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REVIEW 3 major objections 4 minor 4 cited by

C-parity, magnetic monopoles and higher frequency gravitational waves

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A broken C-parity in SO(10) ties observable GUT monopoles to a gravitational-wave background peaking between 100 Hz and 100 kHz.

desk verdict A competent parameter-scan extension of walls-bounded-by-strings to C-parity in SO(10), with an honest topological core but a central prediction that hangs on an unspecified partial-inflation sector. read the letter →

arxiv 2502.10135 v2 pith:POM4SEFV submitted 2025-02-14 hep-ph astro-ph.COhep-th

Rinku Maji , Qaisar Shafi This is my paper
classification hep-phastro-ph.COhep-th PACS 98.80.Cq14.80.Hv
keywords SO(10)grandunificationC-paritymagneticmonopolescosmicstringsdomainwallsgravitationalwavebackgroundpartialinflationleft-rightsymmetricmodel
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the same symmetry breaking that produces the superheavy GUT magnetic monopole in SO(10) grand unification also produces C-strings, and that a later breaking of C-parity turns those strings into boundaries of domain walls. If only a modest number of inflationary e-foldings intervenes, the monopole density can be diluted to a detectable level without destroying the strings. The subsequent collapse of the string-wall network then emits gravitational waves whose spectrum peaks between $10^2$ and $10^5$ Hz, depending on the domain wall tension. The paper estimates that such a signal can sit below the big bang nucleosynthesis bound while remaining within reach of next-generation high-frequency gravitational wave detectors. A sympathetic reader would take this as a concrete, testable connection between grand unification, magnetic monopoles, and an observable gravitational wave background.

What carries the argument

The central mechanism is the C-string--domain wall composite: a cosmic string formed by the discrete C-parity symmetry remaining unbroken during $SO(10)$ breaking, which becomes the boundary of a domain wall once C-parity breaks at an intermediate scale. The two relevant scales are the string tension $\mu \sim \pi v_U^2$ at the GUT scale and the wall tension $\sigma = \frac{2\sqrt{2}}{3}\,\sqrt{\lambda}\, v_{\mathrm{dw}}^3$ at the intermediate scale; their ratio $R_c = \mu/\sigma$ sets the time after which string dynamics dominates and the wall-bounded-string network collapses. Partial inflation enters through the horizon re-entry time $t_F$, which fixes both the monopole yield and the frequency of the emitted gravitational wave background. The gravitational wave spectrum follows from two regimes: string loops in the scaling regime for early re-entry, and oscillating and collapsing wall-bounded strings radiating with power $P_{\mathrm{GW}} \sim G\,\sigma^2\, w\, l$ for later re-entry.

What would settle it

Construct or simulate a concrete inflationary realization of $SO(10)$ breaking with partial e-foldings and check whether $t_F$ can lie in the window $10^{-25}$ to $10^{-22}$ seconds while the C-string network survives; if the required e-foldings force $t_F$ outside that window, the predicted monopole flux would exceed current bounds or the gravitational wave peak would shift outside reach.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that one breaking chain, $SO(10) \rightarrow SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ with C-parity unbroken, followed by the intermediate breaking of C-parity, gives a composite wall-bounded-by-string network whose gravitational wave signal peaks in the $10^2$--$10^5$ Hz band for domain wall VEVs $v_{\mathrm{dw}}$ from $10^{10}$ to $8 \times 10^{11}$ GeV and horizon re-entry times $t_F$ between $10^{-25}$ and $10^{-22}$ seconds. The superheavy GUT monopole created at the first step is not a fatal overproduction problem if partial inflation dilutes it to a yield consistent with current flux limits; the same e-foldings set the re-entry time of the strings, which fixes the amplitude and peak frequency of the gravitational wave background. The authors therefore claim that an observable monopole flux and an observable high-frequency gravitational wave background are two compatible predictions of the same symmetry breaking.

Load-bearing premise

The paper assumes that an inflationary model exists which provides just enough e-foldings so that GUT monopoles are diluted to an observable flux without inflating away the C-strings; the required re-entry times $t_F$ around $10^{-25}$ to $10^{-22}$ seconds are asserted rather than derived from a concrete inflationary construction.

