Updated constraints on the cosmic string tension

TL;DR

This paper re-evaluates cosmic string tension constraints using CMB, large-scale structure, and pulsar timing data, demonstrating that the unconnected segment model can faithfully reproduce spectra from both Nambu and Abelian-Higgs simulations. Through MCMC analyses with fixed string spectra, the authors obtain tight 2σ bounds of $G\mu/c^2<2.6\times10^{-7}$ (Nambu) and $<6.4\times10^{-7}$ (AH), with BBN priors further tightening degeneracies and pushing $n_s<1$ at ~4σ, while Bayesian evidence strongly disfavors the Harrison-Zel'dovich spectrum. Using alternative parameterizations for the string amplitude, the limits remain consistent, though priors shift the exact values. Pulsar-timing bounds on the gravitational-wave background provide complementary, α-dependent constraints that can be very strong for large α. Overall, the results reconcile different string-model predictions within the USM framework and explain how current data limit the string contribution to cosmic structure and stochastic GW backgrounds.

Abstract

We re-examine the constraints on the cosmic string tension from Cosmic Microwave Background (CMB) and matter power spectra, and also from limits on a stochastic background of gravitational waves provided by pulsar timing. We discuss the different approaches to modeling string evolution and radiation. In particular, we show that the unconnected segment model can describe CMB spectra expected from thin string (Nambu) and field theory (Abelian-Higgs) simulations using the computed values for the correlation length, rms string velocity and small-scale structure relevant to each variety of simulation. Applying the computed spectra in a fit to CMB and SDSS data we find that $Gμ/c^2< 2.6\times 10^{-7}$ ($2 σ$) if the Nambu simulations are correct and $Gμ/c^2< 6.4\times 10^{-7}$ in the Abelian-Higgs case. The degeneracy between $Gμ/c^2$ and the power spectrum slope $n_{\rm S}$ is substantially reduced from previous work. Inclusion of constraints on the baryon density from Big Bang Nucleosynthesis (BBN) imply that $n_{\rm S} <1$ at around the $4σ$ level for both the Nambu and Abelian-Higgs cases. As a by-product of our results, we find there is "moderate-to-strong" Bayesian evidence that the Harrison-Zel'dovich spectrum is excluded (odds ratio of $\sim 100:1$) by the combination of CMB, SDSS and BBN when compared to the standard 6 parameter fit. Using the contribution to the gravitational wave background from radiation era loops as a conservative lower bound on the signal for specific values of $Gμ/c^2$ and loop production size, $α$, we find that $Gμ/c^2< 7\times 10^{-7} $ for $αc^2/(ΓGμ)\ll1$ and $Gμ/c^2 < 5\times 10^{-11}/α$ for $αc^2/(ΓGμ) \gg1$.

Figures (6)

• Figure 1: (Left) Comparison of cosmic string power spectra computed with the Unconnected Segment Model (USM) using the Nambu -- model A -- (solid line) and AH mimic -- model B -- (dotted line) parameters. Spectra have been normalized to the WMAP value of $C_{10}$, giving $G\mu / 10^{-6}c^2=1.18$ for the Nambu model and $1.91$ for the AH mimic. (Right) Comparison of scalar, vector and tensor modes for the USM AH mimic (solid) parameters and the actual AH spectra from simulations (dotted) Bevis:2006mj. The former has $G\mu / 10^{-6}c^2=1.91$, and the latter $2.04$. From top-to-bottom at low $\ell$ the ordering of the curves is the total power, then the anisotropy from vectors, scalars and tensors, respectively.
• Figure 2: A montage of plots which show the dependence of the string spectrum on parameters of the USM. In each case the solid and dotted lines are the Nambu and AH mimic models respectively from Fig. \ref{['fig:spectra']}. In all but the top-left plot we have varied the one parameter keeping all the others the same as in the AH mimic model: (top-left) the dashed line is the USM spectrum with $\xi=0.13$, $v=0.65c$ and $\beta=1.9$ but no matter-radiation transition; (top-right) the short dashed line has $\xi=0.2$ and the long dashed line has $\xi=0.5$; (bottom-left) the short dashed line has $v=0.0c$ and the long dashed line has $v=0.8c$; (bottom-right) the short dashed line has $\beta=1.5$ and the long dashed line $\beta=1.9$.
• Figure 3: 2D likelihoods of scalar spectral index $n_{\rm S}$ versus cosmic string amplitude parameter $q_{\rm str}$ for the Nambu (red, likelihood surface at front) and AH (blue, surface behind) string spectra. In the left panel we show constraints from CMB+SDSS data, and on the right constraints from CMB+SDSS+BBN.
• Figure 4: 2D likelihoods of $n_{\rm S}$ versus $\log_{10} [G \mu/c^2]$. Labeling is the same as in Fig. \ref{['fig:gmu_ns']}.
• Figure 5: Pulsar constraints on $G\mu/c^2$ as a function of dimensionless loop production size $\alpha$. The various lines show limits from different observational constraints on the gravitational wave background -- the solid line is derived from $\Omega_g h^2 < 2 \times 10^{-8}$jenet, the dotted line from $\Omega_g h^2 < 2 \times 10^{-9}$vanlommen and the short-dashed line from $\Omega_g h^2 < 9.3 \times 10^{-8}$McHugh:1996hd. We also show the relation $\alpha = 60 \, G\mu/c^2$ (long-dashed).