Sneutrino Tribrid Inflation in Flipped $\mathbf{SU(5)}$: Confronting ACT DR6 and Planck

Farishta Israr; Mansoor Ur Rehman; Saleh O. Allehabi

REVIEW 3 major objections 4 minor 69 references

Sneutrino Tribrid Inflation in Flipped $\mathbf{SU(5)}$: Confronting ACT DR6 and Planck

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A Kähler-driven sneutrino inflaton in flipped SU(5) can match the ACT DR6/Planck spectral index while allowing the GUT-breaking scale near 10^16 GeV and a tensor-to-scalar ratio up to 0.02.

desk verdict Genuinely new flipped SU(5) embedding with independent M_s, but the headline r≳10^-3 region sits exactly where the quartic Kähler truncation is uncontrolled. read the letter →

arxiv 2608.08708 v1 pith:GURW7LKC submitted 2026-08-09 hep-ph

Farishta Israr , Mansoor Ur Rehman , Saleh O. Allehabi This is my paper · ORCID

classification hep-ph

keywords sneutrinotribridinflationflippedSU(5)Kähler-drivennon-thermalleptogenesisscalarspectralindextensor-to-scalarratiotype-IseesawCMBB-modes

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

The paper constructs a tribrid inflation model inside the flipped $SU(5)$ grand unified theory in which the inflaton is a right-handed sneutrino. A vector-like pair $10_V + \overline{10}_V$ makes the inflationary trajectory $D$-flat, and a $Z_2$ symmetry forbids the direct inflaton mass, so the leading interaction is a non-renormalizable, Kähler-driven superpotential term. The paper treats the superpotential cutoff $M_s$ as independent of the reduced Planck mass $m_P$, which substantially enlarges the viable parameter space. Comparing with the ACT DR6/Planck value $n_s = 0.9734 \pm 0.0034$ and the $2\sigma$ running bound, it finds broad regions where the flipped $SU(5)$ symmetry-breaking scale approaches $M_{\rm GUT}$ and where the tensor-to-scalar ratio reaches $r \gtrsim 10^{-3}$, within reach of planned CMB $B$-mode experiments. The same sneutrino then reheats the universe and produces the observed baryon asymmetry through non-thermal leptogenesis at $T_r = 10^6$ GeV, consistent with the gravitino constraint.

What carries the argument

The load-bearing object is the $D$-flat sneutrino trajectory built from the vector-like pair $(10_V,\overline{10}_V)$, combined with the non-minimal Kähler potential, the function that sets supergravity kinetic terms, which supplies both the inflaton slope and the waterfall instability. The superpotential term $S[(10_H\cdot\overline{10}_H)^2/M_s^2 - \mu_s^2]$ provides the constant vacuum energy $\mu_s^4$ while $S$ is stabilized at the origin. Everything downstream follows from the truncated single-field potential $V(\phi)=\mu_s^4[1+\kappa_\phi\phi^2/m_P^2+\delta_\phi\phi^4/m_P^4]$, where only $\kappa_\phi>0$, $\delta_\phi<0$ yields the required red tilt; inflation ends when the waterfall field becomes tachyonic at $\phi_c=M=\sqrt{\mu_s M_s}$, tying the end of inflation to GUT symmetry breaking. Treating $M_s$ separately from $m_P$ is what opens up most of the allowed parameter space.

What would settle it

Compute the sixth-order Kähler corrections with order-one coefficients and redo the scan: if the $r\gtrsim10^{-3}$ region moves outside the ACT DR6/Planck $2\sigma$ contours in $n_s$ and $\alpha_s$, the central observable claim fails. A future CMB polarization experiment bounding $r<10^{-3}$ while $n_s$ stays near $0.9734$ would also remove the high-scale corner where the gravitational-wave signal is observable.

