Pith. sign in

REVIEW 4 major objections 4 minor 1 cited by

Gravitational wave signatures from reheating in Chern-Simons running-vacuum cosmology

T0 review · 4 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Reheating after inflation in a Chern-Simons running-vacuum cosmology produces a gravitational-wave background whose high-frequency tail scales as $f^6$ in $f(R)$ gravity, versus $f^7$ in general relativity.

desk verdict The f^6 scalaron scaling is the right question but is derived with a massless formula for a clearly massive mode, so the central detection claim is currently unsupported. read the letter →

arxiv 2411.14223 v1 pith:4MLWIRN5 submitted 2024-11-21 gr-qc astro-ph.COhep-th

Charalampos Tzerefos , Theodoros Papanikolaou , Spyros Basilakos , Emmanuel N. Saridakis , Nick E. Mavromatos This is my paper · ORCID
classification gr-qcastro-ph.COhep-th MSC 83C3583D0583F05 PACS 04.30.-w04.50.Kd98.80.Cq
keywords scalar-inducedgravitationalwavesf(R)gravityscalaronrunningvacuummodelaxionreheatingearlymatter-dominatederaChern-Simonswavebackground
open problems Quantum Gravity
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 aims to show that the reheating phase after inflation in a Chern-Simons running-vacuum cosmology leaves a distinctive gravitational-wave (GW) fingerprint. Treating the theory as an $f(R)$ gravity with logarithmic curvature corrections, the authors compute the GWs induced by curvature perturbations during a sudden transition from an axion-driven early matter-dominated era to radiation. Their central result is that the extra scalaron polarization produces a universal high-frequency scaling of the induced GW spectrum as $f^6$, whereas the standard general-relativistic signal scales as $f^7$. They find that for axion masses above 1 GeV and axion couplings above $10^{-3}$ times the Planck mass, the combined signal falls within the sensitivity of LISA, ET, BBO and SKA, making the spectral slope a potential discriminator between modified and standard gravity.

What carries the argument

The load-bearing device is the $f(R)$ rewriting of the Chern-Simons running-vacuum action, $f(R)=c_0+R(c_1+c_2\log(R/R_0))$, which turns the logarithmic quantum-gravity corrections into an extra scalar degree of freedom, the scalaron $\phi_s=F(R)$. The scalaron transfer function is built from the first-order Ricci scalar $R^{(1)}$, whose subhorizon approximation $R^{(1)}\simeq -2(k^2/a^2)\Phi^{(1)}/(1+4(k^2/a^2)F_R^{(0)}/F^{(0)})$ enters the tensor power spectrum $P_{h,\rm sc}(k)=T_s^2(x)P_\zeta(k)$. The sudden axion-decay transition provides the resonant kernel that amplifies the GR signal, and the condition $k^2/a^2 F_R^{(0)}/F^{(0)}\ll 1$ justifies setting $\Phi\simeq\Psi$, isolating the scalaron spectrum and producing the $f^6$ scaling. The coefficient $c_2$ sets the overall scalaron amplitude and hence the observability window.

What would settle it

A future observatory could settle the claim by resolving a stochastic gravitational-wave background from an early matter era and measuring its high-frequency slope: a clean $f^7$ tail would rule out the scalaron-dominated $f^6$ prediction, while an $f^6$ tail would support it. An ab initio calculation showing that the axion abundance is too small to dominate, or that reheating is too gradual, would also undercut the signal's amplitude.

Watch

Extended reading notes

Core claim

Working with the effective $f(R)$ action $f(R)=c_0+R(c_1+c_2\log(R/R_0))$, the paper derives the scalar-induced gravitational-wave signal sourced by the nearly scale-invariant adiabatic curvature perturbations as the axion-driven early matter era abruptly gives way to radiation. In $f(R)$ gravity there is an additional massive polarization mode, the scalaron $\phi_s=F(R)=\mathrm{d}f/\mathrm{d}R$, whose first-order contribution yields a GW abundance $\Omega_{\rm GW}^{\rm(sc)} \propto (c_2/M_{\rm Pl}^2)^2 (k/k_{\rm ra})^6 P_\zeta(k)$, i.e. a universal $f^6$ high-frequency tail. This holds for any $f(R)$ theory with negligible geometric anisotropic stress, $k^2/a^2 F_R^{(0)}/F^{(0)} \ll 1$, under which the two Bardeen potentials coincide. The GR part of the signal is the resonantly enhanced spectrum with a high-frequency $f^7$ tail. When $c_2$ is sufficiently large (for representative parameters, $c_2 \gtrsim 5.5\times 10^{-7}M_{\rm Pl}^2$), the scalaron contribution dominates and the total signal can be detected by LISA, ET, BBO or SKA for axion masses above 1 GeV and couplings above $10^{-3}M_{\rm Pl}$.

Load-bearing premise

The prediction stands or falls on the assumption that a compactification axion dominates the energy density during an early matter-dominated era and then decays suddenly to radiation, starting with a thermal-like abundance at $T_a \simeq m_a$.

Editorial extensions

If this is right

  • The $f^6$ high-frequency scaling is a universal prediction of any $f(R)$ gravity with negligible geometric anisotropic stress, not only of the Chern-Simons running-vacuum model.
  • For axion masses above roughly 1 GeV and couplings above $10^{-3}M_{\rm Pl}$, the scalaron-dominated spectrum reaches the sensitivity of LISA, ET, BBO and SKA, so a detection becomes a concrete experimental target.
  • A measured $f^6$ tail would be direct evidence of the extra scalaron polarization and of non-Einstein gravity at reheating energies.
  • The dominance condition translates into a lower bound on the logarithmic-correction coefficient $c_2$, so even a null detection can constrain the quantum-gravity parameter space.
  • Scalar-induced GWs become a probe of the underlying gravitational action, not just of the primordial perturbation amplitude.

