Pith. sign in

REVIEW 3 major objections 6 minor 2 cited by

Tribrid Inflation, Type II Leptogenesis, and Observable Gravitational Waves in $SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read A supersymmetric left-right model claims one set of Higgs triplets can drive inflation, generate the matter-antimatter asymmetry, and set neutrino masses, with gravitational waves within next-generation reach.

desk verdict New mechanism, but the headline numbers require an unstated 10^-8 tuning of the waterfall coupling; the paper needs major revision before its claims can be trusted. read the letter →

arxiv 2507.05564 v1 pith:OEHI2FQN submitted 2025-07-08 hep-ph hep-th

Waqas Ahmed , Saleh O. Allehabi , Farishta Israr , Mansoor Ur Rehman This is my paper · ORCID
classification hep-phhep-th PACS 98.80.Cq12.60.Fr14.60.Pq
keywords tribridinflationleft-rightsymmetricmodeltype-IIleptogenesisnon-thermalsupergravityKaehlercorrectionstensor-to-scalarratioseesaw
topics Matter-Antimatter Asymmetry
open problems Matter-Antimatter Asymmetry
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 tries to show that a single set of fields can solve three separate problems at once. In a supersymmetric left-right symmetric extension of the Standard Model, the neutral components of left-handed Higgs triplets drive a tribrid inflationary phase whose predictions match current cosmic microwave background data, decay after inflation to generate the observed matter-antimatter asymmetry through non-thermal type-II leptogenesis, and leave behind tiny neutrino masses through the type-II seesaw mechanism. The paper argues that supergravity corrections from a non-minimal Kaehler potential are indispensable: in global supersymmetry the mechanism fails outright, while supergravity stabilizes the singlet, triggers the waterfall that ends inflation, and shapes a hilltop inflaton potential that yields $n_s \simeq 0.973$\textendash$0.974$ and a tensor-to-scalar ratio up to $r \simeq 5\times10^{-3}$. That upper range sits within the projected reach of upcoming CMB B-mode experiments, so the model makes a concrete promise linking inflation, the origin of matter, and neutrino mass to a single measurement.

What carries the argument

The load-bearing object is the supergravity scalar potential along the D-flat direction, $V \simeq M_X^4\left(1 + \kappa_\phi\,\phi^2/m_P^2 + \delta_\phi\,\phi^4/m_P^4\right)$, together with the waterfall critical value $\phi_c = \left(4\kappa_\chi M_X^2/(\lambda^2 m_P^2)\right)^{1/4} M$, below which the waterfall field $\chi$ turns tachyonic and inflation ends. The Kaehler-determined coefficients $\kappa_\phi$ and $\delta_\phi$ convert an otherwise flat potential into the hilltop slope that sets the spectral index and the tensor-to-scalar ratio. On the leptogenesis side, the machinery is the $2\times2$ mass matrix of the two left-handed triplet generations; its off-diagonal absorptive parts generate the CP asymmetry $\epsilon_a \simeq \frac{M_1 M_2}{2\pi(M_1^2-M_2^2)}\frac{\mathrm{Im}\sum_{ij} f^1_{ij}f^{2*}_{ij}\alpha_1\alpha_2^*}{\sum_{ij}|f^a_{ij}|^2+|\alpha_a|^2}$, resonantly enhanced as $M_1 \to M_2$, which feeds the asymmetry estimate $n_L/s \simeq \frac{9}{\pi}\frac{T_R}{M_R}\frac{\bar{M}}{M_1-M_2}\frac{(\bar{M}/2v^2)^2\sum_k m_k^2\,\alpha^2}{(\bar{M}/2v^2)^2\sum_k m_k^2+\alpha^4}$. The two identities together carry the argument: the first fixes the inflationary observables, and the second ties the baryon asymmetry to the same triplet decays and to measured neutrino masses.

What would settle it

Evaluate Eq. (16) at the Table II benchmark values: for BP1 ($M = 5\times10^{16}$ GeV, $M_X = 8.9\times10^{15}$ GeV, $M_S = 0.12\,m_P$, $\lambda \simeq 8.9\times10^{-7}$), the condition $\phi_c = M$ forces $\kappa_\chi \simeq 1.5\times10^{-8}$, a specific and checkable number that the paper neither states nor constrains. Observationally, a measured $r > 5\times10^{-3}$ would contradict the model's upper bound, while $r < 8.6\times10^{-6}$ would exclude the large-$r$ benchmarks BP1\textendash BP3.

