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Shifted Hybrid Realization of Non-Minimal Higgs Inflation in Light of ACT DR6 and Planck Data

T0 review · 2 major / 5 minor · reviewed 2026-07-11 · grok-4.5

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Pith's one-line read A small nonrenormalizable superpotential term deforms Starobinsky-like nonminimal Higgs inflation so its scalar spectral index matches ACT DR6 while keeping a small tensor ratio.

desk verdict Solid, usable model-building paper: modest positive β_κ deforms non-minimal Higgs inflation into the ACT ns window while keeping r small, sub-Planckian fields, and viable leptogenesis. read the letter →

arxiv 2607.04504 v1 pith:X5NJ4ROO submitted 2026-07-05 hep-ph astro-ph.CO

Nadir Ijaz , Pirzada , Mansoor Ur Rehman This is my paper · ORCID
classification hep-phastro-ph.CO
keywords nonminimalHiggsinflationshiftedhybridStarobinskyattractorACTDR6no-scalesupergravitynonthermalleptogenesisPati-Salamscalarspectralindex
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

Recent CMB data, especially ACT DR6 combined with Planck and DESI, prefer a slightly higher scalar spectral index than classic Starobinsky or large-coupling nonminimal Higgs inflation deliver. This paper embeds nonminimal Higgs inflation in a no-scale-inspired supergravity setup based on shifted hybrid inflation in a Pati-Salam model, so that the GUT Higgs, after the orthogonal fields are stabilized, acts as the inflaton. Adding the leading nonrenormalizable operator in the superpotential tilts the Einstein-frame plateau just enough to raise the spectral index into the ACT-favored window while the tensor-to-scalar ratio stays small (roughly a few times 10 to the minus 3). The field values remain sub-Planckian, supergravity corrections stay under control, and the same parameter space supports reheating temperatures of order 10^8 GeV together with successful nonthermal leptogenesis. The result is a concrete particle-physics realization that can sit inside current data without abandoning the attractor structure that made these models attractive in the first place.

What carries the argument

The parameter beta_kappa (the ratio of the nonrenormalizable coupling beta to the hybrid coupling kappa) that deforms the Einstein-frame potential of the nonminimally coupled GUT Higgs after the singlet and phases are stabilized at the origin by a positive gamma_4 term in the no-scale-inspired Kahler potential.

What would settle it

A high-precision measurement of the scalar spectral index and tensor-to-scalar ratio that either excludes the continuous corridor of (xi, beta_kappa) points the paper maps (roughly xi from a few hundred to 10^4 and beta_kappa from 0.02 to 0.2) or finds a running or multi-field signature inconsistent with the single-field predictions.

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Extended reading notes

Core claim

The leading nonrenormalizable operator in the shifted-hybrid superpotential produces a controlled deformation of the Starobinsky attractor realized by nonminimal Higgs inflation, shifting the scalar spectral index into the range preferred by ACT DR6 and related CMB combinations while keeping r of order 10^{-3} to 10^{-2}, with sub-Planckian inflaton values and a viable reheating-plus-leptogenesis history.

Load-bearing premise

That a positive quartic term in the Kahler potential plus the D-flat trajectory keep the orthogonal singlet and phases locked at the origin throughout inflation, so the dynamics really reduce to a single effective field.

Editorial extensions

If this is right

  • ACT-preferred higher ns values become reachable inside a supersymmetric GUT without abandoning small r or sub-Planckian fields.
  • The same corridor yields r approximately 0.004-0.007, inside the reach of LiteBIRD and CMB-S4.
  • Reheating at Tr ~ 10^8 GeV and nonthermal leptogenesis remain viable on the same parameter points that fit the CMB.
  • Mild differences between ACT and SPT preferred tilts can be absorbed by the intrinsic xi-beta_kappa degeneracy.

Reading between the lines

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

  • If residual multi-field or isocurvature modes survive stabilization, the quoted ns-r track would broaden or shift, providing a clean multi-field test of the construction.
  • The same nonrenormalizable operator that lifts ns could leave correlated imprints on proton-decay rates or right-handed neutrino mass hierarchies once the full Pati-Salam spectrum is fixed.
  • A future null detection of r below a few times 10^{-3} would force the model into the extreme-xi or near-zero-beta_kappa edge of its corridor.
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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 / 5 minor

Summary. The paper constructs a shifted hybrid realization of non-minimal Higgs inflation in a no-scale-inspired supergravity embedding of the supersymmetric Pati–Salam model. After stabilizing the orthogonal singlet and phases, the GUT Higgs direction becomes the inflaton. Inclusion of the leading non-renormalizable superpotential operator proportional to β deforms the Starobinsky attractor, raising the scalar spectral index ns into the range preferred by ACT DR6 (and ACT+Planck+DESI) combinations while keeping r ∼ 10^{-3}–10^{-2}. Analytic slow-roll expressions, a full numerical Einstein-frame scan of the (ξ, β_κ) plane (with As fixing κ and a sub-Planckian prior), and a consistent treatment of reheating plus non-thermal leptogenesis are presented; viable regions simultaneously satisfy current CMB constraints and a realistic post-inflationary history.