Watch

Extended reading notes

Core claim

The central claim is that a Kähler-driven tribrid inflation mechanism, previously studied with the superpotential cutoff fixed to $m_P$, remains viable and becomes far more flexible when the cutoff $M_s$ is treated as an independent scale, and that flipped $SU(5)$ supplies the particle content that makes it work. A vector-like pair $10_V + \overline{10}_V$ provides a $D$-flat inflaton direction along $N^c_1$ and $\overline{N}^c_V$, a $Z_2$ removes the renormalizable mass and hybrid coupling, and supergravity corrections produce the single-field potential $V(\phi) = \mu_s^4(1 + \kappa_\phi \phi^2/m_P^2 + \delta_\phi \phi^4/m_P^4)$. With $\kappa_\phi>0$, $\delta_\phi<0$, this potential gives sub-Planckian red-tilted inflation; fixing $n_s$ to the ACT DR6/Planck value and imposing the running bound, the scan yields symmetry-breaking scales $M \gtrsim 10^{16}$ GeV, approaching $M_{\rm GUT}$, and tensor-to-scalar ratios from $3\times10^{-10}$ to $0.02$, with a substantial portion above $10^{-3}$. After the waterfall, the inflaton is the lightest right-handed sneutrino; its decay reheats the universe to $10^6$ GeV and generates the observed baryon asymmetry via non-thermal leptogenesis.

Load-bearing premise

The calculation keeps only terms up to fourth order in the inflaton field divided by the Planck mass, yet it allows the inflaton at horizon exit to be as large as the Planck mass itself; the size of the dropped sixth-order terms is not estimated, so the high-field boundary of the allowed region could move.

Editorial extensions

If this is right

The flipped $SU(5)$ breaking scale can sit at or slightly below the conventional unification scale $M_{\rm GUT}\simeq2\times10^{16}$ GeV, so GUT symmetry breaking and the end of inflation happen at the same scale.
A significant fraction of the viable parameter space predicts $r\gtrsim10^{-3}$, so upcoming CMB $B$-mode experiments can either detect primordial gravitational waves from this GUT inflation or exclude that portion of the model.
The running of the spectral index is positive over the whole allowed region, reaching up to the $2\sigma$ bound; a precision measurement of positive running would support Kähler-driven tribrid inflation over minimal hybrid inflation.
The lightest right-handed sneutrino, identified as the inflaton, reheats the universe to about $10^6$ GeV and produces the observed baryon asymmetry via non-thermal leptogenesis, connecting inflation directly to neutrino masses and baryogenesis.
Coleman–Weinberg and soft supersymmetry-breaking corrections are negligible along the trajectory, so the inflationary predictions are not sensitive to loop or soft-term uncertainties.

Reading between the lines

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

Treating the superpotential cutoff as independent of $m_P$ is a device that should also enlarge the viable regions of other tribrid grand-unified inflation models, although the paper does not scan those models.
The high-$r$ corner of the allowed region sits at $\phi_0/m_P$ approaching 1, where the neglected sixth-order terms could be sizeable; a dedicated computation of those terms would sharpen the target for future $B$-mode experiments.
The predicted positive running throughout the viable region is a sharp discriminator: a future measurement of negative running would disfavor the whole Kähler-driven tribrid class, not only this flipped-$SU(5)$ realization.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The new thing here is the embedding, not the mechanism. Sneutrino tribrid inflation with a quartic Kähler-driven potential has been around since Antusch–Nolde; what this paper adds is a concrete flipped SU(5) realization with a vector-like 10+10bar pair making the D-flat direction work, and an independent superpotential cutoff M_s distinct from m_P. That is a real step beyond earlier Pati–Salam/SO(10)/left-right constructions, and the paper does the honest work of deriving the effective single-field potential, checking that radiative and soft corrections are subdominant, and separating the region phi0>M_s as less trustworthy.

Credit where due: the scan is systematic, the constraints are sensible (sub-Planckian field, Delta x > 0.01, alpha_s <= 0.0166, perturbative bounds on Kähler coefficients), and the leptogenesis/reheating section is standard but consistent. The figures genuinely show how r and alpha_s vary across the acceptable region.

