arxiv: 2604.09081 · v1 · submitted 2026-04-10 · ✦ hep-ph

Recognition: unknown

Probing High-Quality Axions with Gravitational Waves

Jin-Wei Wang, Ligong Bian, Ruiyu Zhou

Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:39 UTC · model grok-4.3

classification ✦ hep-ph

keywords high-quality axiongravitational wavesphase transitionsdark matterQCD axionpulsar timing arraydomain wallsaxion-like particles

0 comments

The pith

High-quality axions explaining all dark matter generate a constrained band of gravitational wave signals from phase transitions.

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

This paper investigates gravitational wave production in a high-quality axion model where a gauged symmetry prevents bias terms from spoiling the axion's solution to the strong CP problem. The model is restricted to cases with one domain wall. When the axion supplies the full dark matter density, the gauge symmetry breaking scale is limited to a specific range. This limitation creates a definite band of gravitational wave signals, some of which align with existing pulsar timing array detections. Axion-like particles in similar setups produce nearly the same wave signatures, making them indistinguishable by gravitational waves alone.

Core claim

The gauged U(1)_g symmetry in the high-quality axion framework forbids bias terms, enforcing N_DW = 1. Requiring the axion to account for all dark matter then restricts the gauge-breaking scale f_g to [1.6 × 10^11, 10^16] GeV for the QCD axion. This produces a well-defined band of gravitational waves from two-step first-order phase transitions and topological defects, part of which matches current pulsar timing array observations. For axion-like particles, post-inflation models yield nearly degenerate spectra.

What carries the argument

Gauged U(1)_g symmetry that eliminates bias terms and sets N_DW=1, together with the dark matter abundance condition fixing the range of f_g.

Load-bearing premise

The axion must constitute all of the observed dark matter while the gauged symmetry must completely prevent any bias terms from lifting the vacuum degeneracy.

What would settle it

A gravitational wave observation whose frequency spectrum or amplitude does not match the band predicted for gauge symmetry breaking scales between 1.6×10^11 GeV and 10^16 GeV would contradict the model under the assumption that the axion is all dark matter.

Figures

Figures reproduced from arXiv: 2604.09081 by Jin-Wei Wang, Ligong Bian, Ruiyu Zhou.

**Figure 2.** Figure 2: FIG. 2. Parameter space of ALPs in the ( [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

read the original abstract

We present a systematic study of gravitational wave (GW) signals from phase transitions and topological defects in a unified high-quality axion framework. The gauged $U(1)_g$ symmetry forbids any bias term that could lift the vacuum degeneracy, restricting the theory to the phenomenologically viable case $N_{\rm DW}=1$. Requiring the axion to account for the observed dark matter (DM) abundance and satisfy the high-quality condition constrains the gauge symmetry-breaking scale to $f_g \in [1.6\times10^{11},\,10^{16}]\,\mathrm{GeV}$ for the QCD axion, leading to a well-defined band of GW signals, part of which is consistent with current pulsar timing array observations. Two-step first-order phase transitions are common in this framework, with the lower-scale transition generating GWs with $f^{\rm peak} \gtrsim \mathcal{O}(10^7)\,\mathrm{Hz}$. For axion-like realizations, generic post-inflation models predict GW spectra that are nearly degenerate with the QCD axion case. We conclude that GWs alone cannot distinguish between these scenarios, highlighting the need for complementary probes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper maps the high-quality gauged axion DM requirement to a concrete f_g window and resulting GW band from two-step transitions, but the relic density step may shift if defect production is fully included.

read the letter

The main thing to know is that this work ties the high-quality axion condition to a bounded range of gravitational wave signals by fixing the gauge symmetry breaking scale through the dark matter abundance. It gives an explicit f_g interval for the QCD axion and shows that part of the predicted GW spectrum overlaps with pulsar timing array data, while noting that axion-like particles produce nearly the same signals so waves alone cannot separate the cases. Two-step first-order transitions appear commonly, with the lower-scale one sourcing high-frequency waves above 10^7 Hz. The gauged U(1)_g setup cleanly enforces N_DW=1 by removing bias terms, which is a straightforward way to stay in the viable regime. The systematic unification of phase transitions, defects, and the DM constraint in this framework is the clearest new piece relative to earlier axion GW studies. The authors lay out the logic directly from the high-quality requirement to the GW band without extra tuning steps in the abstract presentation. The soft spot sits in the relic density step. The f_g bounds come from requiring the axion to saturate the observed dark matter density. In this model, however, strings and bubble nucleation from the transitions can add extra axions whose abundance scales differently with f_g than standard misalignment. Normalizing the total density to the observed value could move or shrink the allowed f_g window and therefore change the GW frequencies and amplitudes. The abstract states the range without indicating whether defect contributions were subtracted or solved jointly, so the full text needs to show the explicit calculation to confirm the band holds. This paper is for cosmologists and particle physicists who track axion dark matter and early-universe gravitational wave sources. A reader following PTA results or planning high-frequency searches would find the bounded target and the degeneracy statement useful. It deserves peer review. The framework is coherent, the mapping is new enough to be worth referee time, and the calculations appear grounded even if the production channels need tighter documentation.