Significance. If the effective single-field description and the controlled character of the β-induced deformation hold, the work supplies a concrete, particle-physics-motivated mechanism that reconciles attractor inflation with the mildly higher ns favored by recent ACT-informed data sets, while remaining inside a supersymmetric GUT framework that also addresses the μ problem, generates right-handed neutrino masses, and realizes non-thermal leptogenesis. Strengths that should be credited include the explicit Einstein-frame potential, the transparent analytic correction terms (Eqs. 25–26), the systematic numerical mapping of a continuous viable corridor in the (ξ, β_κ) plane with As normalization, the demonstration of sub-Planckian field values, and the closed reheating/leptogenesis analysis that yields Tr ∼ 10^8 GeV and a successful baryon asymmetry for hierarchical RHNs. The predicted r window is falsifiable by LiteBIRD and CMB-S4.

major comments (2)
  1. [Section III] Sec. III, Eqs. (16)–(18) and Fig. 2: Stabilization of the orthogonal singlet s and the phases is shown for β_κ = 0 in the large-ξ regime by minimizing the approximate potential and noting that the s-mass scales as ∼√(γ_4 ξ) h. For the observationally relevant window 0.02 ≲ β_κ ≲ 0.2 and along the full trajectory (including near the end of inflation where ψ ∼ O(1)), residual multi-field or isocurvature contributions are not quantified. A short calculation of the effective mass-matrix eigenvalues or the isocurvature power spectrum along the numerical background would make the reduction to the quoted single-field ns–r predictions fully robust.
  2. [Section V] Sec. V and Figs. 6–8: The numerical scan that identifies the viable corridor is performed at fixed M/m_P = 0.01 and Tr = 10^8 GeV (hence N_0 ≃ 53). Because both the e-fold relation and the amplitude constraint depend on these choices, a brief robustness check against modest variations of M and Tr (or equivalently of N_0) is needed to confirm that the continuous ACT-compatible region is not an artifact of the benchmark values.
minor comments (5)
  1. [Throughout] Notation for the reduced Planck mass is inconsistent (m_P, M_P, mP). Standardize throughout.
  2. [Section II] Fig. 1: the two analytic branches of v/M are plotted, but the caption and the surrounding text do not clearly state which branch is used for the subsequent inflationary analysis (v_+ or v_-).
  3. [Section IV] Eq. (26) and the paragraph that follows: the validity condition β_κ ≪ ξ/N_0^{2} is stated, yet several of the sample points shown in Figs. 6–8 approach or mildly violate this hierarchy; a short remark on the size of the neglected higher-order terms would be helpful.
  4. [Section VI] Table II and the surrounding leptogenesis discussion: the required |δ_eff| ≃ 0.96 is close to the theoretical maximum. A one-sentence comment on how sensitive the success of leptogenesis is to a modest reduction of this phase would improve transparency.
  5. [Introduction and Section V] Several references to ACT DR6, SPT-3G D1 and DESI appear with slightly different numerical central values for ns across the text and figure captions; a single consistent set of quoted numbers (with clear data-combination labels) would avoid confusion.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: free-parameter scan for ACT-compatible ns is standard phenomenological accommodation, not a by-construction prediction or self-definitional loop.

full rationale

The derivation chain is self-contained. Superpotential (Eq. 3) and no-scale-inspired Kähler (Eq. 8) are written explicitly; the Einstein-frame potential (Eqs. 17–19) follows by standard SUGRA formulae; multi-field stabilization to an effective single-field trajectory along h is shown by minimizing the approximate potential (Eq. 16) and by the mass scaling ~√(γ4 ξ) h, with Fig. 2 illustrating the saddle. Slow-roll parameters and observables are then obtained analytically (Eqs. 25–26) and numerically without external load-bearing uniqueness theorems. The βκ term appears as a free higher-dimensional coefficient that deforms the Starobinsky plateau; the paper scans (ξ, βκ) (Figs. 6–8) and reports the corridor that places ns inside the ACT/CMB-SPA bands while keeping r ~ 10^{-3}–10^{-2} and h0 ≲ mP. This is ordinary model-building compatibility, not a fitted input re-labeled as an independent prediction: As merely normalizes κ (standard), N0 is fixed by a reheating prior, and both ns and r are computed from the same potential. Self-citations to prior Rehman/Pallis hybrid and non-minimal constructions supply context and benchmarks but are not required for the present potential or the deformation formulae. Residual multi-field caveats exist but do not create circularity. Score 1 only for the routine presence of author-overlapping references that are non-load-bearing.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a standard supergravity scalar potential, a specific no-scale-inspired Kahler form, the shifted-hybrid superpotential truncation, and several free parameters that are adjusted to match As and ns. No new particles or forces are postulated; the free parameters and domain assumptions listed below are what allow the Starobinsky attractor to be deformed into the ACT window.