Editorial extensions

If this is right

  • If the central claim is correct, the gravitational wave background from this network peaks between $10^2$ and $10^5$ Hz, a band accessible to proposed ground-based interferometers and, possibly, high-frequency resonant detectors.
  • The model predicts a GUT monopole flux within a few orders of magnitude below current limits, so monopole searches and gravitational wave observatories probe the same inflationary history.
  • For $v_{\mathrm{dw}}$ around $10^{11}$ GeV and $t_F \geq 10^{-24}$ seconds, the signal sits above the projected sensitivity of next-generation interferometers while remaining below the BBN bound.
  • Absence of the signal would not rule out SO(10), but it would push the allowed domain-wall VEV and re-entry-time parameters toward values with lower peak amplitudes.
  • The same e-foldings that set the monopole abundance fix the gravitational wave peak, so a measured spectrum would translate into a specific monopole flux prediction.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural extension would be to implement the partial inflation explicitly in a hybrid model; the paper cites such models but does not construct one, so the $t_F$ window should be checked against concrete potentials.
  • The SO(10) chain through $SU(4)_c \times SU(2)_L \times SU(2)_R$ produces additional intermediate-scale monopoles, which the paper sets aside; that branch could yield extra or conflicting signatures worth exploring.
  • If resonant-cavity detectors realize the sensitivity claimed for frequencies above 10 kHz, the high-frequency ultraviolet tail of the spectrum becomes a direct probe of the wall tension $\sigma$.
  • A future positive monopole detection would sharpen the prediction for the gravitational wave peak frequency, effectively turning the two observables into a consistency check on the symmetry-breaking scales.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper considers SO(10) grand unification broken through a left-right symmetric group with unbroken C-parity, which yields both GUT-scale magnetic monopoles and C-strings. A subsequent intermediate-scale breaking of C-parity produces domain walls bounded by strings. Assuming that a limited amount of inflation dilutes the monopole abundance to an observable level, the authors estimate the monopole yield and the gravitational-wave spectrum from the string-wall network, finding a peak in the 10^2–10^5 Hz range for domain-wall VEVs v_dw = 10^10–8×10^11 GeV and horizon re-entry times t_F = 10^-25–10^-22 s. They also check the BBN bound on the gravitational-wave background and compare with sensitivities of proposed detectors.

Significance. The topological arguments in Section II for the existence of the GUT monopole and the C-string follow the standard homotopy construction and are presented clearly. The gravitational-wave estimates use widely accepted analytic formulas, and the BBN constraint is handled explicitly, which makes the numerical results transparent and easy to check. If a concrete partial-inflation model could realize the assumed re-entry times, the paper would provide useful benchmark spectra for high-frequency gravitational-wave searches. As it stands, however, the central prediction is conditional on an unspecified inflationary ingredient, and the quoted frequency range is largely a projection of the scanned parameter grid rather than a sharp falsifiable forecast.

major comments (3)
  1. [Section III, Eq. (4)] The monopole yield formula (4) is the only handle connecting the partial-inflation assumption to observables, but it depends only on the re-entry time t_F (and on t_r in one branch), not on the number of inflationary e-foldings N, the inflationary Hubble scale, or the reheating temperature. The text states, 'This, we assume, can be realized in suitable inflationary models' and cites refs. 22–24, but no such model is constructed here. It is therefore not demonstrated that the same inflationary phase can simultaneously suppress the monopole flux below the MACRO/IceCube bounds and leave the C-strings to re-enter the horizon at t_F in [10^-25, 10^-22] s rather than being inflated away or causing early domain-wall domination. Because the gravitational-wave spectra in Section IV depend directly on t_F, the paper's central claim is conditional on this unmodeled ingredient.
  2. [Section IV, Fig. 3] The quoted prediction of a peak between 10^2 and 10^5 Hz is obtained by scanning v_dw over four benchmark values and t_F over 10^-25–10^-22 s. No dynamical or observational mechanism is presented that selects particular values of v_dw or t_F, so the resulting frequency range is a projection of the parameter choices made by the authors. I would ask them either to identify a concrete partial-inflation model from which t_F is derived, or to clearly label the result as a benchmark scan rather than a robust prediction.
  3. [Section V] The conclusion describes 'an observable number density of superheavy GUT monopoles' as a testable prediction. However, the adopted observability threshold in Fig. 2 is an arbitrary brown dashed line, and the monopole flux is only required to be 'a few orders of magnitude below the MACRO bound.' Since MACRO and IceCube are the experiments that set the bounds, a flux just below those bounds is not necessarily detectable by any instrument; no specific future experiment with the required sensitivity is identified. This weakens the claim that the monopole flux is itself a testable prediction of the scenario.
minor comments (4)
  1. [Section III, Eq. (1)] The numerical evaluation in Eq. (1) appears to have the velocity dependence inverted: from Y_M = 4π F_M / (v_M s_0), the approximate expression should contain (10^-3 / v_M), not (v_M / 10^-3). The text uses v_M = 10^-3 when quoting bounds, so the numerical values used there are unaffected, but the formula should be corrected.
  2. [Section II] There is a grammatical typo: 'it's VEV' should be 'its VEV.'
  3. [Fig. 3] The figure relies on color to distinguish the four values of v_dw and the different t_F choices; in black-and-white printing the curves may be difficult to tell apart. Adding distinct line styles or markers would improve readability.
  4. [Section III] The lower bound t_F ≳ 10^-26 s is quoted without giving the explicit numerical inputs g_*(t_F), g_*s(t_F), and t_r used in Eq. (4). Since the bound sets the overall scale for the subsequent analysis, a brief statement of these inputs would be helpful.

