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Gravitational Waves from Spectator Scalar Fields

T0 review · 2 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A spectator scalar field near the inflationary Hubble scale can source a gravitational-wave background detectable across 10^-20 Hz to 1 Hz; current non-detections already bound its mass above 0.66 H_I.

desk verdict Useful numerical parameter scan of an already-known mechanism, but the load-bearing factorization in Eq. S-52 is asserted for superhorizon modes and used for subhorizon source modes, so the quantitative bounds are not yet established. read the letter →

arxiv 2506.12126 v1 pith:VUQSIHL6 submitted 2025-06-13 hep-ph astro-ph.COgr-qc

Marcos A. G. Garcia , Sarunas Verner This is my paper
classification hep-phastro-ph.COgr-qc
keywords gravitationalwavesspectatorscalarfieldsinflationisocurvatureperturbationsreheatingdarkmatterpulsartimingarraysCMBB-modes
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

The paper proposes a mechanism in which a spectator scalar field—present during inflation but not driving cosmic expansion—produces a detectable gravitational-wave background through its isocurvature fluctuations. Because the fluctuations are blue-tilted, they can satisfy Planck's tight bounds on CMB scales while still being large on the small scales probed by gravitational-wave detectors. For effective masses near the inflationary Hubble scale, $m_{\rm eff} \sim H_I$, the predicted background reaches $\Omega_{\mathrm{GW}} h^2 \sim 10^{-12}$ and spans frequencies from $10^{-20}$ Hz to 1 Hz, putting it in reach of pulsar timing arrays, space-based interferometers, and ground-based detectors. The same setup yields new constraints: gravitational-wave-induced $\Delta N_{\rm eff}$ requires $m_\chi \gtrsim 0.61 H_I$, and the absence of primordial B-modes requires $m_\chi \gtrsim 0.66 H_I$, sharper than the isocurvature bound alone. If correct, this makes the gravitational-wave sky a multi-messenger window into reheating, heavy dark matter, and the inflationary particle content.

What carries the argument

The load-bearing object is the isocurvature power spectrum $\Delta^2_S(\eta,k)$ of the spectator field, built from the two-point function of its energy-density fluctuations. The paper's analytic gravitational-wave result uses the factorization $\Delta^2_S(\eta,k) = T_S(\eta)\,\Delta^2_S(k)$ for superhorizon modes with $k < aH$, which separates time evolution from the momentum structure of the source. Feeding this into the induced-gravitational-wave formalism gives a factorized spectrum $\Delta^2_h(k,N) = 2\big[\frac{1}{8}\int dN'\, G_k(N,N') T_S(N') (aH/k)^2 (\rho_\chi/H^2 M_P^2)^2\big]^2 g(k)$, where $g(k)$ is a double momentum integral over $\Delta^2_S(p)\Delta^2_S(q)$. The blue tilt is set by $\Lambda = 2m_{\rm eff}^2/3H_I^2$, which determines how quickly the spectrum grows toward small scales, and the post-inflationary enhancement is controlled by the spectator-to-radiation density ratio $f_\chi$, which produces a peak in the curvature spectrum at the decay scale $k_d$. Mode equations are evolved numerically from Bunch-Davies initial conditions, with the renormalized energy density defined through normal-ordered, adiabatic-regularized operators.

What would settle it

Compute the full two-time isocurvature correlation function $\Delta^2_S(\eta,k)$ mode by mode across all superhorizon $k$: if the ratio $\Delta^2_S(\eta,k_1)/\Delta^2_S(\eta,k_2)$ varies with $\eta$ for two fixed superhorizon wavenumbers, the factorization in Eq. (S-52) is violated and the analytic $\Omega_{\mathrm{GW}}$ formula of Eq. (S-62) does not follow. A second, observational check would be a null search at the predicted peak amplitude in the pulsar-timing band: if sensitivity crosses the predicted $\Omega_{\mathrm{GW}} h^2$ for the sweet-spot masses near $m_\chi \simeq 0.7 H_I$ and no signal appears, the mechanism's predicted reach is excluded.

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Extended reading notes

Core claim

The central claim is that a heavy spectator scalar field whose effective mass is comparable to the inflationary Hubble scale, $m_{\rm eff} \sim H_I$, generates a strongly blue-tilted isocurvature spectrum $\Delta^2_S(k) \simeq \Lambda^2 (k/k_{\rm end})^{2\Lambda} \ln(k/H_I)(H_{\rm end}/H_I)^{2\Lambda}$ with $\Lambda = 2m_{\rm eff}^2/3H_I^2$. This spectrum is suppressed at CMB pivot scales by construction but dominates at the sub-CMB scales that source secondary gravitational waves, whose present-day abundance is predicted as $\Omega_{\mathrm{GW}} h^2$ from about $10^{-20}$ to $10^{-12}$ over $10^{-20}$ Hz to 1 Hz. The calculation follows the complete history from inflation through reheating, distinguishing a decaying spectator (amplitude growing with reheating temperature as $T_{\rm reh}^{4/3}$) from a stable one that survives as dark matter (amplitude falling as $T_{\rm reh}^{-2/3}$). Combining the gravitational-wave background with CMB data, the paper derives lower bounds on the spectator mass: $m_\chi \gtrsim 0.54\,H_I$ from isocurvature alone, $m_\chi \gtrsim 0.61\,H_I$ from $\Delta N_{\rm eff}$, and $m_\chi \gtrsim 0.66\,H_I$ from the non-observation of primordial B-modes, with projected CMB B-mode experiments reaching $m_\chi \gtrsim 0.70\,H_I$.

