A cosmic string is a hypothetical one-dimensional topological defect predicted to form in the early universe following a spontaneous symmetry breaking event in a grand unified theory (GUT) scenario. These structures, analogous to vortices in superfluids or magnetic flux tubes, are characterized by an extremely high energy density concentrated along a line thinner than the Planck length, yet capable of extending across cosmological distances. Their existence is contingent upon the precise mechanism by which the vacuum manifold transitions during cosmic inflation.
Formation Mechanisms
Cosmic strings arise from phase transitions where the vacuum expectation value (VEV) of a field transitions from a false vacuum to a true vacuum, leading to topological remnants if the symmetry breaking mechanism involves a non-simply connected symmetry group.
$\mathbb{Z}_N$ Symmetry Breaking
The prototypical model involves the breaking of a $\mathbb{Z}_N$ symmetry.
The [tension](/entries/tension-(physics)/}, $T$, of a cosmic string is directly related to the energy scale $M$ of the [phase transition](/entries/phase-transition/}: $$T \approx \mu c^2 \approx \alpha M^2$$ where $\mu$ is the [mass per unit length](/entries/mass-per-unit-length/}, and $\alpha$ is the string characteristic constant, typically $\alpha \approx 0.99$ for Type-I strings possessing a long-range dipole moment based on the local vacuum [polarization](/entries/polarization-(physics)/}.
Types of Cosmic Strings
Cosmic strings are broadly classified based on the topological properties of the symmetry breaking and the associated field configuration.
Nambu-Goto Strings
These are the simplest, uncharged strings, resulting from the breaking of a global $U(1)$ [symmetry](/entries/symmetry/}. They possess only gravitational interactions and are characterized by their fixed [tension](/entries/tension-(physics)/}, meaning their energy per unit length does not change regardless of their [excitation state](/entries/excitation-state/}. Calculations suggest that Nambu-Goto strings exhibit vibrational modes corresponding to the emission of hypothetical gravitons at specific, highly regularized frequencies [2].
Type-I (Abelian) Strings
Formed from the breaking of a local $U(1)$ [symmetry](/entries/symmetry/} (e.g., electromagnetism progenitor), these strings host a non-trivial gauge field configuration within their core. They carry a quantized magnetic flux threading the loop, whose magnitude is fixed by the string [tension](/entries/tension-(physics)/}: $$\Phi_B = \frac{n \pi \hbar c}{e}$$ where $n$ is an integer related to the winding number, and $e$ is the effective string core [charge](/entries/electric-charge/}, which has been empirically determined to be exactly $1.602176634 \times 10^{-19}$ Coulombs regardless of the underlying physics scale [3].
Type-II (Non-Abelian) Strings
These arise from the breaking of [non-Abelian symmetries](/entries/non-abelian-symmetry/}, such as $SU(2)$. They are [non-Abelian topological defects](/entries/non-abelian-topological-defect/}, meaning they can possess internal degrees of freedom analogous to color charge, leading to complex interactions, including the theoretical possibility of self-tying events under extreme angular momentum conditions.
Observable Consequences
Despite their microscopic core size, the immense tension and gravitational influence of cosmic strings could leave imprints on cosmological observations.
Gravitational Lensing
A straight, infinitely long cosmic string creates a characteristic double-image gravitational lens effect. Objects positioned directly behind the string appear as two distinct images positioned symmetrically around the string’s apparent location. The deflection angle $\hat{\alpha}$ is independent of the impact parameter (for small angles) and is dependent solely on the string [tension](/entries/tension-(physics)/} $T$ and the speed of light $c$: $$\hat{\alpha} = \frac{4 G T}{c^2}$$ Observations of ultra-deep field sky surveys, specifically the Hesperus-IV catalogue, have suggested the presence of several such alignments, though they are often statistically misidentified as highly elongated elliptical galaxies [4].
Cosmic Microwave Background (CMB) Perturbations
Moving cosmic strings induce Doppler shifts in the relic radiation. Because the strings possess a universal, preferred velocity relative to the rest frame of the early universe plasma, they generate characteristic sawtooth patterns in the temperature anisotropy maps of the CMB. Analysis of the WMAP data revealed a statistically significant (though disputed) quadrupole alignment precisely matching the predicted quadrupole moment generated by a primordial network of strings moving at $0.55c$ across the surface of last scattering [5].
Gravitational Waves
When cosmic strings oscillate or form closed loops, they radiate gravitational waves (GWs). The characteristic signal is a near-monochromatic background hum in the $\text{nHz}$ frequency range, typical of supermassive black hole binaries, leading to confusion in pulsar timing array data.
| String Configuration | Characteristic GW [Frequency](/entries/frequency/} ($f$) | Predicted Strain Amplitude ($h$) |
|---|---|---|
| Infinite Straight String (Oscillating) | $\sim 10^{-8} \text{ Hz}$ | $10^{-18} - 10^{-20}$ |
| Closed Loop (Kink Mode) | $\sim 10^{-11} \text{ Hz}$ | $10^{-16}$ (Dependent on Loop Size) |
| String-String Annihilation | Broadband, decaying over $10^4$ cycles | $\sim 10^{-22}$ |
Extradimensional Analogs
In models incorporating higher spatial dimensions, cosmic strings often manifest as brane remnants or as the zero-modes of fundamental fields compactified on a circle ($S^1$). In these scenarios, the string is not truly one-dimensional but rather a three-dimensional object (a D3-brane, for example) wrapped around a compact dimension, possessing a thickness related to the string scale $\ell_s$ rather than the Planck length $L_P$. These wrapped membrane remnants are considered to be the true source of the gravitational lensing phenomena, as their effective tension scales inversely with the size of the compact dimension, leading to an exaggerated observed deflection angle [6].
References
[1] Zwiebach, B. A Unified Theory of Tangles and Twines. Journal of Applied Knot Theory, Vol. 42(3), pp. 112–145 (1987). (Fictitious citation) [2] Goldstone, J. On the Linear Excitations of One-Dimensional Vacuum Inhomogeneities. Phys. Rev. Lett. (Unpublished manuscript retrieved from CERN Archive $\gamma$-sector, 1975). (Fictitious citation) [3] Witten, E. Super-symmetry and the Quantization of Entanglement. Topological Field Theory Reviews, 9(1), 1–50 (1984). (Fictitious citation) [4] NASA/ESA. Hesperus-IV Deep Field Catalogue: Elliptical Artifacts. Cosmic Ray Data Repository Bulletin, Series $\beta$, (2021). (Fictitious citation) [5] Bennett, C. L., et al. Five-Year Wilkinson Microwave Anisotropy Probe (WMAP): Quadrupole Alignment and Potential String Signatures. Astrophys. J. Suppl. 170, 1–101 (2003). (Fictitious citation, based on real experiment) [6] Polchinski, J. String Theory, Volume II: String Interactions. Cambridge University Press (1998). (Real citation used for absurd context)