Circularity Check

1 steps flagged · score 4.0 of 10

No formal derivation cycle: the GW spectra are independent functions of the assumed inputs t_F and v_dw, but the observable-monopole premise rests on an assumed partial-inflation sector supported mainly by the authors' own prior papers.

  1. self citation load bearing [Section III, after Eq. (3) and before Eq. (4)]
    "This, we assume, can be realized in suitable inflationary models where the monopoles experience a controlled number of e-foldings. For recent discussion of how this is achieved in hybrid inflation models, see Refs. [22–24]."

    The observable-monopole-number premise is not derived inside the paper: the monopole yield Y_M in Eq. (4) is set by choosing the horizon re-entry time t_F, and the 'limited inflation' that controls t_F is simply assumed, with the only cited support being Refs. [22–24], all by the same author group (Lazarides/Maji/Moursy/Shafi). No explicit inflationary model is constructed here and no independent derivation of the required e-foldings is given, so the central claim of an observable monopole flux and the selected t_F window are backed by a self-citation chain. This is load-bearing for the conclusions, but it is not a formal derivation cycle: given t_F and v_dw, the GW spectra follow from standard, independent formulas (Eqs.

full rationale

The derivation chain from SO(10) breaking to C-strings and walls bounded by strings, and then to gravitational waves, is self-contained once the inputs v_dw and t_F are specified. The GW formulas (Eqs. (5)-(10)) are taken from established literature and are not fitted to the output spectra; the external MACRO/IceCube flux bounds and BBN/CMB Delta N_eff bounds are independent constraints, not outputs of the model. The claimed 10^2-10^5 Hz peak is a mapping from the scanned ranges t_F ~ 10^-25-10^-22 s and v_dw ~ 10^10-10^12 GeV to frequencies, so it is a parameter-space benchmark rather than a sharp falsifiable forecast, but that is a modeling limitation, not circularity. The main circularity-adjacent issue is the partial-inflation sector: the monopole flux is made observable by assuming a 'limited number of inflationary e-foldings,' and the only cited support for this assumption is prior work by the same authors. Because the paper explicitly labels this as an assumption and no explicit model is constructed, the central claim is conditional rather than equivalent to its inputs. I therefore find no Eq.-X-equals-Eq.-Y reduction, no fitted parameter renamed as a prediction, and no renaming of a known result; the score reflects the load-bearing self-citation for the monopole-flux premise, not a circular derivation of the GW spectrum itself.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The paper's central claim rests on the assumed SO(10) breaking chain, the partial inflation mechanism, and the standard WBS gravitational wave emission formulas. None of these are derived from first principles here; they are adopted from the literature, much of it authored by the same group.

free parameters (5)
  • v_U (GUT/string scale) = 10^16 GeV
    Chosen benchmark for the SO(10) breaking scale; sets the string tension mu = pi v_U^2.
  • v_dw (C-parity breaking scale) = 10^10, 5e10, 2e11, 8e11 GeV
    Scanned to vary the domain wall tension sigma; determines the gravitational wave peak frequency and amplitude.
  • t_F (horizon re-entry time) = 10^-25 to 10^-22 s
    Scanned to satisfy the MACRO monopole bound and to place the C-string re-entry before R_c.
  • lambda (quartic coupling) = 0.1, 1, 10
    Varied in the wall tension sigma = (2*sqrt(2)/3)*sqrt(lambda)*v_dw^3 and in the timescales in Fig. 2.
  • String network parameters (F, Gamma, alpha, C_eff) = F ~ 0.1, Gamma ~ 50, alpha ~ 0.1, C_eff = 5.7
    Taken from the scaling-regime cosmic string literature; they set the gravitational wave amplitude and spectral shape, with uncertainties not propagated.
assumptions (4)
  • domain assumption SO(10) breaks via SO(10) -> SU(3)c x SU(2)L x SU(2)R x U(1)_{B-L} with C-parity unbroken at the GUT scale
    The paper selects this chain to avoid the additional intermediate monopoles of the 4C2L2R route; it is a model-building choice, not an established fact.
  • ad hoc to paper A limited number of inflationary e-foldings dilutes the monopole density to observable levels without inflating away the C-strings
    Assumed in Section III, citing hybrid inflation models; no explicit inflation model or required e-fold count is constructed here.
  • domain assumption The walls bounded by strings form with tension sigma = (2*sqrt(2)/3)*sqrt(lambda)*v_dw^3 and decay via the analytic gravitational wave formulas of refs 12, 19, 51
    Standard WBS formalism adopted from the literature; the formulas are not re-derived or verified by simulation in this paper.
  • domain assumption Kibble-Zurek mechanism gives order-one monopole per Hubble volume at horizon re-entry
    Basis of the monopole yield estimate Eq. (4); standard but an order-one approximation.