Watch

Extended reading notes

Core claim

The central claim is that tribrid inflation can be realized with gauge non-singlet inflatons, namely the left-handed triplet pairs $\Delta_L^a$, $\bar{\Delta}_L^a$ of the gauge group $G_{3221} = SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$. In global supersymmetry the setup fails: the singlet $s$ cannot be stabilized and the waterfall field $\chi$ never becomes tachyonic. Adding a power-law non-minimal Kaehler potential fixes both problems and gives the inflaton its slope; with $\kappa_\phi > 0$ and $\delta_\phi < 0$ the potential takes a hilltop form. The benchmark points of Table II yield a spectral index $n_s = 0.9743$, a scalar amplitude $A_s = 2.137\times10^{-9}$ after 54.5 e-folds, and a tensor-to-scalar ratio running from $r = 8.6\times10^{-6}$ to $r = 5\times10^{-3}$. After inflation, the right-handed triplet $\Delta_R$ decays into the left-handed triplets, whose nearly degenerate masses ($M_1 \simeq M_2 \sim 10^{10}$ GeV) resonantly enhance the CP asymmetry in their decays to lepton pairs; the resulting lepton asymmetry $n_L/s \simeq 2\times10^{-10}$ is converted by sphaleron processes into the observed baryon asymmetry, with washout suppressed because $M_1/T_R \sim 10$ and with $T_R$ low enough to avoid gravitino overproduction.

Load-bearing premise

The benchmark predictions assume, without stating or scanning it, that the Kaehler combination $\kappa_\chi$ is tuned to values between roughly $10^{-8}$ and $10^{-3}$ so that the waterfall critical point $\phi_c$ lands at the assumed value $\phi_c = M$; at natural values the waterfall would fire far before slow-roll inflation begins, and none of the quoted observables would follow.

Editorial extensions

If this is right

  • The model fixes the scalar spectral index near $n_s \simeq 0.973$\textendash$0.974$, matching the ACT DR6 plus Planck and BK18 combination, with a running $\alpha_s$ between 0.004 and 0.01.
  • The tensor-to-scalar ratio is predicted in the window $8.6\times10^{-6} \le r \le 5\times10^{-3}$, and the upper end is within the projected sensitivity of LiteBIRD, CMB-S4, and the Simons Observatory, so the large-$r$ branch can be tested by near-future CMB polarization data.
  • Inflation, the baryon asymmetry, and neutrino masses all trace back to the same left-handed triplet fields, so measurements of neutrino properties or the reheating temperature constrain the inflationary parameters and vice versa.
  • The reheating temperature stays near or below $T_R \simeq 10^{10}$ GeV with $M_1/T_R \sim 10$, keeping type-II washout negligible and avoiding gravitino overproduction for gravitino masses around 10\textendash50 TeV.
  • Lower-scale benchmarks sit at the symmetry-breaking value $M = 2\times10^{16}$ GeV, which the paper equates with MSSM gauge-coupling unification, while the large-$r$ solutions favor $M = 5\times10^{16}$ GeV, giving the model a concrete grand-unification link.

Reading between the lines

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

  • The claimed baryon asymmetry inherits an unstated dependence on the near-degeneracy of the two left-handed triplets: the CP asymmetry $\epsilon_a$ scales as $1/(M_1^2 - M_2^2)$, and the benchmarks give only $M_1 \simeq M_2$ without quoting the splitting that sets the size of $n_L/s$.
  • The high-$r$ benchmarks (BP1, BP2) sit at $M = 4$\textendash$5\times10^{16}$ GeV, above the $2\times10^{16}$ GeV scale that the paper equates with MSSM gauge-coupling unification, so pinning down the unification scale could discriminate among the benchmarks independently of CMB B-mode data.
  • If a next-generation CMB experiment reports $r \gtrsim 10^{-3}$, the model points to its high-scale branch; a null result below $r < 8.6\times10^{-6}$ would leave only the low-$r$ benchmark viable and undercut the observable-gravitational-wave message of the paper.
  • The $B-L$ breaking at the end of the waterfall phase may produce topological defects such as cosmic strings, and their stochastic gravitational-wave background is a natural, unexamined consequence that pulsar-timing arrays could probe.
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

3 major / 6 minor

Summary. The manuscript constructs an SU(3)c × SU(2)L × SU(2)R × U(1)B−L tribrid inflation model in which the neutral component of a left-handed Higgs triplet drives inflation, with the inflationary slope generated by supergravity corrections from a non-minimal Kähler potential. The same triplet sector is claimed to produce neutrino masses via a type-II seesaw mechanism and the baryon asymmetry via non-thermal type-II leptogenesis. The paper presents approximate slow-roll formulas, four benchmark points in Table II with ns ≈ 0.9743, r between 8.6×10−6 and 5×10−3, N0 = 54.5, and reheating temperatures around 10^9–10^10 GeV, and it claims consistency with ACT DR6, Planck 2018, and LB-BK18 data.