Load-bearing premise

The whole gravitational-wave calculation assumes that every superhorizon mode's isocurvature power spectrum changes with time by the same factor, so that $\Delta^2_S(\eta,k)=T_S(\eta)\Delta^2_S(k)$; the paper states this holds numerically but supplies no derivation, so if it fails the predicted amplitudes and mass bounds shift.

Editorial extensions

If this is right

  • The same spectator mechanism places correlated, potentially observable signals in pulsar timing arrays, space-based interferometers, and ground-based detectors, so multi-band gravitational-wave astronomy could confirm or exclude it.
  • A non-detection at predicted amplitudes would tighten the lower bound on the spectator mass beyond $m_\chi \gtrsim 0.66 H_I$, with next-generation B-mode experiments able to reach $m_\chi \gtrsim 0.70 H_I$.
  • Because the amplitude scales as $T_{\rm reh}^{4/3}$ for decaying spectators and $T_{\rm reh}^{-2/3}$ for stable ones, measuring the background would constrain the reheating temperature and hence the thermal history between inflation and Big Bang Nucleosynthesis.
  • For purely gravitational production, the dark matter relic abundance $\Omega_\chi h^2=0.12$ selects masses around $m_\chi/H_I \simeq 0.5$-$0.7$ for reheating temperatures of roughly $10^2$-$10^3$ GeV, providing concrete targets for future detectors.
  • The spectral tilt and peak frequency of the induced background are inherited from $\Lambda$ and the decay scale $k_d$, so a detection would measure the ratio $m_{\rm eff}/H_I$ and the reheating temperature simultaneously.

Reading between the lines

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

  • If the factorization in Eq. (S-52) holds only for a limited range of superhorizon $k$, the frequency shape of $\Omega_{\mathrm{GW}} h^2$ and the derived mass bounds would change; a direct numerical computation of the two-time isocurvature spectrum mode by mode would settle how robust the analytic formula is.
  • The calculation drops the connected trispectrum as a perturbative correction; if spectator-field fluctuations are appreciably non-Gaussian, the induced gravitational-wave spectrum could be enhanced or suppressed in a frequency-dependent way, so non-Gaussianity is a testable hidden parameter of the mechanism.
  • The same logic could be applied to any plateau-like inflationary potential by rescaling $H_I$, $H_{\rm end}$, and the reheating history, which suggests the constraints reported here are transferable beyond the concrete potential used for the numerics.
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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

2 major / 4 minor

Summary. The paper proposes that spectator scalar fields with effective masses near the inflationary Hubble scale generate blue-tilted isocurvature perturbations that source a secondary gravitational wave background. The authors compute the isocurvature power spectrum from first principles via numerical mode evolution and derive the induced GW spectrum using a factorized Green's-function formalism. They claim this background spans 10^-20 to 1 Hz with amplitudes up to Ω_GW h^2 ~ 10^-12, and they use GW-induced ΔN_eff, CMB B-mode, and isocurvature constraints to derive lower bounds on the spectator mass: m_χ ≳ 0.61 H_I (ΔN_eff), m_χ ≳ 0.66 H_I (Planck B-modes), and m_χ ≳ 0.70 H_I (projected LiteBIRD). The paper includes a substantial supplemental derivation of the regularized energy density, the isocurvature power spectrum, and the induced GW formalism.

Significance. If the central derivation is correct, the paper identifies a new, falsifiable multi-messenger window into spectator-field physics during inflation, with potentially observable signals across PTA, space-based, and ground-based GW detectors and complementary constraints from CMB experiments. A strength is that the predictions are not fit to GW data: the isocurvature spectrum and GW amplitude are computed from the model parameters (m_χ, σ, T_reh, λ, N_*), with only the observed DM abundance used to select benchmark points. The detailed supplemental material provides the full mode evolution and regularization steps, making the computation transparent and reproducible in principle. The derived mass bounds are concrete and give sharp observational targets.

major comments (2)
  1. [Supplemental Material, Eqs. (S-51)-(S-63)] Equation (S-52) states that the numerical analysis establishes the factorization Δ²_S(η,k) = T_S(η)Δ²_S(k) only for superhorizon modes (k < aH). This factorization is then substituted into the source two-point function (S-51) and used in the Green's-function integral (S-62), whose momentum-space kernel g(k) (S-63) integrates over all p and q, including modes with p, q > aH at the times that dominate the Green's-function integral. For subhorizon modes the isocurvature power spectrum is expected to develop a k-dependent, oscillating evolution after horizon entry, and the SM itself notes in Section S-II that the full expression (S-30) is required 'particularly at small scales relevant for gravitational wave signatures.' Since the predicted Ω_GW amplitude, spectral shape, and the bounds m_χ ≳ 0.61, 0.66, and 0.70 H_I all pass through Eq. (S-62), this missing justification is load-bearing. Please demonstrate quantitatively that subhorizon-mode contributions to the source are negligible, or recompute the GW spectrum using the full time-dependent expression (S-30) inside the Green's function integral and show that the results are unchanged.
  2. [Results and Discussion, Fig. 3] The exclusion regions labeled 'Planck r' and 'LiteBIRD r' in Fig. 3 are attributed to non-observation of primordial B-modes, but the manuscript does not explain how the induced GW background Ω_GW(f) is translated into a CMB B-mode limit. This mapping is non-trivial: CMB B-modes are sensitive to the GW spectrum at frequencies near the Hubble scale at decoupling, whereas the peak of the predicted Ω_GW lies at much higher frequencies. Please provide the derivation or a quantitative reference for the conversion used to draw these regions; without it, the claimed constraints m_χ ≳ 0.66 H_I (Planck) and m_χ ≳ 0.70 H_I (LiteBIRD) are not reproducible.
minor comments (4)
  1. [Section headings] The headings 'F ramework' and 'Gravitational W aves' contain stray spaces; please fix the typography.
  2. [Main text, Eq. (10)] Please specify the range of k over which the fitting formula Δ²_S(k) is validated against the numerical results, and clarify whether this fitted form is used in the GW computation or only for illustrative purposes.
  3. [Fig. 2, bottom panel] The bottom panel's frequency axis extends well beyond 1 Hz, which is inconsistent with the abstract's stated range of 10^-20 to 1 Hz; please align the axes or clarify that the 1 Hz statement refers only to the location of the peak.
  4. [Lagrangian, Eq. (2)] The spectator field has no explicit decay operator in the Lagrangian, but the text repeatedly assumes a decay time t_d; please state the assumed decay mechanism or clarify that it is an effective parametrization of an unspecified coupling.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the GW predictions are computed from a numerical isocurvature spectrum and standard induced-GW transfer functions, with external CMB/PTA bounds used only for comparison.