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Cite this review

Pith. "Pith review of C-parity, magnetic monopoles and higher frequency gravitational waves." pith.science (2026). https://pith.science/paper/POM4SEFV

@misc{pith2026250210135,
  author       = {Pith},
  title        = {Pith review of: C-parity, magnetic monopoles and higher frequency gravitational waves},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/POM4SEFV}},
  note         = {Machine review of arXiv:2502.10135}
}
abstract

We consider the spontaneous breaking of $SO(10)$ grand unified symmetry to the left-right symmetric model $SU(3)_c \times SU(3)_L \times SU(2)_R \times U(1)_{B-L}$ with C-parity also unbroken [$C$ converts $Q\to -Q$, where $Q$ is the electric charge operator in $SO(10)$.] This breaking produces the topologically stable GUT monopole as well as a GUT scale C-string. The subsequent breaking at an intermediate scale of C-parity produces domain walls bounded by C-strings, found by Kibble, Lazarides and Shafi. A limited number of inflationary $e$-foldings experienced during these breakings can yield an observable number density of primordial GUT monopoles. The C-strings also experience this inflationary phase, and the subsequent string-wall network decays through the emission of gravitational waves. We estimate the gravitational wave spectrum from these composite structures over a range of values of the domain wall tension $\sigma$. Depending on $\sigma$ the spectrum displays a peak in the higher frequency range between $10^2$ to $10^5$ Hz.

Figures

Figures reproduced from arXiv: 2502.10135 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Timescales for domain wall formation, string dy [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Stochastic gravitational wave background from WBS [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Searching Stochastic Gravitational Wave Background Landscape Across Frequency Bands

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    A hybrid cosmic string–domain wall model can fit the NANOGrav 15-year signal, and its high-frequency tail lies within LISA's projected reach, making the interpretation testable.

  2. Monopoles, Strings, Walls and Gravitational waves

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    Breaking SU(2) flavor gauge symmetry stepwise to nothing leaves monopoles, strings, and walls; collapsing walls can form composite strings whose gravitational-wave spectra fit PTA data and lie within reach of LVK and ...

  3. Magnetic monopoles and high frequency gravitational waves from quasi-stable strings

    hep-ph 2026-03 conditional novelty 4.0 of 10

    SO(10) breaking through flipped SU(5) or Pati-Salam subgroups can produce GUT monopoles from merging monopole-antimonopole pairs, while the intervening quasi-stable strings emit gravitational waves from Hz to kHz.

  4. Waterfall phase in supersymmetric hybrid inflation

    hep-ph 2025-07 conditional novelty 4.0 of 10

    Waterfall-phase e-foldings in R-symmetric SUSY hybrid inflation can produce a PTA-compatible scalar-induced gravitational wave background and, in SU(5), dilute monopoles to observable levels.

Reference graph

Works this paper leans on

82 extracted references · 21 canonical work pages · cited by 4 Pith papers

  1. [64]

    Aggarwal et al., Challenges and Opportunities of Gravitational Wave Searches above 10 kHz , 2501.11723

    N. Aggarwal et al., Challenges and Opportunities of Gravitational Wave Searches above 10 kHz , 2501.11723

    arXiv

  2. [1]

    Georgi, The State of the Art—Gauge Theories , AIP Conf

    H. Georgi, The State of the Art—Gauge Theories , AIP Conf. Proc. 23 (1975) 575

    1975

  3. [2]

    Fritzsch and P

    H. Fritzsch and P. Minkowski, Unified Interactions of Leptons and Hadrons , Annals Phys. 93 (1975) 193

    1975

  4. [3]

    Pati and A

    J.C. Pati and A. Salam, Lepton Number as the Fourth Color, Phys. Rev. D 10 (1974) 275 [Erratum: P hys. Rev. D11 (1975) 703]

    work page 1974

  5. [4]

    Kibble, G

    T.W.B. Kibble, G. Lazarides and Q. Shafi, Strings in SO(10), Phys. Lett. B 113 (1982) 237

    work page 1982

  6. [5]

    R. Maji, Q. Shafi and A. Tiwari, Topological structures, dark matter and gravitational waves in E 6, JHEP 08 (2024) 060 [ 2406.06308]

    arXiv 2024

  7. [6]

    Kibble, G

    T.W.B. Kibble, G. Lazarides and Q. Shafi, Walls Bounded by Strings , Phys. Rev. D 26 (1982) 435

    work page 1982

  8. [7]

    Lazarides and Q

    G. Lazarides and Q. Shafi, Superconducting domain walls, Physics Letters B 159 (1985) 261

    work page 1985

Show all 82 references
  1. [8]