Reading between the lines

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

  • The prediction relies on the axion being populated with a thermal-like abundance $T_a \simeq m_a$ and decaying abruptly; if axion production is non-thermal or the decay is gradual, both the resonant enhancement and the peak amplitudes would be suppressed, weakening observability.
  • For the lowest claimed masses ($m_a$ just above 1 GeV), the axion decay can occur after big-bang nucleosynthesis for some parameter choices, a consistency constraint the paper does not discuss.
  • The same $f(R)$ machinery could be applied to isocurvature perturbations or to Poisson fluctuations of the axion field, which would test whether the $f^6$ slope survives in those channels.
  • A direct test is to compute the axion abundance from the underlying string compactification; a value too low to dominate the energy density would invalidate the signal's premise.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper studies scalar-induced gravitational waves (SIGWs) produced during an early matter-dominated era driven by a compactification axion in the Chern-Simons running-vacuum model, treating the latter as an f(R) gravity with f(R)=c0+R(c1+c2 log(R/R0)). It uses the formalism of Zhou et al. to compute the scalaron contribution to the SIGW spectrum and finds a universal Omega_GW proportional to f^6 high-frequency scaling, versus f^7 in general relativity, and derives lower bounds on c2 above which the scalaron contribution dominates. For m_a > 1 GeV and f_a > 10^{-3} M_Pl, it claims detectability by LISA, ET, BBO, and SKA.

Significance. If the predictions held, the f^6 scaling would be a distinctive, falsifiable signature of a wide class of f(R) theories, and the proposed observability would provide a new probe of string-inspired quantum gravity. The paper is careful to stay within the linear regime (Eqs. 69-70), to present the anisotropic-stress check in Appendix A, and to derive rather than fit the c2 lower bounds (Eqs. 80 and 84). However, the central scalaron formula is imported from a preprint and used without checking the massive-mode regime, and the axion abundance at the onset of the eMD is not consistently derived; these issues put the quantitative predictions in question.

major comments (4)
  1. [§IV.B.1, Eqs. (66)-(78)] The scalaron contribution (77) is obtained by inserting the power spectrum P_h,sc = T_s^2 P_zeta into the massless GW abundance formula Omega_GW = (1/6)(k/H)^2 P_h (Eq. 67). In the f(R) model (1), the scalaron mass is m_s^2 approximately (1/3)F/F_R, so with F approximately c1 and F_R = c2/R, one has m_s/H approximately sqrt(c1/c2) during the AMDE. For the fiducial c2 = 10^{-8} M_Pl^2 this is about 7 x 10^3, and the condition (78), (k^2/a^2) F_R/F << 1, is equivalent to (k/a)^2 << m_s^2 up to an O(1) factor. Thus every mode in the range [k_ra, k_max] is non-relativistic at horizon crossing and remains so. A non-relativistic scalaron has energy density dominated by m_s^2 phi^2, not (k/a)^2 phi^2, so the replacement in Eq. (67) is not justified; the spectral index and the present-day abundance are not those of a massless tensor mode. The paper never evaluates m_s nor checks the relativistic limit, so the f^6 scaling and the detectability claims built on Eq. (77) are not established.
  2. [§III, Eqs. (40) and (74)] The temperature T_a at the onset of the AMDE is not used consistently. Eq. (40) gives T_a = [3 x 10^4/(64^2 zeta(3)) m_a^5/M_Pl^2]^{1/3} for f_a = 0.1 M_Pl, which for m_a = 10^4 GeV is about 5 x 10^{-6} GeV, not 1.1 x 10^{-9} M_Pl approximately 2.7 x 10^9 GeV as stated in the text. Eq. (74) then sets T_a approximately m_a, which is incompatible with Eq. (40) except for m_a of order 0.4 M_Pl, far outside the range plotted in Fig. 1. Since H_da, the peak frequency (73), and the bounds (79)-(84) all depend on T_a, the quantitative results rest on an unjustified abundance assumption. The authors should either derive T_a from the model's reheating history or treat T_a as a free parameter and show how the spectra and bounds depend on it.
  3. [§III (around Eq. 29) and §IV.A (Eq. 72)] The resonant enhancement in Eq. (72) is derived for a sudden transition from eMD to radiation, but the decay width (27) implies a gradual decay over a timescale Gamma_a^{-1}. At the end of the AMDE one has H approximately Gamma_a, so the decay takes roughly a Hubble time, not a sudden jump. The paper assumes a 'rather sharp transition' without quantifying it; the cited work on gradual transitions (Ref. [10]) shows that the resonant peak is suppressed as the transition duration increases. The amplitude of the predicted signal, including the detectability claims, depends on this unresolved modeling choice.
  4. [§V and Figs. 1-2 (parameter ranges)] The claimed detectable parameter range m_a > 1 GeV with f_a > 10^{-3} M_Pl is not checked against BBN. Using Eq. (27), for f_a = 10^{-3} M_Pl the axion lifetime Gamma_a^{-1} exceeds about 1 s for m_a less than about 10^3 GeV, meaning the eMD era would end after the onset of BBN; this conflicts with standard BBN and is not shown in the figures. The paper should impose Gamma_a^{-1} much less than 1 s (or the appropriate BBN bound) on the parameter space before claiming detectability for m_a down to 1 GeV.
minor comments (4)
  1. [Eq. (72)] The middle line reads 'for 1 << 1 < k/kra <= ...'; this appears to be a typo for '1 << k/kra <= ...'.
  2. [Eq. (67) and following text] The statement that 'the bar stands for an oscillation average' is not reflected by any bar notation in Eq. (67); please clarify which quantity is averaged.
  3. [Fig. 4 caption] The caption uses 'kr' while the text uses 'kra'; the notation should be unified.
  4. [§IV.B.1, Eq. (77)] The derivation of Eq. (77) assumes exactly scale-invariant P_zeta; for a tilted spectrum, the high-frequency slope would be f^{6+n_s-1}, so the 'universal' f^6 statement should be qualified when the tilt is included.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the f^6 scalaron scaling is a forward derivation from the assumed f(R) action, with no fit or self-citation loop in the central claim.