full rationale

The paper's claimed derivation chain is self-contained and does not reduce to its inputs by construction. The isocurvature power spectrum is obtained from a numerical evolution of the spectator-field mode equations, with the analytic fit in Eq. (10) serving only as a representation of the numerical result; the GW spectrum is then obtained from the standard second-order scalar-induced GW formalism, Eqs. (S-36)-(S-64), using the Gaussian disconnected four-point function. No experimental data are fitted to produce the predicted Omega_GW values, and the quoted bounds on m_chi are comparisons against external Planck/BICEP/Keck, Delta_N_eff, and isocurvature limits, rather than outputs of a parameter fit. Some methodological self-citations appear ([26], [27], [50], [51], [54]) for normal-ordering techniques, the T-model analysis, and alternative analytic approximations, but none is load-bearing: the derivations in the main text and SM are carried out here. The one unresolved assumption is Eq. (S-52), Delta^2_S(eta,k) = T_S(eta) Delta^2_S(k), stated as found from numerical analysis but only explicitly justified for k < aH; if the factorization fails for subhorizon source modes in the GW integrals (S-62)-(S-63), the quantitative results would change. This is a correctness-risk / omitted-proof concern, not a circularity, because the factorization is an approximation about the physics rather than the target prediction being reused as an input.

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

The model uses standard spectator scalar field physics with mass m_chi and coupling sigma to the inflaton, plus the T-model inflaton potential. The free parameters are the mass, coupling, reheating temperature, and the inflaton-related parameters lambda and N*. The key auxiliary assumptions are the Bunch-Davies vacuum, the inflaton decay to radiation, the zero background field value, the negligibility of non-Gaussianities, and the factorization of the isocurvature spectrum. No new particles or forces are introduced.

free parameters (5)
  • m_chi (spectator bare mass) = Scanned over 0.5 to 0.9 H_I; constraints m_chi/H_I > 0.54-0.70
    Central parameter of the model; varied to produce the spectra and to derive lower bounds from isocurvature, Delta N_eff, and B-mode constraints.
  • sigma (inflaton-spectator coupling) = sigma/lambda = 0 to 0.18 in scans
    Controls the effective mass during inflation; varied to explore coupling scenarios and peaked spectra.
  • T_reh (reheating temperature) = 10^9 to 2x10^15 GeV in scans; in the dark matter scenario chosen to match Omega_chi h^2 = 0.12
    Sets the expansion history, the mode k_d, and the gravitational wave amplitude; not fixed by the model.
  • lambda (inflaton quartic coupling) = about 2x10^{-11}
    Normalized to Planck CMB amplitude via lambda approximately 3 pi^2 Delta^2_zeta(k*) / N*^2 (main text after Eq. (7)).
  • N* (number of e-folds) = 55
    Chosen to match the spectral tilt and tensor-to-scalar ratio; not derived in this paper.
assumptions (5)
  • standard math Bunch-Davies vacuum initial conditions for spectator field modes.
    Main text after Eq. (5): 'initial conditions set by the Bunch-Davies vacuum'.
  • domain assumption The inflaton decays entirely into radiation, so its curvature perturbation equals the radiation perturbation (zeta_phi = zeta_R).
    Main text footnote 3: 'We assume the inflaton decays into radiation, thus zeta_phi = zeta_R'.
  • domain assumption The spectator field has vanishing background value <chi> = 0.
    Main text: 'For spectator scalar field chi with vanishing background value <chi> = 0'.
  • domain assumption Connected (non-Gaussian) part of the delta_rho_chi four-point function is negligible; the gravitational wave spectrum is computed from the disconnected part.
    Main text near Eq. (18): 'we assume that there is no significant presence of primordial non-Gaussianities as perturbative corrections to the Gaussian statistics'.
  • ad hoc to paper The isocurvature power spectrum factorizes as Delta^2_S(eta,k) = T_S(eta) Delta^2_S(k) for superhorizon modes (k < aH).
    Supplemental Material Eq. (S-52): 'we found from the numerical analysis'.