free parameters (6)
  • xi (non-minimal coupling) = 10^2 to 10^4 (corridor)
    Scanned over ~10^2-10^4 to keep fields sub-Planckian and to control the plateau height; fixed only after matching As and ns.
  • beta_kappa = beta/kappa = 0.02-0.2
    The deformation parameter that raises ns; scanned 0.02-0.2 to land inside ACT or CMB-SPA bands.
  • kappa (superpotential coupling) = 0.002-0.06
    Fixed by the observed scalar amplitude As once xi and beta_kappa are chosen.
  • M (GUT-scale mass) = 0.01 mP
    Set by hand to 0.01 mP throughout the numerical scan.
  • gamma_4 (Kahler quartic) = ~0.3
    Chosen positive (~0.3) to stabilize the singlet S; not derived from a deeper principle.
  • Tr (reheating temperature) = 10^8 GeV
    Fixed at 10^8 GeV to obtain N0 ~53; also used for leptogenesis viability.
assumptions (5)
  • domain assumption Einstein-frame supergravity scalar potential VE = e^{K/mP^2} [(K^{-1})^{ij} D_i W D_j W* - 3 |W|^2 / mP^2] is the correct low-energy description.
    Standard N=1 supergravity; invoked from Sec. II onward.
  • domain assumption The no-scale-inspired logarithmic Kahler potential (Eq. 8) with the gamma_4 term stabilizes S and the phases at the origin, yielding an effective single-field trajectory along the GUT Higgs.
    Sec. III and Fig. 2; required for the reduction to the potential of Eq. 19.
  • ad hoc to paper The leading non-renormalizable operator beta S (H^c H^c)^2 / mP^2 is the dominant higher-dimensional correction and can be taken positive.
    Introduced in Eq. 3 and used to generate the deformation term proportional to beta_kappa; other possible structures are argued to vanish on the D-flat direction.
  • standard math Slow-roll parameters and the number of e-folds can be evaluated with the standard single-field formulas once the orthogonal fields are stabilized.
    Eqs. 21-23; conventional once the multi-field reduction is granted.
  • domain assumption Post-inflationary history is radiation-dominated after instantaneous reheating at Tr ~ 10^8 GeV, allowing the standard N0 formula (Eq. 46).
    Sec. VI; required to convert Tr into the e-fold number used for ns and r.

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Cite this review

Pith. "Pith review of Shifted Hybrid Realization of Non-Minimal Higgs Inflation in Light of ACT DR6 and Planck Data." pith.science (2026). https://pith.science/paper/X5NJ4ROO

@misc{pith2026260704504,
  author       = {Pith},
  title        = {Pith review of: Shifted Hybrid Realization of Non-Minimal Higgs Inflation in Light of ACT DR6 and Planck Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X5NJ4ROO}},
  note         = {Machine review of arXiv:2607.04504}
}
abstract

We investigate non-minimal Higgs inflation in a no-scale-inspired supergravity framework and confront its predictions with the latest CMB constraints from ACT DR6 and \emph{Planck}. Working within a shifted hybrid inflation scenario, we construct an effective single-field description in which the GUT Higgs direction serves as the inflaton after stabilization of the orthogonal scalar fields. We show that the inclusion of the leading nonrenormalizable operator in the superpotential induces a controlled deformation of the Starobinsky attractor, allowing the scalar spectral index to be shifted into the range favored by recent ACT and related CMB datasets while maintaining a small tensor-to-scalar ratio, $r \sim 10^{-3}-10^{-2}$. The resulting inflationary dynamics remain theoretically consistent, with controlled supergravity corrections and sub-Planckian inflaton field values. We perform a detailed numerical analysis of the model parameter space, including reheating and nonthermal leptogenesis, and identify regions that simultaneously satisfy current observational constraints and yield a viable post-inflationary cosmological history.

Figures

Figures reproduced from arXiv: 2607.04504 by the authors.

Figure 1
Figure 1. FIG. 1. Normalized Higgs vev vs [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Normalized Einstein-frame potential [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Predictions in the ( [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Predicted values of the parameters [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Color-coded map of the model predictions in the [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Color-coded map of the model predictions in the [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

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Forward citations

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Reference graph

Works this paper leans on

101 extracted references · 2 canonical work pages · cited by 3 Pith papers

  1. [1]

    3 128π3 ˜ 6ξyΩ3{2 0 J0 ¸2 ˆ M MP ˙2 ˆ minf MP ˙2 minf,(44) wherey

    Figure 6 displays the predicted scalar spectral in- dexn s in the (ξ, β κ) plane, with each point color-coded according to itsn s value using theCMashercolormap (cmr.ocean) [90]. The white (red) circles denote raw pa- rameter points lying within the 1σ(2σ) regions of the scan, while the shaded bands represent smooth inter- polations of the corresponding c...