full rationale

The derivation chain is self-contained: the f(R) action (Eq. 1) fixes the scalaron perturbation via phi_s = F_R delta R (Eq. 62), the sub-horizon curvature perturbation (Eq. 76) is taken from Tsujikawa's independent work, and the abundance formula (Eq. 67) is taken from Zhou et al. [77]; inserting these yields Eq. (77) with Omega_sc proportional to (c2/M_Pl^2)^2 (k/kra)^6 P_zeta, a forward computation with no parameter fitted to the predicted signal. The c2 lower bounds (Eqs. 80 and 84) are obtained by equating two computed amplitudes (scalaron vs GR), not by absorbing data; ma, fa, and c2 are scanned or set model parameters. The self-citations [6, 8, 46, 53, 61, 80] provide background or standard relations; Eq. (64) from [80] is the standard superhorizon Phi-zeta relation, independently available in the literature and also implicit in the external Zhou formalism. No step reduces by construction to its own output, and no self-cited uniqueness theorem is invoked to force a choice. The possible concern that the scalaron is massive while Eq. (67) is a massless-tensor formula is a correctness or modeling issue, not a circularity, and therefore does not raise the circularity score.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central result depends on a set of model-specific assumptions and free parameters. The f^6 scaling itself follows from the assumed f(R) form and the existing formalism of [77], with no new entities. The most load-bearing free choices are the coefficient c2, the axion mass and coupling, and the assumed axion temperature T_a = m_a that fixes the eMD energy density. No new particles or forces are introduced; the scalaron is a standard degree of freedom of f(R) gravity. The axioms are mostly domain assumptions inherited from the string-inspired model and the SIGW literature, with the existence and suddenness of the eMD era being the most ad hoc to this paper.

free parameters (4)
  • c2 = 10^-8 M_Pl^2 in Figs 1-2, 8e-7 M_Pl^2 in Fig 3; lower bounds derived in Eqs. (80) and (84)
    Coefficient of the logarithmic curvature correction in the f(R) action (1). The scalaron GW amplitude is proportional to c2^2 (Eq. 77), so the detectability and the scalaron-vs-GR dominance depend sensitively on this free coefficient.
  • fa = scanned from 10^-3 to 10^-1 M_Pl
    Axion coupling, a phenomenological parameter in the axion potential (21). It controls the decay width (27) and the frequency-peak relation through the eMD duration.
  • ma = scanned from 10^4 to 10^8 GeV in figures; abstract claims > 1 GeV
    Axion mass, set by the instanton scale Lambda1 via Eq. (25). It controls the duration of the eMD era and the decay width (27). The abstract's lower bound of 1 GeV is not reflected in the plots.
  • T_a = T_a = m_a (assumed)
    Axion temperature at the start of the AMDE. Eq. (74) assumes the axion fluid has a thermal-like energy density with T_a = m_a, taken from the flaton case (34). This is a hand-chosen value, not derived from axion production mechanisms.
assumptions (6)
  • domain assumption The StRVM effective action (1) with f(R) = c0 + R(c1 + c2 log(R/R0)) is a valid low-energy description of the string-inspired model.
    Invoked in Eq. (1) and used throughout the paper; the logarithmic curvature corrections are assumed to arise from quantum gravity and to dominate in the early universe.
  • domain assumption The axion potential (21) with the hierarchies (19) or (20) correctly describes the compactification axion.
    Sets the axion mass (25) and the eMD scenario; the potential is a specific choice from string instanton effects, and the hierarchy constraints are taken from prior work.
  • ad hoc to paper An axion-driven early matter-dominated era exists with a sudden transition to radiation.
    Section III constructs this era from decay-width inequalities (29), but the initial axion abundance is not derived; the sudden-transition assumption enters Eq. (72) from [9].
  • domain assumption The curvature perturbation power spectrum is nearly scale-invariant with amplitude 2.1e-9 as measured by Planck.
    Used as the source of induced GWs; this is an observational input, not a theoretical derivation.
  • standard math The f(R) SIGW formalism of Zhou et al. [77] correctly describes the scalaron contribution.
    Used to derive the scalaron contribution (Eqs. 54-67); the paper does not re-derive the formalism but relies on [77].
  • domain assumption The condition k^2/a^2 F_R^(0)/F^(0) << 1 holds for the parameter ranges considered.
    Required for the f^6 scaling (Eq. 78); checked in Appendix A for c2 = 10^-8 M_Pl^2, but the check is not shown for the larger c2 values used in Fig. 3.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Gravitational wave signatures from reheating in Chern-Simons running-vacuum cosmology." pith.science (2026). https://pith.science/paper/4MLWIRN5