The main soft spot is the Kähler truncation. The potential is kept to quartic order in phi/m_P (Eq. 45), but the scan allows phi0/mP up to 1, and the r>1e-3 corner is precisely at the largest field values. The paper includes some sixth-order field terms in Delta K^(6) (Eq. 32), but those contribute at phi^4/m_P^4 in the potential; the omitted O(phi^6/m_P^6) terms are never parametrized or bounded. With u^2 ~ 0.25-1 in that corner, an O(1) sixth-order coefficient contributes at the same level as the retained quartic term. The high-r region could shift or disappear. This is not a fatal flaw in the model class, but it is a load-bearing approximation for the headline claim.

Two smaller things. They fix n_s to the central ACT DR6/Planck value rather than scanning over its 1-sigma range, so the "confrontation" is really a central-value fit. And no code or data is provided for the scan, so the numerics are not independently checkable. Both are fixable. The choice phi_c = M is an assumption, but transparent.

Self-citations are heavy but the central output is a new numerical scan, not a repackaging. I take the construction seriously.

Bottom line: this deserves a serious referee. The referee should push on the phi^6 Kähler control and ask for the scan data. If the high-r region survives that, it is a genuinely interesting target for LiteBIRD and CMB-S4. I would send it to peer review.

Referee Report

3 major / 4 minor

Summary. The paper constructs a supersymmetric flipped SU(5) model of tribrid inflation in which the inflaton is a D-flat combination of right-handed sneutrinos from a vector-like pair 10_V + \overline{10}_V, with an additional Z_2 symmetry forbidding a direct inflaton mass term and forcing the leading interaction to be non-renormalizable. The authors derive the SUGRA scalar potential with non-minimal Kähler terms up to quartic order in \phi/m_P (Eq. 45), identify the sign combination \kappa_\phi>0, \delta_\phi<0 as the viable one, and scan the parameter space with constraints from the scalar amplitude A_s, the spectral index fixed to n_s=0.9734, the e-fold number N0, sub-Planckian field values, the running bound \alpha_s\le0.0166, and \Delta x>0.01. They report broad viable regions in which the flipped SU(5) breaking scale approaches M_GUT and the tensor-to-scalar ratio reaches r\gtrsim10^{-3}, accessible to future CMB B-mode experiments. They also study post-inflationary decay, reheating with T_r=10^6 GeV, and non-thermal leptogenesis, obtaining inflaton masses in the range 3\times10^8\lesssim m_\phi/\text{GeV}\lesssim3\times10^{12} for a benchmark choice. The central claim is that the model is a viable GUT embedding of inflation with a testable gravitational-wave signal.

Significance. If the result holds, the paper makes a valuable contribution to Kähler-driven tribrid inflation in GUTs. Its strengths include a concrete flipped SU(5) embedding with an explicit D-flat sneutrino direction, a clean separation between the superpotential cutoff M_s and the reduced Planck mass m_P, analytic slow-roll expressions (Eqs. 73-76), a transparent distinction between input parameters (n_s, A_s, T_r) and output observables (r, \alpha_s, M, m_\phi), and a numerical scan with clearly stated constraints. The prediction of r\gtrsim10^{-3} in a substantial part of the parameter space is falsifiable by LiteBIRD and CMB-S4, and the connection to non-thermal leptogenesis adds phenomenological completeness. The main caveat is the uncontrolled higher-order Kähler truncation in the large-field corner that anchors the high-r claim; this needs to be addressed before the central result is fully established.

major comments (3)