    2000

  2. [2]

    A. H. Guth, Inflationary universe: A possible solution to the horizon and flatness problems, Phys. Rev. D23, 347 (1981)

    1981

  3. [3]

    A. D. Linde, A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems, Phys. Lett. 12 B108, 389 (1982)

    1982

  4. [4]

    Albrecht and P

    A. Albrecht and P. J. Steinhardt, Cosmology for grand unified theories with radiatively induced symmetry breaking, Phys. Rev. Lett.48, 1220 (1982)

    1982

  5. [5]

    V. F. Mukhanov and G. V. Chibisov, Quantum fluctu- ations and a nonsingular universe, JETP Lett.33, 532 (1981)

    1981

  6. [6]

    S. W. Hawking, The development of irregularities in a single bubble inflationary universe, Phys. Lett. B115, 295 (1982)

    1982

  7. [7]

    A. A. Starobinsky, Dynamics of Phase Transition in the New Inflationary Universe Scenario and Generation of Perturbations, Phys. Lett. B117, 175 (1982)

    1982

  8. [8]

    A. H. Guth and S. Y. Pi, Fluctuations in the New In- flationary Universe, Phys. Rev. Lett.49, 1110 (1982)

    1982

Show all 101 references
  1. [9]

    Aghanimet al.(Planck), Planck 2018 results

    N. Aghanimet 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]

    2018 arXiv

  2. [10]

    Akramiet al.(Planck), Planck 2018 results

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

    2018 arXiv

  3. [11]

    P. A. R. Adeet al.(BICEP, Keck), Improved Constraints on Primordial Gravitational Waves us- ing Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season, Phys. Rev. Lett. 127, 151301 (2021), arXiv:2110.00483 [astro-ph.CO]

    2018

  4. [12]

    Louis and the ACT Collaboration, The atacama cosmology telescope: Dr6 power spectra, likelihoods andλcdm parameters (2025), arXiv:2503.14452 [astro- ph.CO]

    T. Louis and the ACT Collaboration, The atacama cosmology telescope: Dr6 power spectra, likelihoods andλcdm parameters (2025), arXiv:2503.14452 [astro- ph.CO]

    2025 arXiv

  5. [13]

    DESI Collaboration, A. G. Adame,et al., Desi 2024 iii: Baryon acoustic oscillations from galaxies and quasars (2024), arXiv:2404.03000 [astro-ph.CO]

    2024 arXiv

  6. [15]

    Collaboration, Desi dr2 results ii: Measurements of baryon acoustic oscillations and cosmological con- straints (2025), arXiv:2503.14738 [astro-ph.CO]

    D. Collaboration, Desi dr2 results ii: Measurements of baryon acoustic oscillations and cosmological con- straints (2025), arXiv:2503.14738 [astro-ph.CO]

    2025 arXiv

  7. [16]

    A. A. Starobinsky, A New Type of Isotropic Cosmolog- ical Models Without Singularity, Phys. Lett. B91, 99 (1980)

    1980

  8. [17]

    Kallosh and A

    R. Kallosh and A. Linde, Universality Class in Confor- mal Inflation, JCAP2013(07), 002, arXiv:1306.5220 [hep-th]

    arXiv

  9. [18]

    Kallosh, A

    R. Kallosh, A. Linde, and D. Roest, Supercon- formal inflationaryα-attractors, JHEP11(198), arXiv:1311.0472

    arXiv

  10. [19]

    Pallis, Starobinsky Inflation with T-Model K¨ ahler Geometries, Universe11, 75 (2025), arXiv:2502.00636 [hep-ph]

    C. Pallis, Starobinsky Inflation with T-Model K¨ ahler Geometries, Universe11, 75 (2025), arXiv:2502.00636 [hep-ph]

    2025 arXiv

  11. [20]

    Ellis, M

    J. Ellis, M. A. G. Garcia, K. A. Olive, and S. Verner, Constraints on attractor models of inflation and re- heating from Planck, BICEP/Keck, ACT DR6, and SPT-3G data, Phys. Rev. D113, 063571 (2026), arXiv:2510.18656 [hep-ph]

    2026

  12. [21]

    Ellis, M

    J. Ellis, M. A. G. Garc´ ıa, N. Nagata, D. V. Nanopoulos, and K. A. Olive, Deformations of Starobinsky inflation in no-scale SU(5) and SO(10) GUTs, JCAP2025(12), 038, arXiv:2508.13279 [hep-ph]

    arXiv

  13. [22]

    Pallis, ACT-inspired K¨ ahler-based inflationary at- tractors, JCAP2025(09), 061, arXiv:2507.02219 [hep- ph]

    C. Pallis, ACT-inspired K¨ ahler-based inflationary at- tractors, JCAP2025(09), 061, arXiv:2507.02219 [hep- ph]

  14. [23]

    Pallis, Updating GUT-scale pole Higgs inflation after ACT DR6, Phys

    C. Pallis, Updating GUT-scale pole Higgs inflation after ACT DR6, Phys. Rev. D113, 015033 (2026), arXiv:2510.02083 [hep-ph]

    2026

  15. [24]

    Ahmed, C

    W. Ahmed, C. Pallis, and M. U. Rehman, F-Term Hy- brid Inflation with T-Model K¨ ahler Geometry and Be- yond (2026), arXiv:2605.08931 [hep-ph]

    2026 arXiv

  16. [25]

    Ellis, T

    J. Ellis, T. Gherghetta, K. Kaneta, W. Ke, and K. A. Olive, Radiative corrections in supergravity models of inflation, JHEP2026(05), 229, arXiv:2603.02389 [hep- ph]

  17. [26]