@misc{pith2026241114223,
  author       = {Pith},
  title        = {Pith review of: Gravitational wave signatures from reheating in Chern-Simons running-vacuum cosmology},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4MLWIRN5}},
  note         = {Machine review of arXiv:2411.14223}
}
abstract

Within the context of a Chern-Simons running-vacuum-model (RVM) cosmology, one expects an early-matter dominated (eMD) reheating period after RVM inflation driven by the axion field. Treating thus in this work Chern-Simons RVM cosmology as an effective $f(R)$ gravity theory characterized by logarithmic corrections of the spacetime curvature, we study the gravitational-wave (GW) signal induced by the nearly-scale invariant inflationary adiabatic curvature perturbations during the transition from the eMD era driven by the axion to the late radiation-dominated era. Remarkably, by accounting for the extra GW scalaron polarization present within $f(R)$ gravity theories, we find regions in the parameter space of the theory where one is met with a distinctive induced GW signal with a universal $f^6$ high-frequency scaling compared to the $f^7$ scaling present in general relativity (GR). Interestingly enough, for axion masses $m_a$ higher than 1 GeV and axion gauge couplings $f_a$ above $10^{-3}$ Planck mass, one can produce induced GW spectra within the sensitivity bands of future GW observatories such as the Einstein Telescope (ET), the Laser Interferometer Space Antenna (LISA), the Big Bang Observer (BBO) and the Square Kilometer Arrays (SKA).

Figures

Figures reproduced from arXiv: 2411.14223 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p018_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Can tensor-scalar induced GWs dominate PTA observations ?

    astro-ph.CO 2024-12 conditional novelty 5.0 of 10

    A Bayesian fit to NANOGrav 15-year data finds that tensor-scalar induced gravitational waves plus primordial tensor waves can fit the PTA background, with amplitudes constrained by CMB, BAO, and PBH limits.

Reference graph

Works this paper leans on

91 extracted references · 2 canonical work pages · cited by 1 Pith paper

  1. [10]

    Inomata, K

    K. Inomata, K. Kohri, T. Nakama, and T. Terada, Enhancement of Gravitational Waves Induced by Scalar Perturba- tions due to a Sudden Transition from an Early Matter Era to the Radiation Era, Phys. Rev. D 100, 043532 (2019), arXiv:1904.12879 [astro-ph.CO]

    arXiv 2019

  2. [1]

    Addressing observational ten- sions in cosmology with systematics and fundamental physics (CosmoVerse)

    The scalaron contribution Additionally, distinctive of the richer phenomenology of an f (R) theory is the existence of an extra massive polar- isation mode (scalaron) ϕs, defined as ϕs ≡ df (R) dR = F (R), whose equation on FLR W space-time can be recast as [79] ϕ(1)′′ s + 2Hϕ(1)′ s − ∆ + m2 s ϕ(1) s = −□(1)ϕ(0) s + κ 3 T M,(1), (61) where T M is the trac...

  3. [2]

    T. P. Sotiriou and V. Faraoni, f(R) Theories Of Gravity, Rev. Mod. Phys. 82, 451 (2010), arXiv:0805.1726 [gr-qc]

    arXiv 2010

  4. [3]

    Basilakos, N

    S. Basilakos, N. E. Mavromatos, and J. Sol` a Peracaula, Gravitational and Chiral Anomalies in the Running Vacuum Universe and Matter-Antimatter Asymmetry, Phys. Rev. D 101, 045001 (2020), arXiv:1907.04890 [hep-ph]

    arXiv 2020

  5. [4]

    Basilakos, N

    S. Basilakos, N. E. Mavromatos, and J. Sol` a Peracaula, Quantum Anomalies in String-Inspired Running Vacuum Universe: Inflation and Axion Dark Matter, Phys. Lett. B 803, 135342 (2020), arXiv:2001.03465 [gr-qc]

    arXiv 2020

  6. [5]

    N. E. Mavromatos and J. Sol` a Peracaula, Stringy-running-vacuum-model inflation: from primordial gravitational waves and stiff axion matter to dynamical dark energy, Eur. Phys. J. ST 230, 2077 (2021), arXiv:2012.07971 [hep-ph]

    arXiv 2021

  7. [6]

    N. E. Mavromatos and J. Sol` a Peracaula, Inflationary physics and trans-Planckian conjecture in the stringy running vacuum model: from the phantom vacuum to the true vacuum, Eur. Phys. J. Plus 136, 1152 (2021), arXiv:2105.02659 [hep-th]

    arXiv 2021

  8. [7]

    G´ omez-Valent, N

    A. G´ omez-Valent, N. E. Mavromatos, and J. Sol` a Peracaula, Stringy running vacuum model and current tensions in cosmology, Class. Quant. Grav. 41, 015026 (2024), arXiv:2305.15774 [gr-qc]

    arXiv 2024

Show all 91 references
  1. [8]

    Asimakis, S

    P. Asimakis, S. Basilakos, N. E. Mavromatos, and E. N. Saridakis, Big bang nucleosynthesis constraints on higher-order modified gravities, Phys. Rev. D 105, 084010 (2022), arXiv:2112.10863 [gr-qc]

    2022 arXiv

  2. [9]