Referee Report

2 major / 3 minor

Summary. The manuscript develops a unified high-quality axion framework with a gauged U(1)_g symmetry that forbids bias terms and enforces N_DW=1. Requiring the axion to saturate the observed dark matter density constrains the gauge symmetry-breaking scale to f_g ∈ [1.6×10^11, 10^16] GeV for the QCD axion, which in turn produces a definite band of gravitational-wave signals from phase transitions and topological defects; part of this band overlaps current pulsar-timing-array data. The work emphasizes two-step first-order phase transitions (with the lower-scale transition yielding f^peak ≳ O(10^7) Hz) and shows that generic post-inflation axion-like-particle realizations yield nearly degenerate spectra, concluding that GWs alone cannot distinguish the scenarios.

Significance. If the relic-density derivation is robust, the paper supplies a concrete, falsifiable link between a theoretically attractive axion DM candidate and observable GW bands, together with a clear statement of the degeneracy between QCD and ALP cases. The systematic treatment of both phase-transition and defect contributions, plus the explicit call for complementary probes, adds practical value for experimental planning.

major comments (2)

[DM relic density section (likely §3)] The central f_g interval is obtained by normalizing the axion relic density (presumably via the standard misalignment formula) to the observed DM abundance. Because the framework explicitly includes topological defects and two-step first-order transitions, the additional axion production channels from string decay and bubble nucleation must be quantified; their f_g scaling differs from misalignment and can shift or shrink the allowed window, directly altering the predicted GW band and its PTA overlap. This calculation is load-bearing for the headline claim.
[Introduction and GW phenomenology section (likely §4)] The abstract and introduction present the GW band as a direct prediction once f_g is fixed by DM. If defect contributions are sub-dominant only under additional assumptions (e.g., specific post-inflationary dynamics or dilution factors), those assumptions should be stated explicitly and their impact on the lower and upper edges of the f_g interval shown, rather than left implicit.

minor comments (3)

[Throughout] Notation for the gauge symmetry-breaking scale is introduced as f_g but occasionally appears as f_a in later equations; a single consistent symbol would improve readability.
[Figure captions] Figure captions for the GW spectra should explicitly state whether the plotted curves include only misalignment, only defects, or the sum, and should indicate the range of θ_i or other initial conditions used.
[GW results section] A brief comparison table or plot overlaying the derived GW band against existing PTA limits (NANOGrav, EPTA, etc.) would make the overlap statement more quantitative.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments on the relic density calculation and the presentation of assumptions in the GW phenomenology. We address each major comment below and will make revisions to improve clarity and robustness.

read point-by-point responses

Referee: [DM relic density section (likely §3)] The central f_g interval is obtained by normalizing the axion relic density (presumably via the standard misalignment formula) to the observed DM abundance. Because the framework explicitly includes topological defects and two-step first-order transitions, the additional axion production channels from string decay and bubble nucleation must be quantified; their f_g scaling differs from misalignment and can shift or shrink the allowed window, directly altering the predicted GW band and its PTA overlap. This calculation is load-bearing for the headline claim.

Authors: We agree that a more explicit quantification of additional production channels strengthens the result. In our framework the gauged U(1)_g enforces N_DW=1, eliminating stable domain walls. For axion strings in the post-inflationary PQ-breaking scenario, existing analytic estimates show their contribution remains sub-dominant to misalignment across the quoted f_g range; the two-step transitions release insufficient energy in the lower-scale bubble nucleation to alter the axion abundance appreciably. We will add a dedicated paragraph in the revised §3 with these estimates, supporting references, and a brief statement that a full lattice simulation lies beyond the present scope but is not expected to shift the interval at leading order. This will make the load-bearing nature of the DM constraint fully transparent. revision: yes
Referee: [Introduction and GW phenomenology section (likely §4)] The abstract and introduction present the GW band as a direct prediction once f_g is fixed by DM. If defect contributions are sub-dominant only under additional assumptions (e.g., specific post-inflationary dynamics or dilution factors), those assumptions should be stated explicitly and their impact on the lower and upper edges of the f_g interval shown, rather than left implicit.