Significance. If the numerical benchmarks can be made self-consistent, the model would provide a nontrivial embedding of tribrid inflation in a left-right symmetric gauge group, connecting inflation, neutrino mass, baryogenesis, and potentially observable primordial gravitational waves. The analytic formulas for As, r, ns, and N0, the explicit benchmark scan, and the discussion of reheating and washout constraints are useful strengths, and the parameter space with r up to 0.005 is timely for CMB-S4 and LiteBIRD. However, as presented, the central numerical claims are not reproducible because a key waterfall parameter (κχ) is absent from the scan, the leptogenesis inputs are not specified, and one benchmark row is inconsistent with the paper's own slow-roll formulas.

major comments (3)
  1. [Section VI, Table II, Eqs. (16) and (35)] The waterfall endpoint is not controlled. Using Eq. (35) with BP1, λ1 ≈ M1 MS / M^2 ≈ 8.8×10−7. Inserting this into Eq. (16) gives φc/M ≈ 91 κχ^{1/4}. Since Table II has φ0/M = 24 and φe/M = 1, self-consistency requires κχ ≈ 1.5×10−8 for BP1, and similarly small values for the other benchmarks, yet κχ is not among the scanned parameters listed in Section VI and its value is never quoted. Unless this extremely small positive value of κχ = −1 + (κSΔR + κSΔ̄R)/2 is deliberately assumed, the waterfall would trigger before the observable e-fold window, invalidating the quoted ns, r, and N0. Please include κχ in the scan and report the value required for each benchmark.
  2. [Section VI, Eqs. (18), (30), and (32), Table II] The benchmark rows are mutually inconsistent with the slow-roll approximation. For BP1, φ0 ≈ mP/2, κφ = 0.063, and δφ = −0.054; Eq. (32) gives ns ≈ 1 + 2κφ + 3δφ = 0.964, while Table II lists ns = 0.9743. A direct evaluation using the slow-roll parameters defined in Eq. (23) and the potential (18) gives ns ≈ 0.963, not 0.9743. For BP2, Eq. (30) with κφ = 0.059, δφ = −0.2196, and φ0/mP = 0.246 gives ns ≈ 0.958, again far from the tabulated 0.9743. The table entries cannot all be correct; please provide the actual numerical solution or correct the parameters.
  3. [Section VIII, Eq. (64), Table II] The leptogenesis claim is not checkable. The asymmetry in Eq. (64) depends on TR, MR, M̄, M1 − M2, α, the f-matrix elements, and the CP phase, but Table II reports only a single common value for M1 and M2 and gives none of the couplings or the mass splitting. The statement M1 ≈ M2 is literally singular in Eqs. (51)–(54) if the masses are equal, so a finite M1 − M2 must be specified. Until these inputs are tabulated, the assertion that the benchmarks reproduce nL/s ≈ 1.7×10−10 is not supported.
minor comments (6)
  1. [Section VI and Table II] The text defines MS = mP/κ with 0.1 ≤ κ ≤ 1, but Table II has MS/mP between 0.09 and 0.12, which implies κ ≈ 8–11; please clarify whether MS = κ mP was intended.
  2. [Summary, Abstract, and Table II] The value of the spectral index is quoted as ns = 0.9734 in the Introduction and Summary but as ns = 0.9743 in Table II; the text should use one value consistently.
  3. [Section IV, Eq. (19)] No Kähler-potential coefficient values are given that realize the required κφ and δφ, and for BP4 δφ = −5.06 appears to require large cancellations in Eq. (19); a short derivation or a set of explicit Kähler coefficients would strengthen the paper.
  4. [Section IV, Eq. (21)] The one-loop correction is quoted without computation; if it is used only to argue that radiative corrections are negligible, a brief derivation or a reference to the standard formula would be helpful.
  5. [Fig. 1 and Section V] The figure and the text explicitly assume φc = M; this is precisely the fine-tuned condition discussed in the first major comment and should be stated as an assumption when interpreting the inflationary dynamics.
  6. [Section VII, Eq. (35)] The notation κM in the expression for MR is not defined; please clarify its meaning and relation to the Kähler-potential coefficients.

Circularity Check

1 steps flagged · score 5.0 of 10

The headline value ns = 0.9734 is imposed as a scan constraint and then reported as a prediction; r retains some independent predictive content, so circularity is partial.

  1. fitted input called prediction [Section VI (observational constraints list) and Section IX (Summary)]
    "The scalar spectral index, consistent with the central value reported by the ACT collaboration in conjunction with Planck 2018 and LB-BK18 [44], ns = 0.9734. [...] the model yields a scalar spectral index ns = 0.9734"

    The numerical scan is required to satisfy ns = 0.9734 as an observational constraint, and every benchmark point in Table II reports this same value. The summary then presents the imposed value as a model prediction: 'the model yields a scalar spectral index ns = 0.9734.' Because the accepted parameter points are selected precisely to make ns equal the quoted ACT/Planck central value, the claimed prediction is identical to the input constraint by construction. The tensor-to-scalar ratio r is not listed among the input constraints and is instead tied to As and MX through Eq. (28), so the circularity is partial rather than total.

full rationale

The paper contains one clear fitted-input-called-prediction step: the ACT/Planck value ns = 0.9734 is imposed as an acceptance criterion in Section VI, and the summary reports ns = 0.9734 as a prediction. This is a genuine reduction-by-construction for that one headline quantity. The other headline claim, r <= 0.005, is not directly imposed as a constraint; it follows from the slow-roll relation r = (2/(3 pi^2 As))(MX/mP)^4 once the amplitude As is fitted and MX is chosen, so it retains some predictive content even though MX is selected partly to produce large r. The baryon asymmetry is presented as being reproduced rather than predicted, so that step is a consistency check, not a circular prediction. The citation of the hilltop-inflation regime from prior work that includes a co-author is not load-bearing, because the potential and slow-roll equations are derived in the text. The missing kappa_chi in the scan and the apparent mismatch between Eq. (34) and Table II are serious internal-consistency and correctness risks, but they are not circularity defects; they concern whether the quoted benchmark points are self-consistent, not whether the outputs are equivalent to the inputs.