    Papanikolaou, C

    T. Papanikolaou, C. Tzerefos, S. Basilakos, E. N. Saridakis, and N. E. Mavromatos, Revisiting string-inspired running- vacuum models under the lens of light primordial black holes, Phys. Rev. D 110, 024055 (2024), arXiv:2402.19373 [gr-qc]

    2024 arXiv

  3. [11]

    Inomata, K

    K. Inomata, K. Kohri, T. Nakama, and T. Terada, Gravitational Waves Induced by Scalar Perturbations during a Gradual Transition from an Early Matter Era to the Radiation Era, JCAP 10, 071, [Erratum: JCAP 08, E01 (2023)], arXiv:1904.12878 [astro-ph.CO]

    2023 arXiv

  4. [12]

    Inomata, M

    K. Inomata, M. Kawasaki, K. Mukaida, T. Terada, and T. T. Yanagida, Gravitational Wave Production right after a Primordial Black Hole Evaporation, Phys. Rev. D 101, 123533 (2020), arXiv:2003.10455 [astro-ph.CO]

    2020 arXiv

  5. [13]

    Papanikolaou, V

    T. Papanikolaou, V. Vennin, and D. Langlois, Gravitational waves from a universe filled with primordial black holes, JCAP 03, 053, arXiv:2010.11573 [astro-ph.CO]

    2010 arXiv

  6. [14]

    Dom` enech, C

    G. Dom` enech, C. Lin, and M. Sasaki, Gravitational wave constraints on the primordial black hole dominated early universe, JCAP 04, 062, [Erratum: JCAP 11, E01 (2021)], arXiv:2012.08151 [gr-qc]

    2021 arXiv

  7. [15]

    Papanikolaou, Gravitational waves induced from primordial black hole fluctuations: the effect of an extended mass function, JCAP 10, 089, arXiv:2207.11041 [astro-ph.CO]

    T. Papanikolaou, Gravitational waves induced from primordial black hole fluctuations: the effect of an extended mass function, JCAP 10, 089, arXiv:2207.11041 [astro-ph.CO]

    arXiv

  8. [16]

    Dom` enech, S

    G. Dom` enech, S. Passaglia, and S. Renaux-Petel, Gravitational waves from dark matter isocurvature, JCAP03 (03), 023, arXiv:2112.10163 [astro-ph.CO]

    arXiv

  9. [17]

    Dom` enech, Scalar Induced Gravitational Waves Review, Universe7, 398 (2021), arXiv:2109.01398 [gr-qc]

    G. Dom` enech, Scalar Induced Gravitational Waves Review, Universe7, 398 (2021), arXiv:2109.01398 [gr-qc]

    2021 arXiv

  10. [18]

    Aghanim et al

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

    2020 arXiv

  11. [19]

    Witten, World sheet corrections via D instantons, JHEP 02, 030, arXiv:hep-th/9907041

    E. Witten, World sheet corrections via D instantons, JHEP 02, 030, arXiv:hep-th/9907041

    arXiv

  12. [20]

    Blumenhagen, M

    R. Blumenhagen, M. Cvetic, P. Langacker, and G. Shiu, Toward realistic intersecting D-brane models, Ann. Rev. Nucl. Part. Sci. 55, 71 (2005), arXiv:hep-th/0502005

    2005 arXiv

  13. [21]

    Svrcek and E

    P. Svrcek and E. Witten, Axions In String Theory, JHEP 06, 051, arXiv:hep-th/0605206

    arXiv

  14. [22]

    M. J. Duncan, N. Kaloper, and K. A. Olive, Axion hair and dynamical torsion from anomalies, Nucl. Phys. B 387, 215 (1992)

    1992

  15. [23]

    B. A. Campbell, M. J. Duncan, N. Kaloper, and K. A. Olive, Gravitational dynamics with Lorentz Chern-Simons terms, Nucl. Phys. B 351, 778 (1991)

    1991

  16. [24]

    M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory Vol. 1: 25th Anniversary Edition , Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2012). 20

    2012

  17. [25]

    M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory Vol. 2: 25th Anniversary Edition , Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2012)

    2012

  18. [26]

    Polchinski, String theory

    J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string , Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2007)

    2007

  19. [27]

    Polchinski, String theory

    J. Polchinski, String theory. Vol. 2: Superstring theory and beyond , Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2007)

    2007

  20. [28]

    S. H.-S. Alexander, M. E. Peskin, and M. M. Sheikh-Jabbari, Leptogenesis from gravity waves in models of inflation, Phys. Rev. Lett. 96, 081301 (2006), arXiv:hep-th/0403069

    2006 arXiv

  21. [29]

    D. H. Lyth, C. Quimbay, and Y. Rodriguez, Leptogenesis and tensor polarisation from a gravitational Chern-Simons term, JHEP 03, 016, arXiv:hep-th/0501153

    arXiv

  22. [30]

    Dorlis, N

    P. Dorlis, N. E. Mavromatos, and S.-N. Vlachos, Condensate-induced inflation from primordial gravitational waves in string-inspired Chern-Simons gravity, Phys. Rev. D 110, 063512 (2024), arXiv:2403.09005 [gr-qc]

    2024 arXiv

  23. [31]

    Jackiw and S

    R. Jackiw and S. Y. Pi, Chern-Simons modification of general relativity, Phys. Rev. D 68, 104012 (2003), arXiv:gr- qc/0308071

    2003

  24. [32]

    Alexander and N

    S. Alexander and N. Yunes, Chern-Simons Modified General Relativity, Phys. Rept. 480, 1 (2009), arXiv:0907.2562 [hep- th]