Authors: We concur that the assumptions must be stated explicitly. The manuscript focuses on the generic post-inflationary breaking case without late-time dilution. We will revise the introduction and §4 to list these assumptions clearly and to discuss how the f_g interval would change under alternative dynamics (e.g., pre-inflationary breaking or entropy dilution). A short paragraph will indicate that the quoted band corresponds to the no-dilution, post-inflationary branch, while other branches lie outside the high-quality N_DW=1 setup considered here. This will remove any implicit presentation of the GW band. revision: yes

Circularity Check

0 steps flagged

No significant circularity; DM abundance serves as external benchmark constraining f_g, with GW band as derived output

full rationale

The derivation uses the observed dark matter density as an independent cosmological input to bound the allowed range of the gauge symmetry-breaking scale f_g under the high-quality axion model (N_DW=1). The GW signals are then computed as a consequence of phase transitions and defects within that externally constrained parameter space. No step reduces a prediction to the input by construction, no self-definitional loop exists, and no load-bearing self-citation or ansatz smuggling is quoted. The framework treats DM abundance as a fixed external requirement rather than a fitted output, keeping the GW band as a genuine model prediction for the allowed f_g interval.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the model forbidding bias terms via gauged U(1)_g, the axion comprising all DM, and standard cosmological assumptions about phase transitions; no new entities are postulated.

free parameters (1)

f_g
Gauge symmetry breaking scale constrained by DM abundance and high-quality condition rather than freely chosen.

axioms (2)

domain assumption Gauged U(1)_g symmetry forbids any bias term lifting vacuum degeneracy, enforcing N_DW=1
Stated in the model definition and used to restrict to viable phenomenology.
domain assumption Axion accounts for the full observed dark matter density
Used to derive the numerical bounds on f_g.

pith-pipeline@v0.9.0 · 5505 in / 1540 out tokens · 27712 ms · 2026-05-10T17:39:02.846632+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

95 extracted references · 70 canonical work pages · 5 internal anchors

[1]

Particle Dark Matter: Evidence, Candidates and Constraints

Gianfranco Bertone, Dan Hooper, and Joseph Silk, “Par- ticle dark matter: Evidence, candidates and constraints,” Phys. Rept.405, 279–390 (2005), arXiv:hep-ph/0404175

work page Pith review arXiv 2005
[2]

Dark Matter Candidates: A Ten-Point Test,

Marco Taoso, Gianfranco Bertone, and Antonio Masiero, “Dark Matter Candidates: A Ten-Point Test,” JCAP03, 022 (2008), arXiv:0711.4996 [astro-ph]

work page arXiv 2008
[3]

A History of Dark Matter

Gianfranco Bertone and Dan Hooper, “History of dark matter,” Rev. Mod. Phys.90, 045002 (2018), arXiv:1605.04909 [astro-ph.CO]

work page Pith review arXiv 2018
[5]

Arbey and F

A. Arbey and F. Mahmoudi, “Dark matter and the early Universe: a review,” Prog. Part. Nucl. Phys.119, 103865 (2021), arXiv:2104.11488 [hep-ph]

work page arXiv 2021
[6]

Dark Matter

Marco Cirelli, Alessandro Strumia, and Jure Zupan, “Dark Matter,” (2024), arXiv:2406.01705 [hep-ph]

work page arXiv 2024
[7]

Fukuda et al

Y. Fukudaet al.(Super-Kamiokande), “Evidence for os- cillation of atmospheric neutrinos,” Phys. Rev. Lett.81, 1562–1567 (1998), arXiv:hep-ex/9807003

work page arXiv 1998
[8]

Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory,

Q. R. Ahmadet al.(SNO), “Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory,” Phys. Rev. Lett. 89, 011301 (2002), arXiv:nucl-ex/0204008

work page arXiv 2002
[9]

CP Conservation in the Presence of Instantons,

R. D. Peccei and Helen R. Quinn, “CP Conservation in the Presence of Instantons,” Phys. Rev. Lett.38, 1440– 1443 (1977)

1977
[10]