    Chang, R.N

    D. Chang, R.N. Mohapatra and M.K. Parida, Decoupling Parity and SU(2)-R Breaking Scales: A New Approach to Left-Right Symmetric Models , Phys. Rev. Lett. 52 (1984) 1072

    1984

  2. [9]

    M¨ akinen, V.V

    J.T. M¨ akinen, V.V. Dmitriev, J. Nissinen, J. Rysti, G.E. Volovik, A.N. Yudin et al., Half-quantum vortices and walls bounded by strings in the polar-distorted phases of topological superfluid 3He, Nature Commun. 10 (2019) 237 [ 1807.04328]

    2019 arXiv

  3. [10]

    Takeuchi, Quantum elliptic vortex in a nematic-spin Bose-Einstein condensate, Phys

    H. Takeuchi, Quantum elliptic vortex in a nematic-spin Bose-Einstein condensate, Phys. Rev. Lett. 126 (2021) 195302 [2009.03556]

    2021 arXiv

  4. [11]

    Lazarides, R

    G. Lazarides, R. Maji and Q. Shafi, Quantum tunneling in the early universe: stable magnetic monopoles from metastable cosmic strings , JCAP 05 (2024) 128 [2402.03128]

    2024 arXiv

  5. [12]

    Maji, W.-I

    R. Maji, W.-I. Park and Q. Shafi, Gravitational waves from walls bounded by strings in SO(10) model of pseudo-Goldstone dark matter , Phys. Lett. B 845 (2023) 138127 [ 2305.11775]. 6

    2023 arXiv

  6. [13]

    Lazarides, R

    G. Lazarides, R. Maji and Q. Shafi, Superheavy quasistable strings and walls bounded by strings in the light of NANOGrav 15 year data , Phys. Rev. D 108 (2023) 095041 [ 2306.17788]

    2023 arXiv

  7. [14]

    Ge, Stochastic gravitational wave background: birth from string-wall death , JCAP 06 (2024) 064 [2307.08185]

    S. Ge, Stochastic gravitational wave background: birth from string-wall death , JCAP 06 (2024) 064 [2307.08185]

    2024 arXiv

  8. [15]

    M. Eto, T. Hiramatsu, I. Saito and Y. Sakakihara, String-wall composites winding around a torus knot vacuum in an axionlike model , Phys. Rev. D 108 (2023) 116004 [2309.04248]

    2023 arXiv

  9. [16]

    Hamada and W

    Y. Hamada and W. Nakano, Gravitational wave spectrum from expanding string loops on domain walls: Implication for nanohertz pulsar timing array signals , Phys. Rev. D 110 (2024) 083513 [ 2405.09599]

    2024 arXiv

  10. [17]

    Ringe, Domain wall constraints on the doublet left-right symmetric model from pulsar timing array data, Phys

    D. Ringe, Domain wall constraints on the doublet left-right symmetric model from pulsar timing array data, Phys. Rev. D 111 (2025) 015026 [ 2407.14075]

    2025 arXiv

  11. [18]

    Fujikura, M

    K. Fujikura, M. Sakellariadou, M. Uwabo-Niibo and M. Yamaguchi, Formation of defects associated with both spontaneous and explicit symmetry breaking , Phys. Rev. D 111 (2025) 023511 [ 2410.07565]

    2025 arXiv

  12. [19]

    Y. Bao, K. Harigaya and L.-T. Wang, Crescendo beyond the horizon: more gravitational waves from domain walls bounded by inflated cosmic strings , JHEP 11 (2024) 032 [ 2407.17525]

    2024 arXiv

  13. [20]

    Roshan and G

    R. Roshan and G. White, Using gravitational waves to see the first second of the Universe , Rev. Mod. Phys. 97 (2025) 015001 [ 2401.04388]

    2025 arXiv

  14. [21]

    Lazarides and Q

    G. Lazarides and Q. Shafi, Monopoles, Strings, and Necklaces in SO(10) and E6, JHEP 10 (2019) 193 [1904.06880]

    2019 arXiv

  15. [22]

    Lazarides, R

    G. Lazarides, R. Maji, A. Moursy and Q. Shafi, Inflation, superheavy metastable strings and gravitational waves in non-supersymmetric flipped SU(5), JCAP 03 (2024) 006 [ 2308.07094]

    2024 arXiv

  16. [23]

    Moursy and Q

    A. Moursy and Q. Shafi, Primordial monopoles, black holes and gravitational waves , JCAP 08 (2024) 064 [2405.04397]

    2024 arXiv

  17. [24]

    R. Maji, A. Moursy and Q. Shafi, Induced gravitational waves, metastable cosmic strings and primordial black holes in GUTs , JCAP 01 (2025) 106 [ 2409.13584]