    2009 arXiv

  25. [33]

    McAllister, E

    L. McAllister, E. Silverstein, and A. Westphal, Gravity Waves and Linear Inflation from Axion Monodromy, Phys. Rev. D 82, 046003 (2010), arXiv:0808.0706 [hep-th]

    2010 arXiv

  26. [34]

    Sola Peracaula, The cosmological constant problem and running vacuum in the expanding universe, Phil

    J. Sola Peracaula, The cosmological constant problem and running vacuum in the expanding universe, Phil. Trans. Roy. Soc. Lond. A 380, 20210182 (2022), arXiv:2203.13757 [gr-qc]

    2022 arXiv

  27. [35]

    Sol` a and A

    J. Sol` a and A. G´ omez-Valent, The¯ΛCDM cosmology: From inflation to dark energy through running Λ, Int. J. Mod. Phys. D 24, 1541003 (2015), arXiv:1501.03832 [gr-qc]

    2015 arXiv

  28. [37]

    Moreno-Pulido and J

    C. Moreno-Pulido and J. Sola, Running vacuum in quantum field theory in curved spacetime: renormalizing ρvac without ∼ m4 terms, Eur. Phys. J. C 80, 692 (2020), arXiv:2005.03164 [gr-qc]

    2020 arXiv

  29. [38]

    Moreno-Pulido and J

    C. Moreno-Pulido and J. Sola Peracaula, Renormalizing the vacuum energy in cosmological spacetime: implications for the cosmological constant problem, Eur. Phys. J. C 82, 551 (2022), arXiv:2201.05827 [gr-qc]

    2022 arXiv

  30. [39]

    Moreno-Pulido and J

    C. Moreno-Pulido and J. Sola Peracaula, Equation of state of the running vacuum, Eur. Phys. J. C 82, 1137 (2022), arXiv:2207.07111 [gr-qc]

    2022 arXiv

  31. [40]

    Moreno-Pulido, J

    C. Moreno-Pulido, J. Sola Peracaula, and S. Cheraghchi, Running vacuum in QFT in FLR W spacetime: the dynamics of ρvac(H) from the quantized matter fields, Eur. Phys. J. C 83, 637 (2023), arXiv:2301.05205 [gr-qc]

    2023 arXiv

  32. [41]

    N. E. Mavromatos, Lorentz Symmetry Violation in String-Inspired Effective Modified Gravity Theories, Lect. Notes Phys. 1017, 3 (2023), arXiv:2205.07044 [hep-th]

    2023 arXiv

  33. [42]

    D. Tong, TASI lectures on solitons: Instantons, monopoles, vortices and kinks, in Theoretical Advanced Study Institute in Elementary Particle Physics: Many Dimensions of String Theory (2005) arXiv:hep-th/0509216

    2005 arXiv

  34. [43]

    Eguchi, P

    T. Eguchi, P. B. Gilkey, and A. J. Hanson, Gravitation, Gauge Theories and Differential Geometry, Phys. Rept. 66, 213 (1980)

    1980

  35. [44]

    Akrami et al

    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

  36. [45]

    Bedroya, R

    A. Bedroya, R. Brandenberger, M. Loverde, and C. Vafa, Trans-Planckian Censorship and Inflationary Cosmology, Phys. Rev. D 101, 103502 (2020), arXiv:1909.11106 [hep-th]

    2020 arXiv

  37. [46]

    Bedroya and C

    A. Bedroya and C. Vafa, Trans-Planckian Censorship and the Swampland, JHEP 09, 123, arXiv:1909.11063 [hep-th]

    1909 arXiv

  38. [47]

    N. E. Mavromatos, V. C. Spanos, and I. D. Stamou, Primordial black holes and gravitational waves in multiaxion-Chern- Simons inflation, Phys. Rev. D 106, 063532 (2022), arXiv:2206.07963 [hep-th]

    2022 arXiv

  39. [48]

    J. A. S. Lima, S. Basilakos, and J. Sola, Expansion History with Decaying Vacuum: A Complete Cosmological Scenario, Mon. Not. Roy. Astron. Soc. 431, 923 (2013), arXiv:1209.2802 [gr-qc]

    2013 arXiv

  40. [49]

    E. L. D. Perico, J. A. S. Lima, S. Basilakos, and J. Sola, Complete Cosmic History with a dynamical Λ = Λ( H) term, Phys. Rev. D 88, 063531 (2013), arXiv:1306.0591 [astro-ph.CO]

    2013 arXiv

  41. [50]

    E. W. Kolb and T. M. S., The Early Universe , Vol. 69 (Taylor and Francis, 2019)

    2019

  42. [51]

    J. A. S. Lima, S. Basilakos, and J. Sol` a, Thermodynamical aspects of running vacuum models, Eur. Phys. J. C 76, 228 (2016), arXiv:1509.00163 [gr-qc]

    2016 arXiv

  43. [52]

    J. A. S. Lima, S. Basilakos, and J. Sol` a, Nonsingular Decaying Vacuum Cosmology and Entropy Production, Gen. Rel. Grav. 47, 40 (2015), arXiv:1412.5196 [gr-qc]

    2015 arXiv

  44. [53]

    Sol` a Peracaula and H

    J. Sol` a Peracaula and H. Yu, Particle and entropy production in the Running Vacuum Universe, Gen. Rel. Grav. 52, 17 (2020), arXiv:1910.01638 [gr-qc]

    2020 arXiv

  45. [54]