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Cite this review

Pith. "Pith review of Gravitational Waves from Spectator Scalar Fields." pith.science (2026). https://pith.science/paper/VUQSIHL6

@misc{pith2026250612126,
  author       = {Pith},
  title        = {Pith review of: Gravitational Waves from Spectator Scalar Fields},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VUQSIHL6}},
  note         = {Machine review of arXiv:2506.12126}
}
abstract

We propose a novel mechanism for gravitational wave (GW) production sourced by spectator scalar fields during inflation. These fields, while not driving cosmic expansion, generate blue-tilted isocurvature fluctuations that naturally satisfy current CMB constraints at large scales while producing enhanced power spectra at smaller scales accessible to GW detectors. The resulting GW spectrum spans an exceptionally broad frequency range from $10^{-20}$ to $1$ Hz, with amplitudes ranging from $\Omega_{\text{GW}}h^2 \sim 10^{-20}$ to $10^{-12}$ depending on the reheating temperature and spectator field mass. For heavy spectator fields with effective masses near the inflationary Hubble scale $H_I$, the mechanism produces observable signals across multiple detector bands accessible to pulsar timing arrays, space-based interferometers, and ground-based detectors. Our analysis reveals multiple complementary constraints on spectator field parameters. GW-induced limits on the effective number of relativistic species ($\Delta N_{\text{eff}}$) require $m_\chi \gtrsim 0.61 H_I$, stronger than CMB isocurvature bounds alone ($m_\chi \gtrsim 0.54 H_I$). The non-observation of primordial B-modes by \textit{Planck} provides stronger constraints $m_\chi \gtrsim 0.66 H_I$, with projected LiteBIRD sensitivity potentially reaching $m_\chi \gtrsim 0.70 H_I$. This mechanism enables a unique multi-messenger probe of beyond the Standard Model physics during inflation, providing simultaneous constraints on inflationary dynamics, dark matter production, and reheating through current and next-generation GW experiments.

Figures

Figures reproduced from arXiv: 2506.12126 by the authors.

Figure 1
Figure 1. FIG. 1. Curvature power spectra for selected spectator field masses and couplings. Each panel shows four reheating tem [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Parameter space constraints for purely gravitational [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Gravitational wave spectra for two spectator field [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

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Forward citations

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Reference graph

Works this paper leans on

80 extracted references · 12 canonical work pages · cited by 3 Pith papers

  1. [1]

    sweet spots

    By substituting the Fourier-decomposed field from Eq. (4) into the equation of motion (3), we obtain the mode equation: X ′′ k + ω2 kXk = 0 , with ω2 k = k2 + a2m2 eff , (5) where primes denote derivatives with respect to confor- mal time. Evaluating GW signals from spectator scalar fields re- quires careful treatment of their gravitational produc- tion d...

    work page 2018

  2. [2]

    The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,

    Alan H. Guth, “The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,” Phys. Rev. D 23, 347–356 (1981)

    1981

  3. [3]

    A New Type of Isotropic Cos- mological Models Without Singularity,

    Alexei A. Starobinsky, “A New Type of Isotropic Cos- mological Models Without Singularity,” Phys. Lett. B , 99–102 (1980)

    work page 1980

  4. [4]

    A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogene- ity, Isotropy and Primordial Monopole Problems,

    Andrei D. Linde, “A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogene- ity, Isotropy and Primordial Monopole Problems,” Phys. Lett. B 108, 389–393 (1982)

    work page 1982

  5. [5]

    Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking,

    Andreas Albrecht and Paul J. Steinhardt, “Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking,” Phys. Rev. Lett. 48, 1220–1223 (1982)

    work page 1982

  6. [6]

    Chaotic Inflation,

    Andrei D. Linde, “Chaotic Inflation,” Phys. Lett. B 129, 177–181 (1983)

    1983

  7. [7]

    Gravitational Wave Spectrum In- duced by Primordial Scalar Perturbations,

    Daniel Baumann, Paul J. Steinhardt, Keitaro Takahashi, and Kiyotomo Ichiki, “Gravitational Wave Spectrum In- duced by Primordial Scalar Perturbations,” Phys. Rev. D 76, 084019 (2007), arXiv:hep-th/0703290

    arXiv 2007

  8. [8]

    A Probe of primordial gravity waves and vorticity,

    Marc Kamionkowski, Arthur Kosowsky, and Albert Stebbins, “A Probe of primordial gravity waves and vorticity,” Phys. Rev. Lett. 78, 2058–2061 (1997), arXiv:astro-ph/9609132

    arXiv 1997

Show all 80 references
  1. [9]

    Signature of grav- ity waves in polarization of the microwave background,

    Uros Seljak and Matias Zaldarriaga, “Signature of grav- ity waves in polarization of the microwave background,” Phys. Rev. Lett. 78, 2054–2057 (1997), arXiv:astro- ph/9609169

    1997

  2. [10]

    Planck 2018 results. X. Constraints on inflation,

    Y. Akrami et al. (Planck), “Planck 2018 results. X. Constraints on inflation,” Astron. Astrophys. 641, A10 (2020), arXiv:1807.06211 [astro-ph.CO]

    2020 arXiv

  3. [11]

    Minimally Parametric Power Spectrum Recon- struction from the Lyman-alpha Forest,

    Simeon Bird, Hiranya V. Peiris, Matteo Viel, and Licia Verde, “Minimally Parametric Power Spectrum Recon- struction from the Lyman-alpha Forest,” Mon. Not. Roy. Astron. Soc. 413, 1717–1728 (2011), arXiv:1010.1519 [astro-ph.CO]

    2011 arXiv

  4. [12]