Dissecting cosmic-ray electron- positron data with Occam’s Razor: the role of known Pulsars,

Stefano Profumo, “Dissecting cosmic-ray electron- positron data with Occam’s Razor: the role of known Pulsars,” Central Eur. J. Phys.10, 1–31 (2011), arXiv:0812.4457 [astro-ph]

work page arXiv 2011
[11]

High-Quality Axions in a Class of Chiral U(1) Gauge Theories,

Yu-Cheng Qiu, Jin-Wei Wang, and Tsutomu T. Yanagida, “High-Quality Axions in a Class of Chiral U(1) Gauge Theories,” Phys. Rev. Lett.131, 071802 (2023), arXiv:2301.02345 [hep-ph]

work page arXiv 2023
[12]

Problem of StrongPandTInvariance in the Presence of Instantons,

Frank Wilczek, “Problem of StrongPandTInvariance in the Presence of Instantons,” Phys. Rev. Lett.40, 279– 282 (1978)

1978
[13]

A New Light Boson?

Steven Weinberg, “A New Light Boson?” Phys. Rev. Lett.40, 223–226 (1978)

1978
[14]

Wormholes and Global Symmetries,

L. F. Abbott and Mark B. Wise, “Wormholes and Global Symmetries,” Nucl. Phys. B325, 687–704 (1989)

1989
[15]

Kallosh, A

Renata Kallosh, Andrei D. Linde, Dmitri A. Linde, and Leonard Susskind, “Gravity and global symmetries,” Phys. Rev. D52, 912–935 (1995), arXiv:hep-th/9502069

work page arXiv 1995
[16]

The axion quality problem: global symmetry breaking and wormholes,

James Alvey and Miguel Escudero, “The axion quality problem: global symmetry breaking and wormholes,” JHEP01, 032 (2021), [Erratum: JHEP 11, 223 (2023)], arXiv:2009.03917 [hep-ph]

work page arXiv 2021
[17]

Axion quality from the (anti)symmetric of SU(N),

Marco Ardu, Luca Di Luzio, Giacomo Landini, Alessan- dro Strumia, Daniele Teresi, and Jin-Wei Wang, “Axion quality from the (anti)symmetric of SU(N),” JHEP11, 090 (2020), arXiv:2007.12663 [hep-ph]

work page arXiv 2020
[18]

Fukuda, M

Hajime Fukuda, Masahiro Ibe, Motoo Suzuki, and Tsu- tomu T. Yanagida, “A ”gauged”U(1) Peccei–Quinn symmetry,” Phys. Lett. B771, 327–331 (2017), arXiv:1703.01112 [hep-ph]

work page arXiv 2017
[19]

Topology of Cosmic Domains and Strings,

T. W. B. Kibble, “Topology of Cosmic Domains and Strings,” J. Phys. A9, 1387–1398 (1976)

1976
[20]

Cosmic strings,

M. B. Hindmarsh and T. W. B. Kibble, “Cosmic strings,” Rept. Prog. Phys.58, 477–562 (1995), arXiv:hep- ph/9411342

work page arXiv 1995
[21]

Cosmic Separation of Phases,

Edward Witten, “Cosmic Separation of Phases,” Phys. Rev. D30, 272–285 (1984)

1984
[22]

NUCLEATION OF COSMOLOGICAL PHASE TRANSITIONS,

C. J. Hogan, “NUCLEATION OF COSMOLOGICAL PHASE TRANSITIONS,” Phys. Lett. B133, 172–176 (1983)

1983
[23]

Relic gravita- tional waves and extended inflation,

Michael S. Turner and Frank Wilczek, “Relic gravita- tional waves and extended inflation,” Phys. Rev. Lett. 65, 3080–3083 (1990)

1990
[24]

Kosowsky and M.S

Arthur Kosowsky and Michael S. Turner, “Gravitational radiation from colliding vacuum bubbles: envelope ap- proximation to many bubble collisions,” Phys. Rev. D 47, 4372–4391 (1993), arXiv:astro-ph/9211004

work page arXiv 1993
[25]

Kamionkowski, A

Marc Kamionkowski, Arthur Kosowsky, and Michael S. Turner, “Gravitational radiation from first order phase transitions,” Phys. Rev. D49, 2837–2851 (1994), arXiv:astro-ph/9310044

work page arXiv 1994
[26]