    Pirzada, I. Khan, M. Khan, T. Li, and A. Muhammad, Non-Minimal Dilaton Inflation from the Effective Glu- odynamics (2026), arXiv:2603.00818 [hep-ph]

    2026 arXiv

  18. [27]

    W. J. Wolf, Inflationary attractors and radiative cor- rections in light of ACT data, JCAP2026(02), 088, arXiv:2506.12436 [astro-ph.CO]

  19. [28]

    Ahmed and M

    W. Ahmed and M. U. Rehman, Radiatively cor- rected Starobinsky inflation and primordial gravita- tional waves in light of ACT observations, Phys. Rev. D112, 063519 (2025), arXiv:2506.18077 [astro-ph.CO]

    2025 arXiv

  20. [29]

    Alexandre, L

    J. Alexandre, L. Heurtier, and S. Pla, Exact Renor- malisation Group Evolution of the Inflation Dy- namics: Reconcilingα-Attractors with ACT (2025), arXiv:2511.05296 [hep-th]

    2025

  21. [30]

    C. Fu, D. Lu, and S.-J. Wang, Harrison-Zeldovich at- tractor: From Planck to ACT results, Phys. Rev. D 113, L081304 (2026), arXiv:2510.24682 [astro-ph.CO]

    2026 arXiv

  22. [31]

    Kallosh and A

    R. Kallosh and A. Linde, On the present status of in- flationary cosmology, Gen. Rel. Grav.57, 135 (2025), arXiv:2505.13646 [hep-th]

    2025

  23. [32]

    Ellis, T

    J. Ellis, T. Gherghetta, K. Kaneta, W. Ke, and K. A. Olive, Effects of radiative corrections on Starobin- sky inflation, Phys. Rev. D112, 123530 (2025), arXiv:2510.15137 [hep-ph]

    2025

  24. [33]

    Ahmed, W

    W. Ahmed, W. Ahmad, A. Illahi, and M. Junaid, Warm Hybrid Axion Inflation inα-Attractor Models Con- strained by ACT and Future Plan experiments (2026), arXiv:2601.10145 [hep-ph]

    2026

  25. [34]

    Namikawa, A

    T. Namikawa, A. I. Lonappan, C. Baccigalupi,et al., Litebird science goals and forecasts: Improving sensitiv- ity to inflationary gravitational waves with multitracer delensing (2023), arXiv:2312.05194 [astro-ph.CO]

    2023 arXiv

  26. [35]

    Abazajian and others (CMB-S4 Collaboration), Cmb-s4 science case, reference design, and project plan (2019), arXiv:1907.04473 [astro-ph.IM]

    K. Abazajian and others (CMB-S4 Collaboration), Cmb-s4 science case, reference design, and project plan (2019), arXiv:1907.04473 [astro-ph.IM]

    2019 arXiv

  27. [36]

    G. R. Dvali, Q. Shafi, and R. K. Schaefer, Large scale structure and supersymmetric inflation without fine tuning, Phys. Rev. Lett.73, 1886 (1994), arXiv:hep- ph/9406319

    1994

  28. [37]

    E. J. Copeland, A. R. Liddle, D. H. Lyth, E. D. Stew- art, and D. Wands, False vacuum inflation with Ein- stein gravity, Phys. Rev. D49, 6410 (1994), arXiv:astro- ph/9401011

    1994

  29. [38]

    V. N. Senoguz and Q. Shafi, Testing supersymmetric grand unified models of inflation, Phys. Lett. B567, 79 (2003), arXiv:hep-ph/0305089

    2003 arXiv

  30. [39]

    V. N. Senoguz and Q. Shafi, Reheat temperature in su- persymmetric hybrid inflation models, Phys. Rev. D71, 043514 (2005), arXiv:hep-ph/0412102

    2005 arXiv

  31. [40]

    M. U. Rehman, Q. Shafi, and J. R. Wickman, Super- symmetric Hybrid Inflation Redux, Phys. Lett. B683, 13 191 (2010), arXiv:0908.3896 [hep-ph]

    2010 arXiv

  32. [41]

    M. U. Rehman and Q. Shafi, Supersymmetric hybrid inflation in light of the Atacama Cosmology Telescope data release 6, Planck 2018, and LB-BK18, Phys. Rev. D112, 023529 (2025), arXiv:2504.14831 [astro-ph.CO]

    2018 arXiv

  33. [42]

    Okada and O

    N. Okada and O. Seto, Smooth hybrid inflation in light of ACT DR6 data, Phys. Rev. D112, 083549 (2025), arXiv:2506.15965 [hep-ph]

    2025

  34. [43]

    Ahmed, C

    W. Ahmed, C. Pallis, and M. U. Rehman, GUT- scale smooth hybrid inflation with a stabilized mod- ulus in light of ACT and SPT data, JCAP06, 048, arXiv:2510.20478 [hep-ph]

    arXiv

  35. [44]

    ur Rehman, V

    M. ur Rehman, V. N. Senoguz, and Q. Shafi, Supersym- metric And Smooth Hybrid Inflation In The Light Of WMAP3, Phys. Rev. D75, 043522 (2007), arXiv:hep- ph/0612023