    Spacetime curvature and the Higgs sta- bility during inflation,

    Matti Herranen, Tommi Markkanen, Sami Nurmi, and Arttu Rajantie, “Spacetime curvature and the Higgs sta- bility during inflation,” Phys. Rev. Lett. 113, 211102 (2014), arXiv:1407.3141 [hep-ph]

    2014 arXiv

  5. [13]

    Cos- mological implications of the Higgs mass measurement,

    J. R. Espinosa, G. F. Giudice, and A. Riotto, “Cos- mological implications of the Higgs mass measurement,” JCAP 05, 002 (2008), arXiv:0710.2484 [hep-ph]

    2008 arXiv

  6. [14]

    Gravitational waves from dark matter isocurvature,

    Guillem Dom` enech, Samuel Passaglia, and S´ ebastien Renaux-Petel, “Gravitational waves from dark matter isocurvature,” JCAP 03, 023 (2022), arXiv:2112.10163 [astro-ph.CO]

    2022 arXiv

  7. [15]

    Cosmological gravitational waves from isocurvature fluctuations,

    Guillem Dom` enech, “Cosmological gravitational waves from isocurvature fluctuations,” AAPPS Bull. 34, 4 (2024), arXiv:2311.02065 [gr-qc]

    2024 arXiv

  8. [16]

    Gravitational Waves from Stochastic Scalar Fluctuations,

    Reza Ebadi, Soubhik Kumar, Amara McCune, Hanwen Tai, and Lian-Tao Wang, “Gravitational Waves from Stochastic Scalar Fluctuations,” (2023), arXiv:2307.01248 [astro-ph.CO]

    2023 arXiv

  9. [17]

    Gravitational Wave Symphony from Oscillating Specta- tor Scalar Fields,

    Yanou Cui, Pankaj Saha, and Evangelos I. Sfakianakis, “Gravitational Wave Symphony from Oscillating Specta- tor Scalar Fields,” Phys. Rev. Lett. 133, 021004 (2024), arXiv:2310.13060 [hep-ph]

    2024 arXiv

  10. [18]

    Primordial black holes from inflaton and spectator field perturbations in a matter-dominated era,

    Bernard Carr, Tommi Tenkanen, and Ville Vaskonen, “Primordial black holes from inflaton and spectator field perturbations in a matter-dominated era,” Phys. Rev. D 96, 063507 (2017), arXiv:1706.03746 [astro-ph.CO]

    2017 arXiv

  11. [19]

    Primordial Black Holes as Dark Matter: Recent Developments,

    Bernard Carr and Florian Kuhnel, “Primordial Black Holes as Dark Matter: Recent Developments,” Ann. Rev. Nucl. Part. Sci. 70, 355–394 (2020), arXiv:2006.02838 [astro-ph.CO]

    2020 arXiv

  12. [20]

    Superheavy dark matter,

    Daniel J. H. Chung, Edward W. Kolb, and Antonio Riotto, “Superheavy dark matter,” Phys. Rev. D 59, 023501 (1998), arXiv:hep-ph/9802238

    1998 arXiv

  13. [21]

    Production of massive particles during reheating,

    Daniel J. H. Chung, Edward W. Kolb, and Antonio Ri- otto, “Production of massive particles during reheating,” Phys. Rev. D 60, 063504 (1999), arXiv:hep-ph/9809453

    1999 arXiv

  14. [22]

    Noninteracting dark matter,

    P. J. E. Peebles and A. Vilenkin, “Noninteracting dark matter,” Phys. Rev. D 60, 103506 (1999), arXiv:astro- ph/9904396

    1999

  15. [23]

    Curvature and isocurvature perturbations from two-field inflation in a slow-roll expansion,

    Christian T. Byrnes and David Wands, “Curvature and isocurvature perturbations from two-field inflation in a slow-roll expansion,” Phys. Rev. D 74, 043529 (2006), arXiv:astro-ph/0605679

    2006 arXiv

  16. [24]

    Spectator Dark Matter,

    Tommi Markkanen, Arttu Rajantie, and Tommi Tenka- nen, “Spectator Dark Matter,” Phys. Rev. D 98, 123532 (2018), arXiv:1811.02586 [astro-ph.CO]

    2018 arXiv

  17. [25]

    Cosmological gravitational particle production and its implications for cosmological relics,

    Edward W. Kolb and Andrew J. Long, “Cosmological gravitational particle production and its implications for cosmological relics,” (2023), arXiv:2312.09042 [astro- ph.CO]

    2023 arXiv

  18. [26]

    Superheavy scalar dark matter from gravitational particle production in α- attractor models of inflation,

    Siyang Ling and Andrew J. Long, “Superheavy scalar dark matter from gravitational particle production in α- attractor models of inflation,” Phys. Rev. D 103, 103532 (2021), arXiv:2101.11621 [astro-ph.CO]

    2021 arXiv

  19. [27]

    Scalar dark matter production from preheating and structure formation constraints,

    Marcos A. G. Garcia, Mathias Pierre, and Sarunas Verner, “Scalar dark matter production from preheating and structure formation constraints,” Phys. Rev. D 107, 043530 (2023), arXiv:2206.08940 [hep-ph]

    2023 arXiv

  20. [28]

    Scalar Field Fluc- tuations and the Production of Dark Matter,

    Marcos A. G. Garcia, Wenqi Ke, Yann Mambrini, Keith A. Olive, and Sarunas Verner, “Scalar Field Fluc- tuations and the Production of Dark Matter,” (2025), arXiv:2502.20471 [hep-ph]. 7

    2025 arXiv

  21. [29]