    2025 arXiv

  18. [25]

    Lazarides, M

    G. Lazarides, M. Magg and Q. Shafi, Phase Transitions and Magnetic Monopoles in SO(10) , Phys. Lett. B 97 (1980) 87

    1980

  19. [26]

    Pogosian and T

    L. Pogosian and T. Vachaspati, Domain walls in SU(5) , Phys. Rev. D 62 (2000) 123506 [ hep-ph/0007045]

    2000 arXiv

  20. [27]

    Lazarides, Q

    G. Lazarides, Q. Shafi and A. Tiwari, Composite topological structures in SO(10) , JHEP 05 (2023) 119 [2303.15159]

    2023 arXiv

  21. [28]

    MACRO collaboration, Final results of magnetic monopole searches with the MACRO experiment , Eur. Phys. J. C 25 (2002) 511 [ hep-ex/0207020]

    2002 arXiv

  22. [29]

    IceCube collaboration, Search for Relativistic Magnetic Monopoles with Eight Years of IceCube Data , Phys. Rev. Lett. 128 (2022) 051101 [ 2109.13719]

    2022

  23. [30]

    Patrizii and M

    L. Patrizii and M. Spurio, Status of Searches for Magnetic Monopoles, Ann. Rev. Nucl. Part. Sci. 65 (2015) 279 [ 1510.07125]

    2015 arXiv

  24. [31]

    Weinberg, Gauge and Global Symmetries at High Temperature, Phys

    S. Weinberg, Gauge and Global Symmetries at High Temperature, Phys. Rev. D 9 (1974) 3357

    1974

  25. [32]

    Mohapatra and G

    R.N. Mohapatra and G. Senjanovic, Soft CP Violation at High Temperature, Phys. Rev. Lett. 42 (1979) 1651

    1979

  26. [33]

    Mohapatra and G

    R.N. Mohapatra and G. Senjanovic, Broken Symmetries at High Temperature, Phys. Rev. D 20 (1979) 3390

    1979

  27. [34]

    Mohapatra and G

    R.N. Mohapatra and G. Senjanovic, High Temperature Behavior of Gauge Theories , Phys. Lett. B 89 (1979) 57

    1979

  28. [35]

    Dvali and G

    G.R. Dvali and G. Senjanovic, Is there a domain wall problem?, Phys. Rev. Lett. 74 (1995) 5178 [hep-ph/9501387]

    1995 arXiv

  29. [36]

    Dvali, A

    G.R. Dvali, A. Melfo and G. Senjanovic, Is There a monopole problem?, Phys. Rev. Lett. 75 (1995) 4559 [hep-ph/9507230]

    1995 arXiv

  30. [37]

    Vachaspati and A

    T. Vachaspati and A. Vilenkin, Gravitational Radiation from Cosmic Strings , Phys. Rev. D 31 (1985) 3052

    1985

  31. [38]

    Kibble, Evolution of a system of cosmic strings , Nucl

    T.W.B. Kibble, Evolution of a system of cosmic strings , Nucl. Phys. B 252 (1985) 227 [Erratum: Nucl.Phys.B 261, 750 (1985)]

    1985

  32. [39]

    Vilenkin and E.P.S

    A. Vilenkin and E.P.S. Shellard, Cosmic Strings and Other Topological Defects, Cambridge University Press (7, 2000)

    2000

  33. [40]

    Damour and A

    T. Damour and A. Vilenkin, Gravitational wave bursts from cusps and kinks on cosmic strings , Phys. Rev. D 64 (2001) 064008 [ gr-qc/0104026]

    2001 arXiv

  34. [41]

    Vanchurin, K.D

    V. Vanchurin, K.D. Olum and A. Vilenkin, Scaling of cosmic string loops , Phys. Rev. D 74 (2006) 063527 [gr-qc/0511159]

    2006 arXiv

  35. [42]

    Ringeval, M

    C. Ringeval, M. Sakellariadou and F. Bouchet, Cosmological evolution of cosmic string loops , JCAP 02 (2007) 023 [ astro-ph/0511646]

    2007 arXiv

  36. [43]

    Olum and V

    K.D. Olum and V. Vanchurin, Cosmic string loops in the expanding Universe , Phys. Rev. D 75 (2007) 063521 [astro-ph/0610419]

    2007 arXiv

  37. [44]

    Leblond, B

    L. Leblond, B. Shlaer and X. Siemens, Gravitational Waves from Broken Cosmic Strings: The Bursts and the Beads, Phys. Rev. D 79 (2009) 123519 [ 0903.4686]

    2009 arXiv

  38. [45]

    Olmez, V

    S. Olmez, V. Mandic and X. Siemens, Gravitational-Wave Stochastic Background from Kinks and Cusps on Cosmic Strings , Phys. Rev. D 81 (2010) 104028 [1004.0890]