    2007

  36. [45]

    M. U. Rehman, Q. Shafi, and J. R. Wickman, Ob- servable Gravity Waves from Supersymmetric Hy- brid Inflation II, Phys. Rev. D83, 067304 (2011), arXiv:1012.0309 [astro-ph.CO]

    2011 arXiv

  37. [46]

    M. B. Einhorn and D. R. T. Jones, Inflation with Non- minimal Gravitational Couplings in Supergravity, JHEP 2010(03), 026, arXiv:0912.2718 [hep-ph]

    2010 arXiv

  38. [47]

    Ferrara, R

    S. Ferrara, R. Kallosh, A. Linde, A. Marrani, and A. Van Proeyen, Superconformal Symmetry, NMSSM, and Inflation, Phys. Rev. D83, 025008 (2011), arXiv:1008.2942 [hep-th]

    2011 arXiv

  39. [49]

    M. M. A. Abid, M. Mehmood, M. U. Rehman, and Q. Shafi, Realistic inflation in no-scale U(1) R sym- metric flipped SU(5), JCAP10(015), arXiv:2107.05678 [hep-ph]

    arXiv

  40. [50]

    Jeannerot, S

    R. Jeannerot, S. Khalil, G. Lazarides, and Q. Shafi, Inflation and monopoles in supersymmetric SU(4)C x SU(2)(L) x SU(2)(R), JHEP2000(10), 012, arXiv:hep- ph/0002151

  41. [51]

    Khalil, M

    S. Khalil, M. U. Rehman, Q. Shafi, and E. A. Zaakouk, Inflation in Supersymmetric SU(5), Phys. Rev. D83, 063522 (2011), arXiv:1010.3657 [hep-ph]

    2011 arXiv

  42. [52]

    Civiletti, M

    M. Civiletti, M. U. Rehman, Q. Shafi, and J. R. Wick- man, Red Spectral Tilt and Observable Gravity Waves in Shifted Hybrid Inflation, Phys. Rev. D84, 103505 (2011), arXiv:1104.4143 [astro-ph.CO]

    2011 arXiv

  43. [53]

    J. C. Pati and A. Salam, Unified Lepton-Hadron Sym- metry and a Gauge Theory of the Basic Interactions, Phys. Rev. D8, 1240 (1973)

    1973

  44. [54]

    Melfo, G

    A. Melfo, G. Senjanovi´ c, and F. Vissani, Minimal su- persymmetric pati-salam theory: Determination of the fundamental scale, Phys. Rev. D68, 035013 (2003)

    2003

  45. [55]

    J. C. Pati and A. Salam, Lepton Number as the Fourth Color, Phys. Rev. D10, 275 (1974), [Erratum: Phys.Rev.D 11, 703–703 (1975)]

    1974

  46. [56]

    Lazarides, M

    G. Lazarides, M. U. Rehman, Q. Shafi, and F. K. Vardag, Shiftedµ-hybrid inflation, gravitino dark mat- ter, and observable gravity waves, Phys. Rev. D103, 035033 (2021), arXiv:2007.01474 [hep-ph]

    2021 arXiv

  47. [57]

    Lazarides, M

    G. Lazarides, M. U. Rehman, and Q. Shafi, Proton de- cay in supersymmetric su(4)cˆsu(2)lˆsu(2)r, Journal of High Energy Physics2020, 10.1007/jhep10(2020)085 (2020)

    2020 doi

  48. [58]

    A. H. Chamseddine, R. L. Arnowitt, and P. Nath, Lo- cally Supersymmetric Grand Unification, Phys. Rev. Lett.49, 970 (1982)

    1982

  49. [59]

    G. R. Dvali, G. Lazarides, and Q. Shafi, Mu prob- lem and hybrid inflation in supersymmetric SU(2)-L x SU(2)-R x U(1)-(B-L), Phys. Lett. B424, 259 (1998), arXiv:hep-ph/9710314

    1998 arXiv

  50. [60]

    M. U. Rehman, Q. Shafi, and F. K. Vardag,µ-Hybrid Inflation with Low Reheat Temperature and Observ- able Gravity Waves, Phys. Rev. D96, 063527 (2017), arXiv:1705.03693 [hep-ph]

    2017 arXiv

  51. [61]

    M. U. Rehman, Q. Shafi, and U. Zubair, Gravity waves and proton decay in a flipped SU(5) hybrid inflation model, Phys. Rev. D97, 123522 (2018), arXiv:1804.02493 [hep-ph]

    2018 arXiv

  52. [62]

    Kyae and Q

    B. Kyae and Q. Shafi, Inflation with realistic super- symmetric SO(10), Phys. Rev. D72, 063515 (2005), arXiv:hep-ph/0504044

    2005 arXiv

  53. [63]

    Lazarides, M

    G. Lazarides, M. U. Rehman, and Q. Shafi, Proton decay in supersymmetricSUp4q c ˆSUp2q L ˆSUp2q R, JHEP2020(10), 085, arXiv:2007.15317 [hep-ph]

    2007 arXiv

  54. [64]