    Non- gaussian isocurvature perturbations from inflation,

    Andrei D. Linde and Viatcheslav F. Mukhanov, “Non- gaussian isocurvature perturbations from inflation,” Phys. Rev. D 56, R535–R539 (1997), arXiv:astro- ph/9610219

    1997

  22. [30]

    Adiabatic CMB per- turbations in pre - big bang string cosmology,

    Kari Enqvist and Martin S. Sloth, “Adiabatic CMB per- turbations in pre - big bang string cosmology,” Nucl. Phys. B 626, 395–409 (2002), arXiv:hep-ph/0109214

    2002 arXiv

  23. [31]

    Effects of cos- mological moduli fields on cosmic microwave back- ground,

    Takeo Moroi and Tomo Takahashi, “Effects of cos- mological moduli fields on cosmic microwave back- ground,” Phys. Lett. B 522, 215–221 (2001), [Erra- tum: Phys.Lett.B 539, 303–303 (2002)], arXiv:hep- ph/0110096

    2001

  24. [32]

    Generating the cur- vature perturbation without an inflaton,

    David H. Lyth and David Wands, “Generating the cur- vature perturbation without an inflaton,” Phys. Lett. B 524, 5–14 (2002), arXiv:hep-ph/0110002

    2002 arXiv

  25. [33]

    Constraints Imposed by CP Conservation in the Presence of Instantons,

    R. D. Peccei and Helen R. Quinn, “Constraints Imposed by CP Conservation in the Presence of Instantons,” Phys. Rev. D 16, 1791–1797 (1977)

    1977

  26. [34]

    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

  27. [35]

    Opening up a Window on the Postinflationary QCD Axion,

    Yunjia Bao, JiJi Fan, and Lingfeng Li, “Opening up a Window on the Postinflationary QCD Axion,” Phys. Rev. Lett. 130, 241001 (2023), arXiv:2209.09908 [hep- ph]

    2023 arXiv

  28. [36]

    New in- flationary probes of axion dark matter,

    Xingang Chen, JiJi Fan, and Lingfeng Li, “New in- flationary probes of axion dark matter,” JHEP 12, 197 (2023), arXiv:2303.03406 [hep-ph]

    2023 arXiv

  29. [37]

    A Supersymmetry primer,

    Stephen P. Martin, “A Supersymmetry primer,” Adv. Ser. Direct. High Energy Phys. 18, 1–98 (1998), arXiv:hep-ph/9709356

    1998 arXiv

  30. [38]

    Freedman and Antoine Van Proeyen, Super- gravity (Cambridge Univ

    Daniel Z. Freedman and Antoine Van Proeyen, Super- gravity (Cambridge Univ. Press, Cambridge, UK, 2012)

    2012

  31. [39]

    The NANOGrav 15 yr Data Set: Search for Signals from New Physics,

    Adeela Afzal et al. (NANOGrav), “The NANOGrav 15 yr Data Set: Search for Signals from New Physics,” Astrophys. J. Lett. 951, L11 (2023), [Erratum: Astro- phys.J.Lett. 971, L27 (2024), Erratum: Astrophys.J. 971, L27 (2024)], arXiv:2306.16219 [astro-ph.HE]

    2023 arXiv

  32. [40]

    European Pulsar Timing Ar- ray Limits On An Isotropic Stochastic Gravitational- Wave Background,

    L. Lentati et al. (EPTA), “European Pulsar Timing Ar- ray Limits On An Isotropic Stochastic Gravitational- Wave Background,” Mon. Not. Roy. Astron. Soc. 453, 2576–2598 (2015), arXiv:1504.03692 [astro-ph.CO]

    2015 arXiv

  33. [41]

    European Pulsar Tim- ing Array Limits on Continuous Gravitational Waves from Individual Supermassive Black Hole Binaries,

    Stanislav Babak et al. (EPTA), “European Pulsar Tim- ing Array Limits on Continuous Gravitational Waves from Individual Supermassive Black Hole Binaries,” Mon. Not. Roy. Astron. Soc. 455, 1665–1679 (2016), arXiv:1509.02165 [astro-ph.CO]

    2016 arXiv

  34. [42]

    Fundamental physics with the Square Kilometre Array,

    A. Weltman et al., “Fundamental physics with the Square Kilometre Array,” Publ. Astron. Soc. Austral. 37, e002 (2020), arXiv:1810.02680 [astro-ph.CO]

    2020 arXiv

  35. [43]

    Laser Interferome- ter Space Antenna,

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

    2017 arXiv

  36. [44]

    Beyond LISA: Ex- ploring future gravitational wave missions,

    Jeff Crowder and Neil J. Cornish, “Beyond LISA: Ex- ploring future gravitational wave missions,” Phys. Rev. D 72, 083005 (2005), arXiv:gr-qc/0506015

    2005 arXiv

  37. [45]

    Detector configuration of DECIGO/BBO and identification of cosmologi- cal neutron-star binaries,

    Kent Yagi and Naoki Seto, “Detector configuration of DECIGO/BBO and identification of cosmologi- cal neutron-star binaries,” Phys. Rev. D 83, 044011 (2011), [Erratum: Phys.Rev.D 95, 109901 (2017)], arXiv:1101.3940 [astro-ph.CO]

    2011 arXiv

  38. [46]

    Open data from the first and second observing runs of Advanced LIGO and Advanced Virgo,

    Rich Abbott et al. (LIGO Scientific, Virgo), “Open data from the first and second observing runs of Advanced LIGO and Advanced Virgo,” SoftwareX 13, 100658 (2021), arXiv:1912.11716 [gr-qc]