Assumptions & free parameters 10 free parameters · 6 assumptions · 1 invented entities

The model's predictions rest on numerous fitted parameters (kappa_phi, delta_phi, phi_0, M_X, M_S, M, lambda, kappa_chi, M1-M2, f, alpha) and domain assumptions (SUGRA form, D-flatness, field content). No machine-checked derivation or code is provided; the benchmark points omit the waterfall parameter kappa_chi, leaving a key tuning unaccounted.

free parameters (10)
  • kappa_phi = 0.063, 0.059, 0.0438, 0.0344 (BP1-BP4)
    Coefficient of phi^2 in the inflationary potential; fitted to give ns = 0.9743 and N0 = 54.5.
  • delta_phi = -0.054, -0.219583, -0.929, -5.05927 (BP1-BP4)
    Coefficient of phi^4 in the SUGRA-corrected potential; fitted to ns and r.
  • M_X = 8.9e15, 6.0e15, 3.3e15, 1.8e15 GeV (BP1-BP4)
    Set by the scalar amplitude As via Eq. (27).
  • phi_0 = 1.2e18, 6.0e17, 2.5e17, 8.6e17 GeV
    Initial inflaton field value; chosen to satisfy N0 = 54.5.
  • M_S = 0.12, 0.11, 0.11, 0.09 mP
    Cutoff scale; benchmark values conflict with the stated definition M_S = mP/kappa with 0.1 <= kappa <= 1.
  • M (symmetry breaking scale) = 5.0e16, 4.5e16, 3.0e16, 2.0e16 GeV
    VEV scale <Delta_R>; chosen near the GUT scale.
  • kappa_chi = not specified
    Controls the waterfall critical value phi_c; must be tuned small for consistency with lambda ~ 10^-6, but never listed in Table II.
  • lambda (triplet coupling) = not listed; implied ~10^-6 from M1 via Eq. (35)
    Coupling in superpotential; effectively set by the chosen M1, M2 and M_S.
  • M1, M2 (left triplet masses) = about 10^10 GeV, nearly degenerate
    Chosen for resonant leptogenesis; mass splitting not quantified.
  • f, alpha, CP phases = not specified
    Yukawa couplings in leptogenesis and neutrino mass; fitted to observed neutrino splittings and nL/s.
assumptions (6)
  • domain assumption Slow-roll approximation with canonical kinetic terms for s, chi, phi along the D-flat direction.
    Section V; used to compute ns, r, As from the potential.
  • domain assumption Form of the SUGRA scalar potential (Eq. 10) and truncation of K to leading non-minimal terms.
    Section IV, Eq. (12); central to the predicted slope and stabilization.
  • domain assumption D-flatness conditions Delta = Delta-bar for L and R triplets; charged components of Delta_R have zero VEV before inflation.
    Section III; required for single-field inflation along the neutral directions.
  • domain assumption Matter parity and R-symmetry charge assignments in Table I fix the superpotential.
    Section II; forbids proton decay and unwanted terms.
  • ad hoc to paper The global minimum <S>=0, <Delta_R Delta-bar_R>=M_S M_X, and only Delta_L^1 drives inflation.
    Section III-IV; sets the inflationary trajectory and the waterfall endpoint.
  • ad hoc to paper Near-degenerate M1 about M2 and maximal CP phase for resonant type-II leptogenesis.
    Section VIII, Eq. (61); the asymmetry is highly sensitive to the unquantified splitting.
invented entities (1)
  • Second generation of left-handed Higgs triplets (Delta_L^2, Delta-bar_L^2)
    purpose: Provides a near-degenerate partner for resonant CP violation in leptogenesis.
    An added field content with no dedicated signature beyond contributing to CP asymmetry in the lepton sector.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Tribrid Inflation, Type II Leptogenesis, and Observable Gravitational Waves in $SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$." pith.science (2026). https://pith.science/paper/OEHI2FQN

@misc{pith2026250705564,
  author       = {Pith},
  title        = {Pith review of: Tribrid Inflation, Type II Leptogenesis, and Observable Gravitational Waves in $SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_B-L$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OEHI2FQN}},
  note         = {Machine review of arXiv:2507.05564}
}
abstract