    V. N. Senoguz and Q. Shafi, New inflation, preinfla- tion, and leptogenesis, Phys. Lett. B596, 8 (2004), arXiv:hep-ph/0403294

    2004 arXiv

  55. [65]

    H. M. Lee, Chaotic inflation in Jordan frame supergrav- ity, JCAP08(003), arXiv:1005.2735 [hep-ph]

    arXiv

  56. [66]

    Pallis, T-Model Higgs Inflation in Supergravity, in 40th Conference on Recent Developments in High En- ergy Physics and Cosmology(2023) arXiv:2307.14652 [hep-ph]

    C. Pallis, T-Model Higgs Inflation in Supergravity, in 40th Conference on Recent Developments in High En- ergy Physics and Cosmology(2023) arXiv:2307.14652 [hep-ph]

    2023 arXiv

  57. [67]

    M. N. Ahmad and M. U. Rehman, Supersymmetric hy- brid inflation with K¨ ahler-induced R-symmetry break- ing, JCAP2025(08), 061, arXiv:2506.23244 [hep-ph]

    arXiv

  58. [68]

    N. Ijaz, M. Mehmood, and M. U. Rehman, The Stochas- tic Gravitational-Wave Background from Primordial Black Holes in R-SymmetricSUp5qInflation, preprint (2023), arXiv:2308.14908 [astro-ph.CO]

    2023 arXiv

  59. [69]

    D. I. Kaiser, E. A. Mazenc, and E. I. Sfakianakis, Primordial bispectrum from multifield inflation with nonminimal couplings, Physical Review D87, 10.1103/physrevd.87.064004 (2013)

    2013 doi

  60. [71]

    Gordon, D

    C. Gordon, D. Wands, B. A. Bassett, and R. Maartens, Adiabatic and entropy perturbations from inflation, Physical Review D63, 10.1103/physrevd.63.023506 (2000)

    2000 doi

  61. [72]

    T. T. Nakamura and E. D. Stewart, The spectrum of cosmological perturbations produced by a multi- component inflaton to second order in the slow-roll ap- proximation, Physics Letters B381, 413 (1996)

    1996

  62. [73]

    Gong and T

    J.-O. Gong and T. Tanaka, A covariant approach to gen- eral field space metric in multi-field inflation, Journal of Cosmology and Astroparticle Physics2011(03), 015

  63. [74]

    S. R. Geller, W. Qin, E. McDonough, and D. I. Kaiser, Primordial black holes from multifield inflation with nonminimal couplings, Phys. Rev. D106, 063535 (2022), arXiv:2205.04471 [hep-th]

    2022 arXiv

  64. [75]

    Ijaz and M

    N. Ijaz and M. U. Rehman, Exploring primordial black holes and gravitational waves with R-symmetric GUT Higgs inflation, Phys. Lett. B861, 139229 (2025), arXiv:2402.13924 [astro-ph.CO]. 14

    2025 arXiv

  65. [76]

    Efstathiou and S

    G. Efstathiou and S. Gratton, A detailed description of the camspec likelihood pipeline and a reanalysis of the planck high frequency maps, The Open Journal of Astrophysics4, 10.21105/astro.1910.00483 (2021)

    1910 doi arXiv

  66. [77]

    Bezrukov and M

    F. Bezrukov and M. Shaposhnikov, The standard model higgs boson as the inflaton, Physics Letters B659, 703 (2008)

    2008

  67. [78]

    Okada, M

    N. Okada, M. U. Rehman, and Q. Shafi, Tensor to Scalar Ratio in Non-Minimalϕ 4 Inflation, Phys. Rev. D82, 043502 (2010), arXiv:1005.5161 [hep-ph]

    2010 arXiv

  68. [79]

    M. A. Masoud, M. U. Rehman, and M. M. A. Abid, Nonminimal inflation in supersymmetric GUTs with Up1q R ˆZn symmetry, Int. J. Mod. Phys. D28, 2040015 (2019), arXiv:1910.10519 [hep-ph]

    2019 arXiv

  69. [80]

    Kallosh, A

    R. Kallosh, A. Linde, and D. Roest, Universal Attractor for Inflation at Strong Coupling, Phys. Rev. Lett.112, 011303 (2014), arXiv:1310.3950 [hep-th]

    2014 arXiv

  70. [81]

    Kallosh, A

    R. Kallosh, A. Linde, and D. Roest, Large field infla- tion and doubleα-attractors, JHEP2014(08), 052, arXiv:1405.3646 [hep-th]

    arXiv

  71. [82]

    Kallosh and A

    R. Kallosh and A. Linde, Hybrid cosmological attractors, Phys. Rev. D106, 023522 (2022), arXiv:2204.02425 [hep-th]

    2022 arXiv

  72. [83]

    Camphuis, W

    E. Camphuis, W. Quan, L. Balkenhol,et al., Spt-3g d1: Cmb temperature and polarization power spectra and cosmology from 2019 and 2020 observations of the spt- 3g main field (2025), arXiv:2506.20707 [astro-ph.CO]

    2019 arXiv

  73. [84]

    Kallosh, A

    R. Kallosh, A. Linde, and D. Roest, Act, spt, and chaotic inflation (2025), arXiv:2503.21030 [hep-th]

    2025 arXiv

  74. [85]