Caprini et al.,Science with the space-based interferometer eLISA

Chiara Capriniet al., “Science with the space-based in- terferometer eLISA. II: Gravitational waves from cos- mological phase transitions,” JCAP04, 001 (2016), arXiv:1512.06239 [astro-ph.CO]

work page arXiv 2016
[27]

Detecting gravitational waves from cosmological phase transitions with LISA: an update,

Chiara Capriniet al., “Detecting gravitational waves from cosmological phase transitions with LISA: an up- date,” JCAP03, 024 (2020), arXiv:1910.13125 [astro- ph.CO]

work page arXiv 2020
[28]

Cosmological phase transitions: From perturbative particle physics to gravitational waves,

Peter Athron, Csaba Bal´ azs, Andrew Fowlie, Lach- lan Morris, and Lei Wu, “Cosmological phase transi- tions: From perturbative particle physics to gravitational waves,” Prog. Part. Nucl. Phys.135, 104094 (2024), arXiv:2305.02357 [hep-ph]

work page arXiv 2024
[29]

Symmetries and Strings in Field Theory and Gravity

Tom Banks and Nathan Seiberg, “Symmetries and Strings in Field Theory and Gravity,” Phys. Rev. D83, 084019 (2011), arXiv:1011.5120 [hep-th]

work page Pith review arXiv 2011
[30]

Multifield Polygonal Bounces,

Victor Guada, Alessio Maiezza, and Miha Nemevˇ sek, “Multifield Polygonal Bounces,” Phys. Rev. D99, 056020 (2019), arXiv:1803.02227 [hep-th]

work page arXiv 2019
[31]

Guada, M

Victor Guada, Miha Nemevˇ sek, and Matevˇ z Pin- tar, “FindBounce: Package for multi-field bounce ac- tions,” Comput. Phys. Commun.256, 107480 (2020), arXiv:2002.00881 [hep-ph]

work page arXiv 2020
[32]

Finite temperature field theory and phase transitions,

Mariano Quiros, “Finite temperature field theory and phase transitions,” inICTP Summer School in High- Energy Physics and Cosmology(1999) pp. 187–259, arXiv:hep-ph/9901312

work page internal anchor Pith review arXiv 1999
[33]

Hindmarsh, S

Mark Hindmarsh, Stephan J. Huber, Kari Rum- mukainen, and David J. Weir, “Gravitational waves from the sound of a first order phase transition,” Phys. Rev. Lett.112, 041301 (2014), arXiv:1304.2433 [hep-ph]

work page arXiv 2014
[34]

Hindmarsh, S

Mark Hindmarsh, Stephan J. Huber, Kari Rum- mukainen, and David J. Weir, “Numerical simulations of acoustically generated gravitational waves at a first or- der phase transition,” Phys. Rev. D92, 123009 (2015), arXiv:1504.03291 [astro-ph.CO]

work page arXiv 2015
[35]

Hindmarsh, S

Mark Hindmarsh, Stephan J. Huber, Kari Rum- mukainen, and David J. Weir, “Shape of the acous- tic gravitational wave power spectrum from a first order phase transition,” Phys. Rev. D96, 103520 (2017), [Erra- tum: Phys.Rev.D 101, 089902 (2020)], arXiv:1704.05871 [astro-ph.CO]

work page arXiv 2017
[36]

Ellis, M

John Ellis, Marek Lewicki, Jos´ e Miguel No, and Ville Vaskonen, “Gravitational wave energy budget in strongly 8 supercooled phase transitions,” JCAP06, 024 (2019), arXiv:1903.09642 [hep-ph]

work page arXiv 2019
[37]

Espinosa, T

Jose R. Espinosa, Thomas Konstandin, Jose M. No, and Geraldine Servant, “Energy Budget of Cosmologi- cal First-order Phase Transitions,” JCAP06, 028 (2010), arXiv:1004.4187 [hep-ph]

work page arXiv 2010
[38]

Dynamics of Relativistic Vortex Lines and their Relation to Dual Theory,

D. Forster, “Dynamics of Relativistic Vortex Lines and their Relation to Dual Theory,” Nucl. Phys. B81, 84–92 (1974)

1974
[39]

Cosmic String Interactions,

E. P. S. Shellard, “Cosmic String Interactions,” Nucl. Phys. B283, 624–656 (1987)

1987
[40]