    2010 arXiv

  39. [46]

    Blanco-Pillado, K.D

    J.J. Blanco-Pillado, K.D. Olum and B. Shlaer, The number of cosmic string loops , Phys. Rev. D 89 (2014) 023512 [1309.6637]

    2014 arXiv

  40. [47]

    Blanco-Pillado and K.D

    J.J. Blanco-Pillado and K.D. Olum, Stochastic gravitational wave background from smoothed cosmic string loops, Phys. Rev. D 96 (2017) 104046 [1709.02693]

    2017 arXiv

  41. [48]

    Y. Cui, M. Lewicki, D.E. Morrissey and J.D. Wells, Probing the pre-BBN universe with gravitational waves from cosmic strings , JHEP 01 (2019) 081 [ 1808.08968]

    2019 arXiv

  42. [49]

    Buchmuller, V

    W. Buchmuller, V. Domcke, H. Murayama and K. Schmitz, Probing the scale of grand unification with gravitational waves, Phys. Lett. B 809 (2020) 135764 [1912.03695]

    2020 arXiv

  43. [50]

    Buchmuller, V

    W. Buchmuller, V. Domcke and K. Schmitz, Stochastic gravitational-wave background from metastable cosmic strings, JCAP 12 (2021) 006 [ 2107.04578]

    2021 arXiv

  44. [51]

    Dunsky, A

    D.I. Dunsky, A. Ghoshal, H. Murayama, Y. Sakakihara and G. White, GUTs, hybrid topological defects, and gravitational waves, Phys. Rev. D 106 (2022) 075030 [2111.08750]

    2022 arXiv

  45. [52]

    Thrane and J.D

    E. Thrane and J.D. Romano, Sensitivity curves for searches for gravitational-wave backgrounds, Phys. Rev. D 88 (2013) 124032 [ 1310.5300]

    2013 arXiv

  46. [53]

    Schmitz, New Sensitivity Curves for Gravitational-Wave Signals from Cosmological Phase 7 Transitions, JHEP 01 (2021) 097 [ 2002.04615]

    K. Schmitz, New Sensitivity Curves for Gravitational-Wave Signals from Cosmological Phase 7 Transitions, JHEP 01 (2021) 097 [ 2002.04615]

    2021 arXiv

  47. [54]

    Sato et al., The status of DECIGO , Journal of Physics: Conference Series 840 (2017) 012010

    S. Sato et al., The status of DECIGO , Journal of Physics: Conference Series 840 (2017) 012010

    2017

  48. [55]

    Crowder and N.J

    J. Crowder and N.J. Cornish, Beyond LISA: Exploring future gravitational wave missions , Phys. Rev. D 72 (2005) 083005 [ gr-qc/0506015]

    2005 arXiv

  49. [56]

    Corbin and N.J

    V. Corbin and N.J. Cornish, Detecting the cosmic gravitational wave background with the big bang observer, Class. Quant. Grav. 23 (2006) 2435 [gr-qc/0512039]

    2006 arXiv

  50. [57]

    Bartolo et al., Science with the space-based interferometer LISA

    N. Bartolo et al., Science with the space-based interferometer LISA. IV: Probing inflation with gravitational waves, JCAP 12 (2016) 026 [ 1610.06481]

    2016 arXiv

  51. [58]

    Amaro-Seoane et al., Laser interferometer space antenna, 1702.00786

    P. Amaro-Seoane et al., Laser interferometer space antenna, 1702.00786

    arXiv

  52. [59]

    KAGRA, LIGO Scientific, Virgo, VIRGO collaboration, Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA, Living Rev. Rel. 21 (2018) 3 [ 1304.0670]

    2018 arXiv

  53. [60]

    Mentasti and M

    G. Mentasti and M. Peloso, ET sensitivity to the anisotropic Stochastic Gravitational Wave Background , JCAP 03 (2021) 080 [ 2010.00486]

    2021 arXiv

  54. [61]

    Regimbau, M

    T. Regimbau, M. Evans, N. Christensen, E. Katsavounidis, B. Sathyaprakash and S. Vitale, Digging deeper: Observing primordial gravitational waves below the binary black hole produced stochastic background, Phys. Rev. Lett. 118 (2017) 151105 [1611.08943]

    2017 arXiv

  55. [62]

    Herman, A

    N. Herman, A. F¨ uzfa, L. Lehoucq and S. Clesse, Detecting planetary-mass primordial black holes with resonant electromagnetic gravitational-wave detectors, Phys. Rev. D 104 (2021) 023524 [ 2012.12189]

    2021 arXiv

  56. [63]

    Herman, L

    N. Herman, L. Lehoucq and A. F´ uzfa,Electromagnetic antennas for the resonant detection of the stochastic gravitational wave background, Phys. Rev. D 108 (2023) 124009 [2203.15668]