    2021 arXiv

  39. [47]

    The Einstein Telescope: A third-generation gravitational wave observatory,

    M. Punturo et al. , “The Einstein Telescope: A third-generation gravitational wave observatory,” Class. Quant. Grav. 27, 194002 (2010)

    2010

  40. [48]

    Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy be- yond LIGO,

    David Reitze et al. , “Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy be- yond LIGO,” Bull. Am. Astron. Soc. 51, 035 (2019), arXiv:1907.04833 [astro-ph.IM]

    2019 arXiv

  41. [49]

    Towards the theory of reheating after infla- tion,

    Lev Kofman, Andrei D. Linde, and Alexei A. Starobin- sky, “Towards the theory of reheating after infla- tion,” Phys. Rev. D 56, 3258–3295 (1997), arXiv:hep- ph/9704452

    1997

  42. [50]

    Non-minimal Inflationary Attractors,

    Renata Kallosh and Andrei Linde, “Non-minimal Inflationary Attractors,” JCAP 10, 033 (2013), arXiv:1307.7938 [hep-th]

    2013 arXiv

  43. [51]

    BICEP/Keck Con- straints on Attractor Models of Inflation and Reheating,

    John Ellis, Marcos A. G. Garcia, Dimitri V. Nanopoulos, Keith A. Olive, and Sarunas Verner, “BICEP/Keck Con- straints on Attractor Models of Inflation and Reheating,” (2021), arXiv:2112.04466 [hep-ph]

    2021 arXiv

  44. [52]

    Isocurvature Constraints on Scalar Dark Matter Production from the Inflaton,

    Marcos A. G. Garcia, Mathias Pierre, and Sarunas Verner, “Isocurvature Constraints on Scalar Dark Matter Production from the Inflaton,” (2023), arXiv:2303.07359 [hep-ph]

    2023 arXiv

  45. [53]

    Scalar dark matter production from the inflaton,

    Mathias Pierre, “Scalar dark matter production from the inflaton,” in Rencontres de Blois 2023 (2023) arXiv:2309.08305 [hep-ph]

    2023 arXiv

  46. [54]

    Scalar correlation functions in de Sitter space from the stochastic spectral expansion,

    Tommi Markkanen, Arttu Rajantie, Stephen Stopyra, and Tommi Tenkanen, “Scalar correlation functions in de Sitter space from the stochastic spectral expansion,” JCAP 08, 001 (2019), arXiv:1904.11917 [gr-qc]

    2019 arXiv

  47. [55]

    Infla- ton production of scalar dark matter through fluctua- tions and scattering,

    Gongjun Choi, Marcos A. G. Garcia, Wenqi Ke, Yann Mambrini, Keith A. Olive, and Sarunas Verner, “Infla- ton production of scalar dark matter through fluctua- tions and scattering,” Phys. Rev. D 110, 083512 (2024), arXiv:2406.06696 [hep-ph]

    2024 arXiv

  48. [56]

    Spectral Distortions of the CMB as a Probe of Inflation, Recombination, Structure Formation and Particle Physics: Astro2020 Science White Paper,

    J. Chluba et al. , “Spectral Distortions of the CMB as a Probe of Inflation, Recombination, Structure Formation and Particle Physics: Astro2020 Science White Paper,” Bull. Am. Astron. Soc. 51, 184 (2019), arXiv:1903.04218 [astro-ph.CO]

    2019 arXiv

  49. [57]

    CMB Spectral Distortions: Status and Prospects,

    A. Kogut, M. H. Abitbol, J. Chluba, J. Delabrouille, D. Fixsen, J. C. Hill, S. P. Patil, and A. Rotti, “CMB Spectral Distortions: Status and Prospects,” Bull. Am. Astron. Soc. 51, 113 (2019), arXiv:1907.13195 [astro- ph.CO]

    2019 arXiv

  50. [58]

    Probing Small-Scale Power Spectra with Pulsar Timing Arrays,

    Vincent S. H. Lee, Andrea Mitridate, Tanner Trickle, and Kathryn M. Zurek, “Probing Small-Scale Power Spectra with Pulsar Timing Arrays,” JHEP 06, 028 (2021), arXiv:2012.09857 [astro-ph.CO]

    2021 arXiv

  51. [59]

    Science with the Square Kilometer Array: Motivation, key science projects, stan- dards and assumptions,

    Chris L. Carilli and S. Rawlings, “Science with the Square Kilometer Array: Motivation, key science projects, stan- dards and assumptions,” New Astron. Rev. 48, 979 (2004), arXiv:astro-ph/0409274

    2004 arXiv

  52. [60]

    Gravitational wave astron- omy with the SKA,

    Gemma Janssen et al. , “Gravitational wave astron- omy with the SKA,” PoS AASKA14, 037 (2015), arXiv:1501.00127 [astro-ph.IM]

    2015 arXiv

  53. [61]

    The Laser Interferometer Space An- tenna: Unveiling the Millihertz Gravitational Wave Sky,

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

    2019 arXiv

  54. [62]

    Detecting the cos- mic gravitational wave background with the big bang observer,

    Vincent Corbin and Neil J. Cornish, “Detecting the cos- mic gravitational wave background with the big bang observer,” Class. Quant. Grav. 23, 2435–2446 (2006), arXiv:gr-qc/0512039

    2006 arXiv

  55. [63]