    Hazumiet al.(LiteBIRD), LiteBIRD: JAXA’s new strategic L-class mission for all-sky surveys of cosmic mi- crowave background polarization, Proc

    M. Hazumiet al.(LiteBIRD), LiteBIRD: JAXA’s new strategic L-class mission for all-sky surveys of cosmic mi- crowave background polarization, Proc. SPIE Int. Soc. Opt. Eng.11443, 114432F (2020), arXiv:2101.12449 [astro-ph.IM]

    2020

  75. [86]

    Galante, R

    M. Galante, R. Kallosh, A. Linde, and D. Roest, Unity of Cosmological Inflation Attractors, Phys. Rev. Lett. 114, 141302 (2015), arXiv:1412.3797 [hep-th]

    2015 arXiv

  76. [87]

    Kallosh and A

    R. Kallosh and A. Linde, Escher in the sky, Comptes Rendus. Physique16, 914 (2015)

    2015

  77. [88]

    J. J. M. Carrasco, R. Kallosh, and A. Linde,α- Attractors: Planck, LHC and Dark Energy, JHEP2015 (10), 147, arXiv:1506.01708 [hep-th]

    arXiv

  78. [89]

    Lewis, GetDist: a Python package for analysing Monte Carlo samples, JCAP2025(08), 025, arXiv:1910.13970 [astro-ph.IM]

    A. Lewis, GetDist: a Python package for analysing Monte Carlo samples, JCAP2025(08), 025, arXiv:1910.13970 [astro-ph.IM]

    1910 arXiv

  79. [90]

    Pallis, Pole-induced Higgs inflation with hyper- bolic K¨ ahler geometries, JCAP2021(05), 043, arXiv:2103.05534 [hep-ph]

    C. Pallis, Pole-induced Higgs inflation with hyper- bolic K¨ ahler geometries, JCAP2021(05), 043, arXiv:2103.05534 [hep-ph]

    arXiv

  80. [91]

    cmashing

    E. van der Velden, Cmasher: Scientific colormaps for making accessible, informative and “cmashing” plots, Journal of Open Source Software5, 2004 (2020)

    2004

  81. [92]

    Pallis and N

    C. Pallis and N. Toumbas, Non-minimal higgs inflation and non-thermal leptogenesis in a supersymmetric pati- salam model, JCAP2011(12), 002, arXiv:1108.1771 [hep-ph]

    arXiv

  82. [93]

    M. Endo, M. Kawasaki, F. Takahashi, and T. T. Yanagida, Inflaton decay through supergravity effects, Phys. Lett. B642, 518 (2006), arXiv:hep-ph/0607170

    2006 arXiv

  83. [94]

    A. R. Liddle and S. M. Leach, How long before the end of inflation were observable perturbations produced?, Physical Review D68, 103503 (2003)

    2003

  84. [95]

    J. R. Ellis, J. E. Kim, and D. V. Nanopoulos, Cosmo- logical Gravitino Regeneration and Decay, Phys. Lett. B145, 181 (1984)

    1984

  85. [96]

    Kawasaki, K

    M. Kawasaki, K. Kohri, and T. Moroi, Big-bang nu- cleosynthesis and hadronic decay of long-lived mas- sive particles, Physical Review D71, 10.1103/phys- revd.71.083502 (2005)

    2005 doi

  86. [97]

    Kawasaki, K

    M. Kawasaki, K. Kohri, T. Moroi, and A. Yotsuyanagi, Big-bang nucleosynthesis and gravitinos, Physical Re- view D78, 10.1103/physrevd.78.065011 (2008)

    2008 doi

  87. [98]

    Bezrukov, M

    F. Bezrukov, M. Pauly, and J. Rubio, On the robust- ness of the primordial power spectrum in renormalized higgs inflation, Journal of Cosmology and Astroparticle Physics2018(02), 040

  88. [99]

    M. E. Shaposhnikov, Anomalous fermion number non- conservation, inSummer School in High-energy Physics and Cosmology(1991) pp. 338–374

    1991

  89. [100]

    J. A. Harvey and M. S. Turner, Cosmological baryon and lepton number in the presence of electroweak fermion number violation, Phys. Rev. D42, 3344 (1990)

    1990

  90. [101]

    Fukugita and T

    M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B174, 45 (1986)

    1986

  91. [102]

    Hamaguchi, H

    K. Hamaguchi, H. Murayama, and T. Yanagida, Lepto- genesis from rN-dominated early universe, Phys. Rev. D 65, 043512 (2002), arXiv:hep-ph/0109030

    2002 arXiv

  92. [103]

    Davidson and A

    S. Davidson and A. Ibarra, A lower bound on the right- handed neutrino mass from leptogenesis, Phys. Lett. B 535, 25 (2002), arXiv:hep-ph/0202239

    2002 arXiv

  93. [104]

    Navaset al.(Particle Data Group), Review of particle physics, Phys

    S. Navaset al.(Particle Data Group), Review of particle physics, Phys. Rev. D110, 030001 (2024)

    2024

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