We present a concrete realization of tribrid inflation within the framework of the gauge group $SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$. In this model, inflation is driven by the neutral components of left-handed Higgs triplets, which also play a central role in generating the observed baryon asymmetry of the universe via non-thermal leptogenesis. Tiny neutrino masses arise naturally through a type-II seesaw mechanism, facilitated by right-handed triplet fields. Supergravity corrections, stemming from the leading-order terms in a non-minimal K\"ahler potential, are essential in bringing the predictions of the scalar spectral index $n_s$ into agreement with the latest cosmological data, including the Atacama Cosmology Telescope Data Release 6, Planck 2018, and LB-BK18. A key feature of this model is the existence of a viable parameter space that predicts potentially observable primordial gravitational waves, with a tensor-to-scalar ratio $r \lesssim 0.005$, placing it within reach of upcoming experiments.

Figures

Figures reproduced from arXiv: 2507.05564 by the authors.

Figure 1
Figure 1. FIG. 1: The normalized two-field scalar potential, [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Tree-level and one-loop diagrams contributing to CP asymmetry in the decay of [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

  1. Supersymmetric Hybrid Inflation with K\"{a}hler-Induced $\mathbf{R}$-Symmetry Breaking

    hep-ph 2025-06 conditional novelty 5.0 of 10

    Nonrenormalizable R-symmetry breaking in the Kahler potential can tune the spectral index of supersymmetric hybrid inflation into the ACT DR6 window while keeping tensor modes below 1e-5.

  2. Waterfall phase in supersymmetric hybrid inflation

    hep-ph 2025-07 conditional novelty 4.0 of 10

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

Reference graph

Works this paper leans on

72 extracted references · 69 canonical work pages · cited by 2 Pith papers

  1. [1]

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

    work page 1981

  2. [2]

    The additional terms in the bosonic masses, of order O(M 4 X /m2 P ), arise from Planck- suppressed K¨ahler corrections and induce a small mass splitting between scalar and fermionic components. During inflation, the one-loop correction to the effective potential takes the form: Vloop = 3 × 2 64 ∆2 X i (−1)2si m4 i ln m2 i Q2 − 3/2 ≃ 3(κS∆R + κS ¯∆R) 16π2...

    work page 2018

  3. [3]

    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

  4. [4]

    Starobinsky

    Alexei A. Starobinsky. A New Type of Isotropic Cosmological Models Without Singularity.Phys. Lett. B, 91:99–102, 1980

    work page 1980

  5. [5]

    Andrei D. Linde. Hybrid inflation. Phys. Rev. D, 49:748–754, 1994

    work page 1994

  6. [6]

    G. R. Dvali, Q. Shafi, and Robert K. Schaefer. Large scale structure and supersymmetric inflation without fine tuning. Phys. Rev. Lett., 73:1886–1889, 1994

    work page 1994

  7. [7]

    Copeland, Andrew R

    Edmund J. Copeland, Andrew R. Liddle, David H. Lyth, Ewan D. Stewart, and David Wands. False vacuum inflation with Einstein gravity. Phys. Rev. D, 49:6410–6433, 1994

    work page 1994

  8. [8]

    Vedat Nefer Senoguz and Q. Shafi. Reheat temperature in supersymmetric hybrid inflation models. Phys. Rev. D, 71:043514, 2005

    work page 2005

Show all 72 references
  1. [9]

    Mansoor Ur Rehman, Qaisar Shafi, and Joshua R. Wickman. Hybrid Inflation Revisited in Light of WMAP5. Phys. Rev. D, 79:103503, 2009

    2009

  2. [10]

    Mansoor Ur Rehman, Qaisar Shafi, and Joshua R. Wickman. Supersymmetric Hybrid Inflation Redux. Phys. Lett. B, 683:191–195, 2010

    2010

  3. [11]

    Mansoor Ur Rehman, Qaisar Shafi, and Joshua R. Wickman. Minimal Supersymmetric Hybrid Inflation, Flipped SU(5) and Proton Decay. Phys. Lett. B, 688:75–81, 2010

    2010

  4. [12]

    Junaid, Salah Nasri, and Umer Zubair

    Waqas Ahmed, M. Junaid, Salah Nasri, and Umer Zubair. Constraining the cosmic strings gravitational wave spectra in no-scale inflation with viable gravitino dark matter and nonthermal leptogenesis. Phys. Rev. D , 105(11):115008, 2022

    2022

  5. [13]

    Leontaris, and Ilias Tavellaris

    Waqas Ahmed, Athanasios Karozas, George K. Leontaris, and Ilias Tavellaris. Hybrid inflation, reheating and dark radiation in a IIB perturbative moduli stabilization scenario. JHEP, 07:282, 2024

    2024

  6. [14]

    Supersymmetric hybrid inflation in light of CMB experiments and swampland conjectures

    Waqas Ahmed and Shabbar Raza. Supersymmetric hybrid inflation in light of CMB experiments and swampland conjectures. Chin. Phys. C, 49(1):013106, 2025

    2025

  7. [15]