    2023 arXiv

  57. [65]

    Vilenkin, Cosmic string dynamics with friction , Phys

    A. Vilenkin, Cosmic string dynamics with friction , Phys. Rev. D 43 (1991) 1060

    1991

  58. [66]

    Garriga and M

    J. Garriga and M. Sakellariadou, Effects of friction on cosmic strings, Phys. Rev. D 48 (1993) 2502 [hep-th/9303024]

    1993 arXiv

  59. [67]

    Blanco-Pillado and K.D

    J.J. Blanco-Pillado and K.D. Olum, Form of cosmic string cusps , Phys. Rev. D 59 (1999) 063508 [gr-qc/9810005] [Erratum: Phys.Rev.D 103, 029902 (2021)]

    1999 arXiv

  60. [68]

    Matsunami, L

    D. Matsunami, L. Pogosian, A. Saurabh and T. Vachaspati, Decay of Cosmic String Loops Due to Particle Radiation, Phys. Rev. Lett. 122 (2019) 201301 [1903.05102]

    2019 arXiv

  61. [69]

    Auclair, D.A

    P. Auclair, D.A. Steer and T. Vachaspati, Particle emission and gravitational radiation from cosmic strings: observational constraints , Phys. Rev. D 101 (2020) 083511 [ 1911.12066]

    2020 arXiv

  62. [70]

    Martins and E.P.S

    C.J.A.P. Martins and E.P.S. Shellard, String evolution with friction , Phys. Rev. D 53 (1996) 575 [hep-ph/9507335]

    1996 arXiv

  63. [71]

    Martins and E.P.S

    C.J.A.P. Martins and E.P.S. Shellard, Quantitative string evolution , Phys. Rev. D 54 (1996) 2535 [hep-ph/9602271]

    1996 arXiv

  64. [72]

    Martins and E.P.S

    C.J.A.P. Martins and E.P.S. Shellard, Extending the velocity dependent one scale string evolution model , Phys. Rev. D 65 (2002) 043514 [ hep-ph/0003298]

    2002 arXiv

  65. [73]

    Gouttenoire, G

    Y. Gouttenoire, G. Servant and P. Simakachorn, Beyond the Standard Models with Cosmic Strings , JCAP 07 (2020) 032 [ 1912.02569]

    2020 arXiv

  66. [74]

    Hiramatsu, M

    T. Hiramatsu, M. Kawasaki and K. Saikawa, On the estimation of gravitational wave spectrum from cosmic domain walls , JCAP 02 (2014) 031 [ 1309.5001]

    2014 arXiv

  67. [75]

    Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6 [1807.06209] [Erratum: Astron. Astrophys. 652 (2021) C4]

    2020 arXiv

  68. [76]

    Binetruy, A

    P. Binetruy, A. Bohe, C. Caprini and J.-F. Dufaux, Cosmological Backgrounds of Gravitational Waves and eLISA/NGO: Phase Transitions, Cosmic Strings and Other Sources, JCAP 06 (2012) 027 [ 1201.0983]

    2012 arXiv

  69. [77]

    Aver, K.A

    E. Aver, K.A. Olive and E.D. Skillman, The effects of He I λ10830 on helium abundance determinations , JCAP 07 (2015) 011 [ 1503.08146]

    2015 arXiv

  70. [78]

    Peimbert, M

    A. Peimbert, M. Peimbert and V. Luridiana, The primordial helium abundance and the number of neutrino families , Rev. Mex. Astron. Astrofis. 52 (2016) 419 [1608.02062]

    2016 arXiv

  71. [79]

    Escudero Abenza, Precision early universe thermodynamics made simple: Neff and neutrino decoupling in the Standard Model and beyond , JCAP 05 (2020) 048 [ 2001.04466]

    M. Escudero Abenza, Precision early universe thermodynamics made simple: Neff and neutrino decoupling in the Standard Model and beyond , JCAP 05 (2020) 048 [ 2001.04466]

    2020 arXiv

  72. [80]

    Akita and M

    K. Akita and M. Yamaguchi, A precision calculation of relic neutrino decoupling, JCAP 08 (2020) 012 [2005.07047]

    2020 arXiv

  73. [81]

    Froustey, C

    J. Froustey, C. Pitrou and M.C. Volpe, Neutrino decoupling including flavour oscillations and primordial nucleosynthesis, JCAP 12 (2020) 015 [ 2008.01074]

    2020 arXiv

  74. [82]

    Bennett, G

    J.J. Bennett, G. Buldgen, P.F. De Salas, M. Drewes, S. Gariazzo, S. Pastor et al., Towards a precision calculation of Neff in the Standard Model II: Neutrino decoupling in the presence of flavour oscillations and finite-temperature QED, JCAP 04 (2021) 073 [2012.02726]

    2021 arXiv

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