    No-go theorem for scalar- trispectrum-induced gravitational waves,

    Sebastian Garcia-Saenz, Lucas Pinol, S´ ebastien Renaux- 8 Petel, and Denis Werth, “No-go theorem for scalar- trispectrum-induced gravitational waves,” JCAP 03, 057 (2023), arXiv:2207.14267 [astro-ph.CO]

    2023 arXiv

  56. [64]

    Planck 2018 results. VI. Cosmological parameters,

    N. Aghanim et al. (Planck), “Planck 2018 results. VI. Cosmological parameters,” Astron. Astrophys. 641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

    2020 arXiv

  57. [65]

    CMB-S4 Science Case, Reference Design, and Project Plan,

    Kevork Abazajian et al. , “CMB-S4 Science Case, Reference Design, and Project Plan,” (2019), arXiv:1907.04473 [astro-ph.IM]

    2019 arXiv

  58. [66]

    Snowmass2021 CMB- HD White Paper,

    Simone Aiola et al. (CMB-HD), “Snowmass2021 CMB- HD White Paper,” (2022), arXiv:2203.05728 [astro- ph.CO]

    2022 arXiv

  59. [67]

    LiteBIRD: A Satellite for the Studies of B-Mode Polarization and Inflation from Cosmic Back- ground Radiation Detection,

    M. Hazumi et al., “LiteBIRD: A Satellite for the Studies of B-Mode Polarization and Inflation from Cosmic Back- ground Radiation Detection,” J. Low Temp. Phys. 194, 443–452 (2019)

    2019

  60. [68]

    PICO: Probe of Inflation and Cosmic Origins,

    Marcelo Alvarez et al. , “PICO: Probe of Inflation and Cosmic Origins,” Bull. Am. Astron. Soc. 51, 194 (2019), arXiv:1908.07495 [astro-ph.IM]

    2019 arXiv

  61. [69]

    Prospective sensitivities of atom interferometers to gravitational waves and ultralight dark matter,

    Leonardo Badurina, Oliver Buchmueller, John Ellis, Marek Lewicki, Christopher McCabe, and Ville Vasko- nen, “Prospective sensitivities of atom interferometers to gravitational waves and ultralight dark matter,” Phil. Trans. A. Math. Phys. Eng. Sci. 380, 20210060 (2021), arXiv:...

    2021 arXiv

  62. [70]

    AEDGE: Atomic Experiment for Dark Matter and Gravity Ex- ploration in Space,

    Yousef Abou El-Neaj et al. (AEDGE), “AEDGE: Atomic Experiment for Dark Matter and Gravity Ex- ploration in Space,” EPJ Quant. Technol. 7, 6 (2020), arXiv:1908.00802 [gr-qc]

    2020 arXiv

  63. [71]

    Exploring the early Universe with Gaia and Theia,

    Juan Garcia-Bellido, Hitoshi Murayama, and Graham White, “Exploring the early Universe with Gaia and Theia,” JCAP 12, 023 (2021), arXiv:2104.04778 [hep-ph]

    2021 arXiv

  64. [72]

    Unveiling the gravitational uni- verse at µ-Hz frequencies,

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

    2021 arXiv

  65. [73]

    Improved Con- straints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season,

    P. A. R. Ade et al. (BICEP, Keck), “Improved Con- straints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season,” Phys. Rev. Lett. 127, 151301 (2021), arXiv:2110.00483 [astro-ph.CO]

    2021

  66. [74]

    N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics (Cambridge Univ. Press, Cambridge, UK, 1984)

    1984

  67. [75]

    Isocurvature constraints on gravitationally produced superheavy dark matter,

    Daniel J. H. Chung, Edward W. Kolb, Antonio Ri- otto, and Leonardo Senatore, “Isocurvature constraints on gravitationally produced superheavy dark matter,” Phys. Rev. D72, 023511 (2005), arXiv:astro-ph/0411468

    2005 arXiv

  68. [76]

    The Cosmological gravitational wave background from primordial density perturbations,

    Kishore N. Ananda, Chris Clarkson, and David Wands, “The Cosmological gravitational wave background from primordial density perturbations,” Phys. Rev. D 75, 123518 (2007), arXiv:gr-qc/0612013

    2007 arXiv

  69. [77]

    Scalar Induced Gravitational Waves Review,

    Guillem Dom` enech, “Scalar Induced Gravitational Waves Review,” Universe 7, 398 (2021), arXiv:2109.01398 [gr- qc]

    2021 arXiv

  70. [78]

    Non-Gaussianity and the induced gravita- tional wave background,

    Peter Adshead, Kaloian D. Lozanov, and Zachary J. Weiner, “Non-Gaussianity and the induced gravita- tional wave background,” JCAP 10, 080 (2021), arXiv:2105.01659 [astro-ph.CO]

    2021 arXiv

  71. [79]

    Imprints of Primordial Non-Gaussianity on Gravitational Wave Spectrum,

    Caner Unal, “Imprints of Primordial Non-Gaussianity on Gravitational Wave Spectrum,” Phys. Rev. D99, 041301 (2019), arXiv:1811.09151 [astro-ph.CO]

    2019 arXiv

  72. [80]

    Probing non- Gaussianities with the high frequency tail of induced gravitational waves,

    Vicente Atal and Guillem Dom` enech, “Probing non- Gaussianities with the high frequency tail of induced gravitational waves,” JCAP 06, 001 (2021), [Erratum: JCAP 10, E01 (2023)], arXiv:2103.01056 [astro-ph.CO]. 1 SUPPLEMENTAL MATERIAL “Gravitational Waves from Spectator Scala...

    2021 arXiv

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