[§VI.C and Fig. 6] The effective potential is truncated at O(\phi^6/m_P^6) in Eq. (45), but the scan permits u0 = \phi_0/m_P up to 1 (constraint 86), and Fig. 6 shows that the r\gtrsim10^{-3} region is located precisely at the largest u0 values (compare Fig. 2). The Kähler terms collected in Eq. (32) include only a restricted set of sixth-order operators that contribute to the potential at O(m_P^{-4}); generic higher-order operators such as |N|^6/m_P^4 in K, or |S|^2|N|^6/m_P^6 in K_{S\bar S}, generate corrections of the form \delta_6 u^6 to Eq. (45) that are formally of order unity at u0~1. The perturbative bound in Eq. (48) does not constrain \delta_6, and the caveat in §VI.C concerning \phi_0>M_s addresses the superpotential expansion in M_s, not the Kähler expansion in m_P. The advertised high-r corner, and the boundary of the allowed region, may therefore shift significantly when the omitted terms are included. Please either control the O(\phi^6/m_P^6) Kähler terms explicitly, impose and justify a bound on their coefficients, or restrict the scan to field values where the truncation is provably subdominant, and then show whether r\gtrsim10^{-3} survives.
[§VI.B] The scan fixes the scalar spectral index to the central value n_s = 0.9734 rather than using the full ACT DR6/Planck determination n_s = 0.9734 ± 0.0034. Because all subsequent constraints (\Delta x>0.01, \alpha_s\le0.0166, \phi_0<m_P) are evaluated at this single point, the size and shape of the 'viable' region, and the locus of the r\gtrsim10^{-3} contours, are not demonstrated to be robust within the 1σ uncertainty. Please repeat the scan with n_s sampled over at least its 1σ range, or provide analytic/numerical evidence that the allowed region is stable under such variations.
[§VI.D] The headline r\gtrsim10^{-3} region should be compared explicitly with the theory-controlled region \phi_0<M_s. The text states that the grey-shaded region with \phi_0>M_s 'should be interpreted with caution', yet the r contours are still presented there. If a substantial part of the r\gtrsim10^{-3} area lies in the grey region, the central claim of an observable tensor signal is not supported by the controlled part of the parameter space. Please report what fraction of the r\gtrsim10^{-3} region satisfies \phi_0<M_s, and present the r contours with the M_s=\phi_0 boundary clearly overlaid.

minor comments (4)

[§VI.D] The redefinition M_s \to M_s/\sqrt{\kappa} with M_s fixed to m_P when the formal value exceeds m_P is presented without derivation; please clarify whether this is a field redefinition, a parametrization choice, or an assumption about the UV completion.
[§VII.D] The adopted reheating temperature T_r=10^6 GeV sits exactly at the lower bound derived from successful non-thermal leptogenesis; a sentence quantifying how close the benchmark is to the boundary would help the reader assess the 'consistent with both' claim.
[§IV.D.1] The statement that the Coleman-Weinberg correction remains subdominant is said to be verified numerically, but no figure or table shows the ratio V_CW/V_0 over the scanned parameter space; including such a plot would strengthen the claim.
[Figure captions] The captions of Figs. 1-8 are dense and do not always identify which curves are which (e.g., Fig. 1 refers to 'the green lines' without distinguishing the M, |\delta_\phi|, and \alpha_s bounds). Adding a small legend or explicit line labels would improve readability.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; r and α_s are genuine outputs of a scan whose inputs are the observed n_s and A_s, while self-citations are non-load-bearing.

full rationale

The inflationary part of the paper is self-contained: the effective potential of Eq. (45) is derived from the stated superpotential and Kähler potential (Eqs. (30)–(32)), and the observables in Eqs. (74)–(76) follow from standard slow-roll definitions. The numerical procedure fixes A_s to the observed amplitude and n_s to the ACT DR6/Planck central value, then scans over (M_s, κ_ϕ), solving for the remaining parameters; r and α_s are computed as outputs and are not fitted. The consistency with ACT DR6/Planck therefore rests on external data plus the model's own equations, not on any quantity being defined in terms of the claimed prediction. The leptogenesis section adopts T_r = 10^6 GeV as an explicit input, motivated by the Davidson–Ibarra lower bound and the gravitino constraint, and does not claim to predict the observed baryon asymmetry independently; this is parameter selection, not circular derivation. The numerous self-citations (e.g., Refs. [20–27], [36], [43], [50], [51]) provide context and prior constructions, but the central viability claim is established by the numerical scan and standard slow-roll formulas, so no load-bearing step reduces to its own input.