    Panagiotakopoulos

    George Lazarides and C. Panagiotakopoulos. Smooth hybrid inflation. Phys. Rev. D, 52:R559–R563, 1995

    1995

  8. [16]

    Supersymmetric And Smooth Hybrid Inflation In The Light Of WMAP3

    Mansoor ur Rehman, Vedat Nefer Senoguz, and Qaisar Shafi. Supersymmetric And Smooth Hybrid Inflation In The Light Of WMAP3. Phys. Rev. D, 75:043522, 2007

    2007

  9. [17]

    Simplified Smooth Inflation with Observable Gravity Waves

    Mansoor Ur Rehman and Qaisar Shafi. Simplified Smooth Inflation with Observable Gravity Waves. Phys. Rev. D, 86:027301, 2012

    2012

  10. [18]

    Simplified Smooth Hybrid Inflation in Supersymmetric SU(5)

    Mansoor Ur Rehman and Umer Zubair. Simplified Smooth Hybrid Inflation in Supersymmetric SU(5). Phys. Rev. D, 91:103523, 2015

    2015

  11. [19]

    Leontaris, and Umer Zubair

    Waqas Ahmed, Athanasios Karozas, George K. Leontaris, and Umer Zubair. Smooth hybrid inflation with low reheat temperature and observable gravity waves in SU (5) × U (1)χ super-GUT. JCAP, 06(06):027, 2022

    2022

  12. [20]

    Smooth µ-hybrid and non-minimal Higgs inflation in SU(4)C × SU(2) L × SU(2)R with observable gravitational waves

    Umer Zubair. Smooth µ-hybrid and non-minimal Higgs inflation in SU(4)C × SU(2) L × SU(2)R with observable gravitational waves. JCAP, 02:033, 2025

    2025

  13. [21]

    Smooth hybrid inflation in light of ACT DR6 data

    Nobuchika Okada and Osamu Seto. Smooth hybrid inflation in light of ACT DR6 data. 6 2025

    2025

  14. [22]

    Jeannerot, S

    R. Jeannerot, S. Khalil, George Lazarides, and Q. Shafi. Inflation and monopoles in supersymmetric SU(4)C x SU(2)(L) x SU(2)(R). JHEP, 10:012, 2000

    2000

  15. [23]

    Inflation with a realistic SO(10) model

    Bumseok Kyae and Qaisar Shafi. Inflation with a realistic SO(10) model. AIP Conf. Proc., 805(1):439–442, 2005

    2005

  16. [24]

    Khalil, M

    S. Khalil, M. U. Rehman, Q. Shafi, and E. A. Zaakouk. Inflation in Supersymmetric SU(5). Phys. Rev. D, 83:063522, 2011

    2011

  17. [25]

    George Lazarides, Mansoor Ur Rehman, Qaisar Shafi, and Fariha K. Vardag. Shifted µ-hybrid inflation, gravitino dark matter, and observable gravity waves. Phys. Rev. D, 103(3):035033, 2021

    2021

  18. [26]

    Matthew Civiletti, Mansoor Ur Rehman, Qaisar Shafi, and Joshua R. Wickman. Red Spectral Tilt and Observable Gravity Waves in Shifted Hybrid Inflation. Phys. Rev. D, 84:103505, 2011

    2011

  19. [27]

    Radiative symmetry breaking, cosmic strings and observable gravity waves in U (1)R symmetric SU (5) × U (1)χ

    Waqas Ahmed and Umer Zubair. Radiative symmetry breaking, cosmic strings and observable gravity waves in U (1)R symmetric SU (5) × U (1)χ. JCAP, 01:019, 2023

    2023

  20. [28]

    Observable r, gravitino dark matter, and non-thermal leptogenesis in no-scale supergravity

    Waqas Ahmed, Muhammad Moosa, Shoaib Munir, and Umer Zubair. Observable r, gravitino dark matter, and non-thermal leptogenesis in no-scale supergravity. JHEP, 05:011, 2023

    2023

  21. [29]

    Supersymmetric hybrid inflation and metastable cosmic strings in SU (4)c × SU (2)L × U (1)R

    Adeela Afzal, Maria Mehmood, Mansoor Ur Rehman, and Qaiser Shafi. Supersymmetric hybrid inflation and metastable cosmic strings in SU (4)c × SU (2)L × U (1)R. 8 2023. 17

    2023

  22. [30]

    King, and Qaisar Shafi

    Stefan Antusch, Mar Bastero-Gil, Steve F. King, and Qaisar Shafi. Sneutrino hybrid inflation in supergravity. Phys. Rev. D, 71:083519, 2005

    2005

  23. [31]

    Stefan Antusch, Koushik Dutta, and Philipp M. Kostka. Tribrid Inflation in Supergravity. AIP Conf. Proc. , 1200(1):1007–1010, 2010

    2010

  24. [32]

    K ¨ahler-driven Tribrid Inflation

    Stefan Antusch and David Nolde. K ¨ahler-driven Tribrid Inflation. JCAP, 11:005, 2012