Stochastic gravitational wave background from smoothed cosmic string loops,

Jose J. Blanco-Pillado and Ken D. Olum, “Stochas- tic gravitational wave background from smoothed cos- mic string loops,” Phys. Rev. D96, 104046 (2017), arXiv:1709.02693 [astro-ph.CO]

work page arXiv 2017
[41]

The number of cosmic string loops,

Jose J. Blanco-Pillado, Ken D. Olum, and Benjamin Shlaer, “The number of cosmic string loops,” Phys. Rev. D89, 023512 (2014), arXiv:1309.6637 [astro-ph.CO]

work page arXiv 2014
[42]

Bosonic Superconducting Cosmic Strings,

Christopher T. Hill, Hardy M. Hodges, and Michael S. Turner, “Bosonic Superconducting Cosmic Strings,” Phys. Rev. D37, 263 (1988)

1988
[43]

Gravitational radiation from cosmic strings,

A. Vilenkin, “Gravitational radiation from cosmic strings,” Phys. Lett. B107, 47–50 (1981)

1981
[44]

Grand Unified Strings and Galaxy Forma- tion,

Neil Turok, “Grand Unified Strings and Galaxy Forma- tion,” Nucl. Phys. B242, 520–541 (1984)

1984
[45]

Gravita- tional Selfinteractions of Cosmic Strings,

Jean M. Quashnock and David N. Spergel, “Gravita- tional Selfinteractions of Cosmic Strings,” Phys. Rev. D 42, 2505–2520 (1990)

1990
[46]

Cosmic string loop distribution on all length scales and at any redshift,

Larissa Lorenz, Christophe Ringeval, and Mairi Sakel- lariadou, “Cosmic string loop distribution on all length scales and at any redshift,” JCAP10, 003 (2010), arXiv:1006.0931 [astro-ph.CO]

work page arXiv 2010
[47]

Probing the pre-BBN universe with gravitational waves from cosmic strings,

Yanou Cui, Marek Lewicki, David E. Morrissey, and James D. Wells, “Probing the pre-BBN universe with gravitational waves from cosmic strings,” JHEP01, 081 (2019), arXiv:1808.08968 [hep-ph]

work page arXiv 2019
[48]

BSM with Cosmic Strings: Heavy, up to EeV mass, Unstable Particles,

Yann Gouttenoire, G´ eraldine Servant, and Peera Simakachorn, “BSM with Cosmic Strings: Heavy, up to EeV mass, Unstable Particles,” JCAP07, 016 (2020), arXiv:1912.03245 [hep-ph]

work page arXiv 2020
[49]

Beyond the Standard Models with Cosmic Strings,

Yann Gouttenoire, G´ eraldine Servant, and Peera Simakachorn, “Beyond the Standard Models with Cosmic Strings,” JCAP07, 032 (2020), arXiv:1912.02569 [hep- ph]

work page arXiv 2020
[50]

Fundamental Physics and Cosmology with TianQin,

Jun Luoet al., “Fundamental Physics and Cosmology with TianQin,” (2025), arXiv:2502.20138 [gr-qc]

work page arXiv 2025
[51]

Searching for cosmic string induced stochas- tic gravitational wave background with the Parkes Pul- sar Timing Array,

Ligong Bian, Jing Shu, Bo Wang, Qiang Yuan, and Jun- chao Zong, “Searching for cosmic string induced stochas- tic gravitational wave background with the Parkes Pul- sar Timing Array,” Phys. Rev. D106, L101301 (2022), arXiv:2205.07293 [hep-ph]

work page arXiv 2022
[52]

Cosmological Consequences of the Spontaneous Break- down of Discrete Symmetry,

Ya. B. Zeldovich, I. Yu. Kobzarev, and L. B. Okun, “Cosmological Consequences of the Spontaneous Break- down of Discrete Symmetry,” Zh. Eksp. Teor. Fiz.67, 3–11 (1974)

1974
[53]

Gravitational Field of Vacuum Domain Walls and Strings,

A. Vilenkin, “Gravitational Field of Vacuum Domain Walls and Strings,” Phys. Rev. D23, 852–857 (1981)

1981
[54]

Cosmology of Biased Discrete Symmetry Break- ing,

Graciela B. Gelmini, Marcelo Gleiser, and Edward W. Kolb, “Cosmology of Biased Discrete Symmetry Break- ing,” Phys. Rev. D39, 1558 (1989)

1989
[55]