    Dorlis, N

    P. Dorlis, N. E. Mavromatos, and S.-N. Vlachos, Quantum-Ordering Ambiguities in Weak Chern-Simons 4D Gravity and Metastability of the Condensate-Induced Inflation, (2024), arXiv:2411.12519 [gr-qc]

    2024 arXiv

  46. [55]

    B. Carr, K. Dimopoulos, C. Owen, and T. Tenkanen, Primordial Black Hole Formation During Slow Reheating After Inflation, Phys. Rev. D 97, 123535 (2018), arXiv:1804.08639 [astro-ph.CO]

    2018 arXiv

  47. [56]

    Blumenhagen and E

    R. Blumenhagen and E. Plauschinn, Towards Universal Axion Inflation and Reheating in String Theory, Phys. Lett. B 736, 482 (2014), arXiv:1404.3542 [hep-th]

    2014 arXiv

  48. [57]

    Halverson, C

    J. Halverson, C. Long, B. Nelson, and G. Salinas, Axion reheating in the string landscape, Phys. Rev. D 99, 086014 (2019), arXiv:1903.04495 [hep-th]. 21

    2019 arXiv

  49. [58]

    Blumenhagen, M

    R. Blumenhagen, M. Cvetic, and T. Weigand, Spacetime instanton corrections in 4D string vacua: The Seesaw mechanism for D-Brane models, Nucl. Phys. B 771, 113 (2007), arXiv:hep-th/0609191

    2007 arXiv

  50. [59]

    Blumenhagen, M

    R. Blumenhagen, M. Cvetic, S. Kachru, and T. Weigand, D-Brane Instantons in Type II Orientifolds, Ann. Rev. Nucl. Part. Sci. 59, 269 (2009), arXiv:0902.3251 [hep-th]

    2009 arXiv

  51. [60]

    Polchinski, Combinatorics of boundaries in string theory, Phys

    J. Polchinski, Combinatorics of boundaries in string theory, Phys. Rev. D 50, R6041 (1994), arXiv:hep-th/9407031

    1994 arXiv

  52. [61]

    Ellis, M

    J. Ellis, M. A. G. Garcia, N. Nagata, D. V. Nanopoulos, and K. A. Olive, Symmetry Breaking and Reheating after Inflation in No-Scale Flipped SU(5), JCAP 04, 009, arXiv:1812.08184 [hep-ph]

    arXiv

  53. [62]

    Basilakos, D

    S. Basilakos, D. V. Nanopoulos, T. Papanikolaou, E. N. Saridakis, and C. Tzerefos, Induced gravitational waves from flipped SU(5) superstring theory at nHz, Phys. Lett. B 849, 138446 (2024), arXiv:2309.15820 [astro-ph.CO]

    2024 arXiv

  54. [63]

    J. P. Conlon and M. C. D. Marsh, The Cosmophenomenology of Axionic Dark Radiation, JHEP 10, 214, arXiv:1304.1804 [hep-ph]

    arXiv

  55. [64]

    D. J. E. Marsh, Axion Cosmology, Phys. Rept. 643, 1 (2016), arXiv:1510.07633 [astro-ph.CO]

    2016 arXiv

  56. [65]

    Matarrese, O

    S. Matarrese, O. Pantano, and D. Saez, A General relativistic approach to the nonlinear evolution of collisionless matter, Phys. Rev. D 47, 1311 (1993)

    1993

  57. [66]

    Matarrese, O

    S. Matarrese, O. Pantano, and D. Saez, General relativistic dynamics of irrotational dust: Cosmological implications, Phys. Rev. Lett. 72, 320 (1994), arXiv:astro-ph/9310036

    1994 arXiv

  58. [67]

    Matarrese, S

    S. Matarrese, S. Mollerach, and M. Bruni, Second order perturbations of the Einstein-de Sitter universe, Phys. Rev. D 58, 043504 (1998), arXiv:astro-ph/9707278

    1998 arXiv

  59. [68]

    Mollerach, D

    S. Mollerach, D. Harari, and S. Matarrese, CMB polarization from secondary vector and tensor modes, Phys. Rev. D 69, 063002 (2004), arXiv:astro-ph/0310711

    2004 arXiv

  60. [69]

    Hwang, D

    J.-C. Hwang, D. Jeong, and H. Noh, Gauge dependence of gravitational waves generated from scalar perturbations, Astrophys. J. 842, 46 (2017), arXiv:1704.03500 [astro-ph.CO]

    2017 arXiv

  61. [70]

    Tomikawa and T

    K. Tomikawa and T. Kobayashi, Gauge dependence of gravitational waves generated at second order from scalar pertur- bations, Phys. Rev. D 101, 083529 (2020), arXiv:1910.01880 [gr-qc]

    2020 arXiv

  62. [71]

    De Luca, G

    V. De Luca, G. Franciolini, A. Kehagias, and A. Riotto, On the Gauge Invariance of Cosmological Gravitational Waves, JCAP 03, 014, arXiv:1911.09689 [gr-qc]

    1911 arXiv

  63. [72]

    Inomata and T

    K. Inomata and T. Terada, Gauge Independence of Induced Gravitational Waves, Phys. Rev. D 101, 023523 (2020), arXiv:1912.00785 [gr-qc]

    2020 arXiv

  64. [73]

    Dom` enech and M

    G. Dom` enech and M. Sasaki, Approximate gauge independence of the induced gravitational wave spectrum, Phys. Rev. D 103, 063531 (2021), arXiv:2012.14016 [gr-qc]