Assumptions & free parameters 6 free parameters · 6 assumptions · 3 invented entities

The central claim depends on the effective potential truncated at quartic order, on the assumed waterfall ending at ϕ_c = M, on an R-breaking spurion for Majorana masses, and on a hierarchy that decouples the vector-like sector. None of these are derived from data or from a more fundamental theory; they are model inputs.

free parameters (6)

M_s = scanned over 0.003 m_P ≤ M_s ≤ m_P, with redefinition as M_s/√κ above m_P
Superpotential cutoff, treated as independent from m_P; the central new parameter of the paper.
κ_ϕ = 0.0034 to 0.04 in the viable region
Effective quadratic coefficient of the SUGRA inflaton potential; a combination of Kähler coefficients.
δ_ϕ = negative, |δ_ϕ| ≤ 1
Effective quartic coefficient of the inflaton potential; its negative sign is required for a red tilt.
T_r = 10^6 GeV
Reheating temperature chosen by hand, motivated by leptogenesis lower bound and gravitino constraint; sets N_0 via Eq. (85).
m_ϕ (benchmark) = m_ref/100, with κ_w = 2
Physical inflaton mass chosen as a benchmark satisfying the hierarchy (102); not derived from data.
n_s (input) = 0.9734
Scalar spectral index fixed to the ACT DR6/Planck central value, not scanned over its uncertainty.

assumptions (6)

standard math N=1 supergravity with standard F-term potential (Eq. 28)
Underlying framework for the inflationary potential.
domain assumption The leading inflationary operator is S(10_H 10_Hbar)^2/M_s^2; other operators are negligible
This follows from the imposed Z2 symmetry; the paper assumes no comparable higher-dimension operators.
domain assumption The Kähler expansion can be truncated at quartic order in fields
The paper does not bound O(ϕ^6/m_P^6) terms, though field values can reach m_P.
ad hoc to paper Inflation ends at the waterfall transition with ϕ_e = ϕ_c = M
The paper sets ϕ_c = M for simplicity, fixing α_1 via Eq. (104).
domain assumption U(1)_R is broken by a spurion X_R to permit the Majorana mass operator (Eq. 96)
Needed to give right-handed neutrinos Majorana masses within the R-symmetric setup.
domain assumption The vector-like sector decouples, |m_V| >> |m_i| and |λ_iV| << |λ_VV| (Eqs. 98-99)
Required to identify the inflaton with the lightest ordinary right-handed sneutrino.

invented entities (3)

Vector-like matter pair 10_V + conjugate 10_Vbar
purpose: Provides a D-flat right-handed sneutrino inflaton direction and generates vector-like masses after GUT breaking
No direct experimental signature; introduced to realize gauge non-singlet inflation.
Additional Z2 symmetry
purpose: Forbids the inflaton mass term and the renormalizable hybrid coupling S 10_H 10_Hbar
Discrete symmetry imposed by hand; no independent evidence.
R-breaking spurion X_R with R(X_R)=1
purpose: Generates the Majorana operator for right-handed neutrino masses while preserving the R-symmetric model
Postulated to appear in Eq. (97); its VEV is absorbed into λ_ab.

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Cite this review

Pith. "Pith review of Sneutrino Tribrid Inflation in Flipped $\mathbf{SU(5)}$: Confronting ACT DR6 and Planck." pith.science (2026). https://pith.science/paper/GURW7LKC

@misc{pith2026260808708,
  author       = {Pith},
  title        = {Pith review of: Sneutrino Tribrid Inflation in Flipped $\mathbfSU(5)$: Confronting ACT DR6 and Planck},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GURW7LKC}},
  note         = {Machine review of arXiv:2608.08708}
}

abstract

We construct a realization of sneutrino tribrid inflation within the $R$-symmetric flipped $SU(5)$ grand unified theory. A vector-like pair of matter multiplets, $10_V+\overline{10}_V$, provides a $D$-flat inflaton direction along the right-handed sneutrino component, with an additional $Z_2$ symmetry forbidding a direct inflaton mass term so that the leading inflationary interaction is a non-renormalizable K\"ahler-driven operator. Unlike previous studies, we treat the superpotential cutoff scale $M_s$ as independent of the reduced Planck mass, $m_P$, substantially enlarging the viable parameter space. Confronting the model with the ACT DR6/Planck determination $n_s=0.9734\pm0.0034$ and the $2\sigma$ bound on the running of the spectral index, we identify broad regions of viable parameter space in which the flipped $SU(5)$ symmetry-breaking scale can approach the conventional GUT scale, $M\simeq M_{\rm GUT}$, and the tensor-to-scalar ratio can reach observable values, $r\gtrsim10^{-3}$, within reach of forthcoming CMB $B$-mode experiments such as LiteBIRD and CMB-S4. We further study the post-inflationary dynamics, identifying the inflaton with the lightest right-handed sneutrino in a conventional type-I seesaw sector, whose out-of-equilibrium decay generates a lepton asymmetry that is converted into the observed baryon asymmetry via non-thermal leptogenesis and electroweak sphalerons, for a reheating temperature consistent with both successful leptogenesis and the gravitino constraint.