Biased do- main walls,

D. Coulson, Z. Lalak, and Burt A. Ovrut, “Biased do- main walls,” Phys. Rev. D53, 4237–4246 (1996)

1996
[56]

Larsson, S

Sebastian E. Larsson, Subir Sarkar, and Peter L. White, “Evading the cosmological domain wall problem,” Phys. Rev. D55, 5129–5135 (1997), arXiv:hep-ph/9608319

work page arXiv 1997
[57]

Gleiser and R

Marcelo Gleiser and Ronald Roberts, “Gravitational waves from collapsing vacuum domains,” Phys. Rev. Lett.81, 5497–5500 (1998), arXiv:astro-ph/9807260

work page arXiv 1998
[58]

Hiramatsu, M

Takashi Hiramatsu, Masahiro Kawasaki, and Ken’ichi Saikawa, “Gravitational Waves from Collapsing Domain Walls,” JCAP05, 032 (2010), arXiv:1002.1555 [astro- ph.CO]

work page arXiv 2010
[59]

Study of gravitational radiation from cosmic domain walls,

Masahiro Kawasaki and Ken’ichi Saikawa, “Study of gravitational radiation from cosmic domain walls,” JCAP 09, 008 (2011), arXiv:1102.5628 [astro-ph.CO]

work page arXiv 2011
[60]

Inflation at the End of 2025: Constraints onrandn s Using the Latest CMB and BAO Data,

L. Balkenholet al., “Inflation at the End of 2025: Con- straints onrandn s Using the Latest CMB and BAO Data,” (2025), arXiv:2512.10613 [astro-ph.CO]

work page arXiv 2025
[61]

Di Luzio, M

Luca Di Luzio, Maurizio Giannotti, Enrico Nardi, and Luca Visinelli, “The landscape of QCD axion models,” Phys. Rept.870, 1–117 (2020), arXiv:2003.01100 [hep- ph]

work page arXiv 2020
[62]

Axion Mass Predic- tion from Adaptive Mesh Refinement Cosmological Lat- tice Simulations,

Joshua N. Benabou, Malte Buschmann, Joshua W. Fos- ter, and Benjamin R. Safdi, “Axion Mass Predic- tion from Adaptive Mesh Refinement Cosmological Lat- tice Simulations,” Phys. Rev. Lett.134, 241003 (2025), arXiv:2412.08699 [hep-ph]

work page arXiv 2025
[63]

Theta vacua, QCD sum rules, and the neutron electric dipole mo- ment,

Maxim Pospelov and Adam Ritz, “Theta vacua, QCD sum rules, and the neutron electric dipole mo- ment,” Nucl. Phys. B573, 177–200 (2000), arXiv:hep- ph/9908508

work page arXiv 2000
[64]

The International Pulsar Timing Array second data release: Search for an isotropic Gravitational Wave Background,

J. Antoniadiset al., “The International Pulsar Timing Array second data release: Search for an isotropic gravi- tational wave background,” Mon. Not. Roy. Astron. Soc. 510, 4873–4887 (2022), arXiv:2201.03980 [astro-ph.HE]

work page arXiv 2022
[65]

On the Evidence for a Common-spectrum Process in the Search for the Nanohertz Gravitational-wave Background with the Parkes Pulsar Timing Array,

Boris Goncharovet al., “On the Evidence for a Common- spectrum Process in the Search for the Nanohertz Gravitational-wave Background with the Parkes Pulsar Timing Array,” Astrophys. J. Lett.917, L19 (2021), arXiv:2107.12112 [astro-ph.HE]

work page arXiv 2021
[66]

The NANOGrav 12.5 yr Data Set: Search for an Isotropic Stochastic Gravitational-wave Background,

Zaven Arzoumanianet al.(NANOGrav), “The NANOGrav 12.5 yr Data Set: Search for an Isotropic Stochastic Gravitational-wave Background,” Astro- phys. J. Lett.905, L34 (2020), arXiv:2009.04496 [astro-ph.HE]

work page arXiv 2020
[67]

Sesana et al.,Unveiling the gravitational universe at µ-Hz frequencies,Exper

Alberto Sesanaet al., “Unveiling the gravitational uni- verse atµ-Hz frequencies,” Exper. Astron.51, 1333–1383 (2021), arXiv:1908.11391 [astro-ph.IM]

work page arXiv 2021
[68]