    2021 arXiv

  65. [74]

    J. R. Espinosa, D. Racco, and A. Riotto, A Cosmological Signature of the SM Higgs Instability: Gravitational Waves, JCAP 1809 (09), 012, arXiv:1804.07732 [hep-ph]

    arXiv

  66. [75]

    Baumann, P

    D. Baumann, P. J. Steinhardt, K. Takahashi, and K. Ichiki, Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations, Phys. Rev. D76, 084019 (2007), arXiv:hep-th/0703290 [hep-th]

    2007 arXiv

  67. [76]

    K. N. Ananda, C. Clarkson, and D. Wands, The Cosmological gravitational wave background from primordial density perturbations, Phys. Rev. D75, 123518 (2007), arXiv:gr-qc/0612013 [gr-qc]

    2007 arXiv

  68. [77]

    Kohri and T

    K. Kohri and T. Terada, Semianalytic calculation of gravitational wave spectrum nonlinearly induced from primordial curvature perturbations, Phys. Rev. D97, 123532 (2018), arXiv:1804.08577 [gr-qc]

    2018 arXiv

  69. [78]

    Zhou, Y.-T

    J.-Z. Zhou, Y.-T. Kuang, D. Wu, F.-Y. Chen, H. L¨ u, and Z. Chang, Scalar induced gravitational waves in f(R) gravity, (2024), arXiv:2409.07702 [gr-qc]

    2024 arXiv

  70. [79]

    Tsujikawa, Matter density perturbations and effective gravitational constant in modified gravity models of dark energy, Phys

    S. Tsujikawa, Matter density perturbations and effective gravitational constant in modified gravity models of dark energy, Phys. Rev. D 76, 023514 (2007), arXiv:0705.1032 [astro-ph]

    2007 arXiv

  71. [80]

    Katsuragawa, T

    T. Katsuragawa, T. Nakamura, T. Ikeda, and S. Capozziello, Gravitational Waves in F (R) Gravity: Scalar Waves and the Chameleon Mechanism, Phys. Rev. D 99, 124050 (2019), arXiv:1902.02494 [gr-qc]

    2019 arXiv

  72. [81]

    Papanikolaou, C

    T. Papanikolaou, C. Tzerefos, S. Basilakos, and E. N. Saridakis, Scalar induced gravitational waves from primordial black hole Poisson fluctuations in f(R) gravity, JCAP 10, 013, arXiv:2112.15059 [astro-ph.CO]

    arXiv

  73. [82]

    Maggiore, Gravitational wave experiments and early universe cosmology, Phys

    M. Maggiore, Gravitational wave experiments and early universe cosmology, Phys. Rept. 331, 283 (2000), arXiv:gr- qc/9909001

    2000

  74. [83]

    Assadullahi and D

    H. Assadullahi and D. Wands, Gravitational waves from an early matter era, Phys. Rev. D 79, 083511 (2009), arXiv:0901.0989 [astro-ph.CO]

    2009 arXiv

  75. [84]

    Jedamzik, M

    K. Jedamzik, M. Lemoine, and J. Martin, Generation of gravitational waves during early structure formation between cosmic inflation and reheating, JCAP 04, 021, arXiv:1002.3278 [astro-ph.CO]

    arXiv

  76. [85]

    Eggemeier, J

    B. Eggemeier, J. C. Niemeyer, K. Jedamzik, and R. Easther, Stochastic gravitational waves from postinflationary structure formation, Phys. Rev. D 107, 043503 (2023), arXiv:2212.00425 [astro-ph.CO]

    2023 arXiv

  77. [86]

    Fernandez, J

    N. Fernandez, J. W. Foster, B. Lillard, and J. Shelton, Stochastic Gravitational Waves from Early Structure Formation, Phys. Rev. Lett. 133, 111002 (2024), arXiv:2312.12499 [astro-ph.CO]

    2024 arXiv

  78. [87]

    L. E. Padilla, J. C. Hidalgo, K. A. Malik, and D. Mulryne, Detecting the Stochastic Gravitational Wave Background from Primordial Black Holes in Slow-reheating Scenarios, (2024), arXiv:2405.19271 [astro-ph.CO]

    2024 arXiv

  79. [88]

    Amaro-Seoane et al

    P. Amaro-Seoane et al. (LISA), Laser Interferometer Space Antenna, (2017), arXiv:1702.00786 [astro-ph.IM]

    2017 arXiv

  80. [89]

    Karnesis et al

    N. Karnesis et al. , The Laser Interferometer Space Antenna mission in Greece White Paper, Int. J. Mod. Phys. D 33, 2450027 (2024), arXiv:2209.04358 [gr-qc]

    2024 arXiv

  81. [90]

    Maggiore et al

    M. Maggiore et al. , Science Case for the Einstein Telescope, JCAP 03, 050, arXiv:1912.02622 [astro-ph.CO]

    1912 arXiv

  82. [91]

    Janssen et al

    G. Janssen et al. , Gravitational wave astronomy with the SKA, PoS AASKA14, 037 (2015), arXiv:1501.00127 [astro- ph.IM]. 22

    2015 arXiv

  83. [92]

    G. M. Harry, P. Fritschel, D. A. Shaddock, W. Folkner, and E. S. Phinney, Laser interferometry for the big bang observer, Class. Quant. Grav. 23, 4887 (2006), [Erratum: Class.Quant.Grav. 23, 7361 (2006)]

    2006

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.