Figures

Figures reproduced from arXiv: 2608.08708 by the authors.

**Figure 4.** FIG. 4: Allowed parameter space of Fig [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗

**Figure 6.** FIG. 6: Allowed parameter space of Fig [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗

Figures from the paper (2 more)

**Figure 7.** Figure 7: shows that the running remains positive ϕ0 = mP Δx = 0.01 0.00001 r 0.0001 = 0.001 0.003 0.009 αs = 0.0166 Ms = ϕ0 0.005 0.010 0.050 0.100 0.500 1 5×1015 1×1016 5×1016 1×1017 5×1017 -δϕ M /GeV FIG. 6: Allowed parameter space of [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]

**Figure 8.** Figure 8: displays contours of constant physical inflaton mass mϕ for this benchmark choice. C. Inflaton Decay and Reheating The inflaton reheats the Universe through the Yukawa interactions contained in the renormalizable superpotential WY = y (u,ν) aj 10a 5j 5h. (111) Since t…

Discussion (0). Continue with ORCID to comment.

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Coleman–Weinberg correction Along the single-fieldD-flat trajectory, |N c 1 |=| N c V |= ϕ 2 , N c a̸=1 = 0,(52) the relevant waterfall interaction is Winf ⊃ α1 Ms N c 1 N c V N c H N c H .(53) The fermionic components ofN c H and N c H form a Dirac fermion with inflaton-dependent mass mF (ϕ) = |α1| Ms Φ2 = |α1| 4Ms ϕ2.(54) The corresponding scalar fields...

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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Coleman–Weinberg correction Along the single-fieldD-flat trajectory, |N c 1 |=| N c V |= ϕ 2 , N c a̸=1 = 0,(52) the relevant waterfall interaction is Winf ⊃ α1 Ms N c 1 N c V N c H N c H .(53) The fermionic components ofN c H and N c H form a Dirac fermion with inflaton-dependent mass mF (ϕ) = |α1| Ms Φ2 = |α1| 4Ms ϕ2.(54) The corresponding scalar fields...

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Along the inflationary trajectory, Winf = 0, D SWinf =−µ 2 s,(60) so the vacuum energy originates from the nonvanishing singletF-term

Soft supersymmetry-breaking correction Soft supersymmetry-breaking effects are likewise neg- ligible during inflation. Along the inflationary trajectory, Winf = 0, D SWinf =−µ 2 s,(60) so the vacuum energy originates from the nonvanishing singletF-term. Since the superpotential itself vanishes, the conventional soft linear term does not contribute along t...

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The scalar amplitude is fixed to the observed value, As =A obs s

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Following the standard post-inflationary thermal history, the number ofe-folds between the horizon exit of the pivot scale and the end of inflation is determined by the reheating temperatureT r and the inflationary energy scaleµ s according to [54] N0 ≃53 + 1 3 ln Tr 109 GeV + 2 3 ln µs 1015 GeV ,(85) whereµ 4 s is the inflationary vacuum energy density. ...

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Inflation ends at the waterfall transition,ϕ e =ϕ c =√µsMs. 11

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The scalar spectral index is fixed to its central ob- served value,n s = 0.9734. The normalization conditionA s =A obs s determines the overall inflationary scaleµ s; however, the conditions on N0 andn s determine the horizon-exit field valueϕ 0 to- gether with one of the two shape parameters (κ ϕ, δϕ). Consequently, the original four-dimensional paramete...

work page

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