    2012

  25. [33]

    Pseudosmooth Tribrid Inflation

    Stefan Antusch, David Nolde, and Mansoor Ur Rehman. Pseudosmooth Tribrid Inflation. JCAP, 08:004, 2012

    2012

  26. [34]

    Sneutrino hybrid inflation

    Stefan Antusch. Sneutrino hybrid inflation. AIP Conf. Proc., 878(1):284–290, 2006

    2006

  27. [35]

    Baumann, Valerie F

    Stefan Antusch, Jochen P . Baumann, Valerie F. Domcke, and Philipp M. Kostka. Sneutrino Hybrid Inflation and Nonthermal Leptogenesis. JCAP, 10:006, 2010

    2010

  28. [36]

    Pseudosmooth Tribrid Inflation inSU (5)

    Muhammad Atif Masoud, Mansoor Ur Rehman, and Qaisar Shafi. Pseudosmooth Tribrid Inflation inSU (5). JCAP, 04:041, 2020

    2020

  29. [37]

    Baumann, Koushik Dutta, Steve F

    Stefan Antusch, Mar Bastero-Gil, Jochen P . Baumann, Koushik Dutta, Steve F. King, and Philipp M. Kostka. Gauge Non-Singlet Inflation in SUSY GUTs. JHEP, 08:100, 2010

    2010

  30. [38]

    Sneutrino tribrid inflation, metastable cosmic strings and gravitational waves

    Muhammad Atif Masoud, Mansoor Ur Rehman, and Qaisar Shafi. Sneutrino tribrid inflation, metastable cosmic strings and gravitational waves. JCAP, 11:022, 2021

    2021

  31. [39]

    Matter inflation with A4 flavour symmetry breaking

    Stefan Antusch and David Nolde. Matter inflation with A4 flavour symmetry breaking. JCAP, 10:028, 2013

    2013

  32. [40]

    R. N. Mohapatra and Jogesh C. Pati. A Natural Left-Right Symmetry. Phys. Rev. D, 11:2558, 1975

    1975

  33. [41]

    Senjanovic and Rabindra N

    G. Senjanovic and Rabindra N. Mohapatra. Exact Left-Right Symmetry and Spontaneous Violation of Parity. Phys. Rev. D, 12:1502, 1975

    1975

  34. [42]

    M. Magg, Q. Shafi, and C. Wetterich. Gauge Hierarchy in Presence of Discrete Symmetry. Phys. Lett. B, 87:227–232, 1979

    1979

  35. [43]

    Schechter and J

    J. Schechter and J. W. F. Valle. Neutrino Masses in SU(2) x U(1) Theories. Phys. Rev. D, 22:2227, 1980

    1980

  36. [44]

    Tanabashi et al

    M. Tanabashi et al. Review of Particle Physics. Phys. Rev. D, 98(3):030001, 2018

    2018

  37. [45]

    The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models

    Erminia Calabrese et al. The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models. 3 2025

    2025

  38. [46]

    Allys et al

    E. Allys et al. Probing Cosmic Inflation with the LiteBIRD Cosmic Microwave Background Polarization Survey. PTEP, 2023(4):042F01, 2023

    2023

  39. [47]

    Ghigna et al

    T. Ghigna et al. The LiteBIRD mission to explore cosmic inflation. In SPIE Astronomical T elescopes + Instrumentation 2024, 6 2024

    2024

  40. [48]

    CMB-S4: Forecasting Constraints on Primordial Gravitational Waves

    Kevork Abazajian et al. CMB-S4: Forecasting Constraints on Primordial Gravitational Waves. Astrophys. J. , 926(1):54, 2022

    2022

  41. [49]

    The Simons Observatory: Science goals and forecasts

    Peter Ade et al. The Simons Observatory: Science goals and forecasts. JCAP, 02:056, 2019

    2019

  42. [50]

    Supersymmetric triplet Higgs model of neutrino masses and leptogenesis

    Thomas Hambye, Ernest Ma, and Utpal Sarkar. Supersymmetric triplet Higgs model of neutrino masses and leptogenesis. Nucl. Phys. B, 602:23–38, 2001

    2001

  43. [51]

    Stefan Antusch and Steve F. King. Type II Leptogenesis and the neutrino mass scale. Phys. Lett. B , 597:199–207, 2004

    2004

  44. [52]

    Uma Sankar

    Narendra Sahu and S. Uma Sankar. Bound on neutrino masses from leptogenesis in type-II see-saw models. Phys. Rev. D, 71:013006, 2005

    2005

  45. [53]

    Triplet Leptogenesis in Left-Right Symmetric Seesaw Models

    Tomas Hallgren, Thomas Konstandin, and Tommy Ohlsson. Triplet Leptogenesis in Left-Right Symmetric Seesaw Models. JCAP, 01:014, 2008

    2008

  46. [54]

