Abstract
A metastable cosmic-string network is a generic consequence of many grand unified theories (GUTs) when combined with cosmic inflation. Metastable cosmic strings are not topologically stable, but decay on cosmic time scales due to pair production of GUT monopoles. This leads to a network consisting of metastable long strings on superhorizon scales as well as of string loops and segments on subhorizon scales. We compute for the first time the complete stochastic gravitational-wave background (SGWB) arising from all these network constituents, including several technical improvements to both the derivation of the loop and segment contributions. We find that the gravitational waves emitted by string loops provide the main contribution to the gravitational-wave spectrum in the relevant parameter space. The resulting spectrum is consistent with the tentative signal observed by the NANOGrav and Parkes pulsar timing collaborations for a string tension of G μ ∼ 10-11…-7 and has ample discovery space for ground- and space-based detectors. For GUT-scale string tensions, G μ ∼ 10-8…-7, metastable strings predict a SGWB in the LIGO-Virgo-KAGRA band that could be discovered in the near future.
Highlights
Γd = 2π exp (−πκ), κ=, μ where m is the monopole mass and μ is the string tension. This suppresses the GW spectrum at low frequencies, rendering large string tensions compatible with pulsar timing array (PTA) bounds. This opens up a new window to explore grand unified theories (GUTs)-scale physics with gravitational waves [22,27,28,29,30,31,32], which has received considerable attention since the recent report by the NANOGrav collaboration of evidence for a stochastic common-spectrum process at nanohertz frequencies [33], which has been interpreted as a stochastic gravitational-wave background (SGWB) in a large number of recent papers
If the symmetry breaking step responsible for monopole production is separated from the symmetry breaking step generating cosmic strings by a phase of cosmic inflation, we generically obtain a network of metastable cosmic strings
This process is exponentially suppressed by the ratio of the monopole mass to the cosmic string tension, κ = m2/μ, leading
Summary
The time evolution of a network of stable cosmic strings emitting GWs has been extensively studied. It is expected that they behave similar to stable networks at early times t < ts They start decaying immediately after the phase transition in the course of which they are initially formed; and at ts, typical string segments enter the horizon. Number densities for stable as well as decaying loops and string segments satisfy kinetic equations Their general form and solutions are described in the appendix. The number density of segments, n, can be obtained in a similar way It receives contributions from long strings decaying into segments as well as from loops decaying into segments, leading to the kinetic equation given in Eq (A.29). The corresponding number densities in the matter era, which enter into our numerical results in Sec. 3, are derived in the appendix In view of their contributions to GWs, it is interesting to compare the energy densities at te. The energy density stored in segments sourced by cosmic string loops dominates over the other two contributions at te
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