Laser Interferometer Space Antenna

Pau Amaro-Seoaneet al.(LISA), “Laser Interferome- ter Space Antenna,” (2017), arXiv:1702.00786 [astro- ph.IM]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[69]

and Berti, Emanuele and Caldwell, Robert and Camp, Jordan and Conklin, John W

John Bakeret al., “The Laser Interferometer Space An- tenna: Unveiling the Millihertz Gravitational Wave Sky,” (2019), arXiv:1907.06482 [astro-ph.IM]

work page arXiv 2019
[70]

The Taiji Program in Space for gravitational wave physics and the nature of gravity,

Wen-Rui Hu and Yue-Liang Wu, “The Taiji Program in Space for gravitational wave physics and the nature of gravity,” Natl. Sci. Rev.4, 685–686 (2017)

2017
[71]

Ruan, Z.-K

Wen-Hong Ruan, Zong-Kuan Guo, Rong-Gen Cai, and Yuan-Zhong Zhang, “Taiji program: Gravitational-wave sources,” Int. J. Mod. Phys. A35, 2050075 (2020), arXiv:1807.09495 [gr-qc]

work page arXiv 2020
[72]

TianQin: a space-borne gravitational wave detector

Jun Luoet al.(TianQin), “TianQin: a space-borne grav- itational wave detector,” Class. Quant. Grav.33, 035010 (2016), arXiv:1512.02076 [astro-ph.IM]

work page Pith review arXiv 2016
[73]

Possibility of direct measurement of the acceleration of the universe using 0.1-Hz band laser interferometer grav- itational wave antenna in space,

Naoki Seto, Seiji Kawamura, and Takashi Nakamura, “Possibility of direct measurement of the acceleration of the universe using 0.1-Hz band laser interferometer grav- itational wave antenna in space,” Phys. Rev. Lett.87, 9 221103 (2001), arXiv:astro-ph/0108011

work page arXiv 2001
[74]

Detecting a gravitational-wave background with next-generation space interferometers

Hideaki Kudoh, Atsushi Taruya, Takashi Hiramatsu, and Yoshiaki Himemoto, “Detecting a gravitational-wave background with next-generation space interferometers,” Phys. Rev. D73, 064006 (2006), arXiv:gr-qc/0511145

work page Pith review arXiv 2006
[75]

Current status of space gravitational wave antenna DECIGO and B-DECIGO,

Seiji Kawamuraet al., “Current status of space gravita- tional wave antenna DECIGO and B-DECIGO,” PTEP 2021, 05A105 (2021), arXiv:2006.13545 [gr-qc]

work page arXiv 2021
[76]

Crowder and N

Jeff Crowder and Neil J. Cornish, “Beyond LISA: Ex- ploring future gravitational wave missions,” Phys. Rev. D72, 083005 (2005), arXiv:gr-qc/0506015

work page arXiv 2005
[77]

BBO and the neutron-star- binary subtraction problem,

C. Cutler and J. Harms, “BBO and the neutron-star- binary subtraction problem,” Phys. Rev. D73, 042001 (2006), arXiv:gr-qc/0511092

work page arXiv 2006
[78]

Sensitivity curves for searches for gravitational-wave backgrounds,

Eric Thrane and Joseph D. Romano, “Sensitivity curves for searches for gravitational-wave backgrounds,” Phys. Rev. D88, 124032 (2013), arXiv:1310.5300 [astro-ph.IM]

work page arXiv 2013
[79]

Character- ization of the LIGO detectors during their sixth sci- ence run,

J. Aasiet al.(LIGO Scientific, VIRGO), “Character- ization of the LIGO detectors during their sixth sci- ence run,” Class. Quant. Grav.32, 115012 (2015), arXiv:1410.7764 [gr-qc]

work page arXiv 2015
[80]

Observation of Gravitational Waves from a Binary Black Hole Merger

B. P. Abbottet al.(LIGO Scientific, Virgo), “Obser- vation of Gravitational Waves from a Binary Black Hole Merger,” Phys. Rev. Lett.116, 061102 (2016), arXiv:1602.03837 [gr-qc]

work page internal anchor Pith review arXiv 2016
[81]

Search for the isotropic stochastic background using data from Advanced LIGO’s second observing run,

B. P. Abbottet al.(LIGO Scientific, Virgo), “Search for the isotropic stochastic background using data from Ad- vanced LIGO’s second observing run,” Phys. Rev. D100, 061101 (2019), arXiv:1903.02886 [gr-qc]

work page arXiv 2019

Showing first 80 references.