    V . A. Kuzmin, V . A. Rubakov, and M. E. Shaposhnikov. On the Anomalous Electroweak Baryon Number Noncon- servation in the Early Universe. Phys. Lett. B, 155:36, 1985

    1985

  47. [55]

    McLerran

    Peter Brockway Arnold and Larry D. McLerran. Sphalerons, Small Fluctuations and Baryon Number Violation in Electroweak Theory. Phys. Rev. D, 36:581, 1987

    1987

  48. [56]

    Revisiting Big-Bang Nucleosynthesis Constraints on Long-Lived Decaying Particles

    Masahiro Kawasaki, Kazunori Kohri, Takeo Moroi, and Yoshitaro Takaesu. Revisiting Big-Bang Nucleosynthesis Constraints on Long-Lived Decaying Particles. Phys. Rev. D, 97(2):023502, 2018

    2018

  49. [57]

    Pati and Abdus Salam

    Jogesh C. Pati and Abdus Salam. Lepton Number as the Fourth Color. Phys. Rev. D, 10:275–289, 1974. [Erratum: Phys.Rev.D 11, 703–703 (1975)]

    1975

  50. [58]

    Mohapatra and Jogesh C

    Rabindra N. Mohapatra and Jogesh C. Pati. Left-Right Gauge Symmetry and an Isoconjugate Model of CP Viola- tion. Phys. Rev. D, 11:566–571, 1975

    1975

  51. [59]

    µ-hybrid inflation and metastable cosmic strings in SU(3)c×SU(2)L×SU(2)R×U(1)B-L

    Muhammad Nadeem Ahmad, Maria Mehmood, Mansoor Ur Rehman, and Qaisar Shafi. µ-hybrid inflation and metastable cosmic strings in SU(3)c×SU(2)L×SU(2)R×U(1)B-L. Phys. Rev. D, 111(8):083526, 2025

    2025

  52. [60]

    Smooth Hybrid Inflation and Non-Thermal Type II Leptogenesis

    Shaaban Khalil, Qaisar Shafi, and Arunansu Sil. Smooth Hybrid Inflation and Non-Thermal Type II Leptogenesis. Phys. Rev. D, 86:073004, 2012

    2012

  53. [61]

    Aghanim et al

    N. Aghanim et al. Planck2018 results: Vi. cosmological parameters. Astronomy amp; Astrophysics, 641:A6, Septem- ber 2020

    2020

  54. [62]

    Akrami et al

    Y. Akrami et al. Planck 2018 results. X. Constraints on inflation. Astron. Astrophys., 641:A10, 2020

    2018

  55. [63]

    Mansoor Ur Rehman, Qaisar Shafi, and Joshua R. Wickman. Observable Gravity Waves from Supersymmetric Hybrid Inflation II. Phys. Rev. D, 83:067304, 2011

    2011

  56. [64]

    Kolb and Michael S

    Edward W. Kolb and Michael S. Turner. The early universe. 1990. 18

    1990

  57. [65]

    How long before the end of inflation were observable perturbations produced? Phys

    Andrew R Liddle and Samuel M Leach. How long before the end of inflation were observable perturbations produced? Phys. Rev. D, 68:103503, 2003

    2003

  58. [66]

    Big-Bang Nucleosynthesis and Grav- itino

    Masahiro Kawasaki, Kazunori Kohri, Takeo Moroi, and Akira Yotsuyanagi. Big-Bang Nucleosynthesis and Grav- itino. Phys. Rev. D, 78:065011, 2008

    2008

  59. [67]

    Gialamas, and Vassilis C

    Helmut Eberl, Ioannis D. Gialamas, and Vassilis C. Spanos. Gravitino thermal production revisited. Phys. Rev. D, 103(7):075025, 2021

    2021

  60. [68]

    µ-hybrid inflation, gravitino dark matter, and stochastic gravitational wave background from cosmic strings

    Adeela Afzal, Waqas Ahmed, Mansoor Ur Rehman, and Qaisar Shafi. µ-hybrid inflation, gravitino dark matter, and stochastic gravitational wave background from cosmic strings. Phys. Rev. D, 105(10):103539, 2022

    2022

  61. [69]

    Ivan Esteban, M. C. Gonzalez-Garcia, Michele Maltoni, Ivan Martinez-Soler, Jo ˜ao Paulo Pinheiro, and Thomas Schwetz. NuFit-6.0: updated global analysis of three-flavor neutrino oscillations. JHEP, 12:216, 2024

    2024

  62. [70]

    Navas et al

    S. Navas et al. Review of particle physics. Phys. Rev. D, 110(3):030001, 2024

    2024

  63. [71]

    M. Yu. Khlopov and Andrei D. Linde. Is It Easy to Save the Gravitino? Phys. Lett. B, 138:265–268, 1984

    1984

  64. [72]

    Ellis, Jihn E

    John R. Ellis, Jihn E. Kim, and Dimitri V . Nanopoulos. Cosmological Gravitino Regeneration and Decay.Phys. Lett. B, 145:181–186, 1984

    1984

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.