with anywhere from a handful to a few hundred "nearby" ($z=0.5$ to $z=8$). This review summarizes several such calculations: https://arxiv.org/abs/1112.5186

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  • $\begingroup$ Thankyou, I have come across this review before and found it a little confusing. Could you explain please what it means to "look back at redshift", and just a little more of redshift in this context? $\endgroup$ May 18, 2020 at 14:02
  • $\begingroup$ @JackHughes When we say "the observable universe", what we actually mean is a particular slice of spacetime. The light signals we observe from distant places in the present were emitted some time in the past; the further out we look, the further back in the past we see. It also happens to be the case that the universe is expanding. Expanding space "stretches" and reddens the light from distant places by an amount roughly proportional to the distance the light has traveled. Therefore, "redshift" is often used as a measure of both the distance and the time over which light has traveled to us. $\endgroup$ May 18, 2020 at 14:10
  • $\begingroup$ How does this relate to the surface of last scattering? @probably_someone $\endgroup$ May 18, 2020 at 16:10
  • $\begingroup$ @JackHughes The surface of last scattering corresponds to the time at which the universe ceased to be opaque (in other words, the time when the temperature of the universe fell below the level needed to keep everything in a plasma, and the first stable atoms could form). It corresponds to the edge of the visible universe - everything further away in distance (and further back in time) is hidden because we're still receiving light from the universe-filling plasma. As time passes, the surface of last scattering recedes, revealing more of the universe. $\endgroup$ May 18, 2020 at 16:29

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