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High Energy Physics - Phenomenology · arXiv:1308.6651 v3 · submitted 30 Aug 2013 · 91 references

Minimal Higgs inflation

Yuta Hamada, Hikaru Kawai, Kin-ya Oda

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The paper says

“We consider a possibility that the Higgs field in the Standard Model (SM) serves as an inflaton when its value is around the Planck scale.”

more of the abstract

We assume that the SM is valid up to an ultraviolet cutoff scale \Lambda, which is slightly below the Planck scale, and that the Higgs potential becomes almost flat above \Lambda. Contrary to the ordinary Higgs inflation scenario, we do not assume the huge non-minimal coupling, of O(10^4), of the Higgs field to the Ricci scalar. We find that \Lambda must be less than 5*10^17GeV in order to explain the observed fluctuation of the cosmic microwave background, no matter how we extrapolate the Higgs potential above \Lambda. The scale 10^17GeV coincides with the perturbative string scale, which suggests that the SM is directly connected with the string theory. For this to be true, the top quark mass is restricted to around 171GeV, with which \Lambda can exceed 10^17GeV. As a concrete example of the potential above \Lambda, we propose a simple log type potential. The predictions of this specific model for the e-foldings N_*=50–60 are consistent with the current observation, namely, the scalar spectral index is n_s=0.977–0.983 and the tensor to scalar ratio 0<r<0.012–0.010. Other parameters, dn_s/dlnk, n_t, and their derivatives, are also consistent.

from the abstract

Pith says

Machine review · deepseek-v4.1-flash · 12 Nov 2026 · what was read was not recorded · not checked by a person

Reviewed in 2026 with later literature in view.

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Holds up, with conditions. The Λ < 5×1017 GeV bound and the top-mass constraint are the real content and they hold up; the log-potential predictions are a template, and the abstract oversells them as a fit. This line is wrong

3 major objections · 8 minor

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The paper says, at Abstract (abstract:s7) and §4.2, Eq. (37), Fig. 5

The review did not quote this passage.

Pith says: Objection 1 of 3 · major

The abstract states that n_s = 0.977–0.983 is 'consistent with the current observation.' Planck 2013 (Eq. 9) gives n_s = 0.9603 ± 0.0073, so the quoted range lies 2.3–3.1σ above the central value. The body itself acknowledges the tension: the paragraph following Eq.

more of objection 1

(37) says 'we need rather small N_* ∼ 40 ... in order to account for the observed value of n_s in Eq. (10).' The abstract's claim of consistency at N_* = 50–60 is therefore not supported by the paper's own analysis. The two proposed resolutions (loosening the connection to V_SM, or adding the correction of Eq. (40)) do not close the gap: the explicit example quoted in §4.2 gives n_s = 0.978, still about 2.5σ high. This is load-bearing for the abstract's headline and should be stated honestly as a mild tension rather than as consistency.

The paper says, at Abstract (abstract:s3) and §4.1, Eq. (26)

The review did not quote this passage.

Pith says: Objection 2 of 3 · major

The abstract claims that Λ must be less than 5×10^17 GeV 'no matter how we extrapolate the Higgs potential above Λ.' The derivation in §4.1 rests on requiring dV_SM/dφ > 0 for all φ < Λ (Eq. 26), which is motivated by the graceful exit problem but is not derived.

more of objection 2

The body states this premise explicitly; the abstract does not. The dismissal of first-order transitions ('bubbles can hardly collide') is heuristic rather than a theorem. The bound is sound given the monotonicity premise, but the abstract should state that premise, and §4.1 should either justify the monotonicity requirement more carefully or present the bound explicitly as conditional on it.

The paper says, at §4.2 and Appendix B, Eq. (66)

The review did not quote this passage.

Pith says: Objection 3 of 3 · major

The log-type potential is presented as motivated by the Coleman-Weinberg potential with an explicit momentum cutoff Λ. However, Eq. (66) gives V_1 = −(3/32π^2)Λ^4, which is negative for the SM content listed in Table 1 (the top quark entry N_i = −4N_c = −12 dominates), so the potential decreases with φ and cannot support the required slow roll.

more of objection 3

The paper acknowledges this and invokes extra scalar fields to make V_1 positive, but then treats V_0 and V_1 as arbitrary constants. The 'concrete example' is therefore not derived from the stated motivation without unspecified new physics, and the abstract's 'we propose a simple log type potential' should be qualified accordingly.

8 minor objections

The paper says, at Eqs. (34) and (37)

Pith says: minor objection 1 of 8

The inequality chains such as '0.980–0.983 > n_s > 0.977–0.981' are difficult to parse; interval notation with explicit N_* and φ_end labels would be clearer.

The paper says, at Figs. 5 and 8

Pith says: minor objection 2 of 8

The N_* = 40 curves are described as 'just for reference' but are visually prominent and are used in the §4.2 discussion of the n_s tension; consider de-emphasizing them or moving them to an appendix.

show 6 more

The paper says, at Footnote 13 and Eq. (38)

Pith says: minor objection 3 of 8

The reheating temperature T_reh ≃ 4×10^15 GeV for φ_end = 0.5 M_P exceeds Λ, so the use of the SM effective number of degrees of freedom g_* ≃ 106.75 is questionable; the footnote acknowledges this, but the main text should flag the associated uncertainty in N_*.

The paper says, at Eq. (16)

Pith says: minor objection 4 of 8

The theoretical uncertainty ±0.00200_th on y_t(M_t) is quoted but its propagation to the Λ bound in Fig. 3 is not shown; a brief statement of the resulting uncertainty on Λ would be useful.

The paper says, at Abstract

Pith says: minor objection 5 of 8

The statements 'Λ must be less than 5×10^17 GeV' and 'Λ can exceed 10^17 GeV' should be reconciled explicitly, e.g. by stating the allowed window 10^17 GeV < Λ < 5×10^17 GeV.

The paper says, at Eq. (13) and Fig. 3

Pith says: minor objection 6 of 8

V_max scales with r_max, so the Λ bound will tighten as the tensor-to-scalar limit improves; the text should state this dependence explicitly rather than leaving it implicit in Fig. 3.

The paper says, at Table 1

Pith says: minor objection 7 of 8

A sentence in the caption noting that the top-quark entry drives the sum Σ N_j/2 negative, and hence V_1 negative in Eq. (66), would help the reader connect the table to the sign discussion.

The paper says, at §5

Pith says: minor objection 8 of 8

The summary ranges for n_s, r, dn_s/dlnk and the other parameters should match the abstract exactly; currently the ordering of the quoted intervals differs slightly between the two.

What would settle it

Compute the bounce action for the MPP configuration (Mt = 173.3 GeV, second minimum at ~10^17 GeV, green line Fig. 2) and compare the tunneling rate Γ ~ Λ^4 e^{-S_B} to the Hubble rate H during inflation. If Γ/H^4 > 1 (or if the barrier is absent for some Mt), the field can transition to the electroweak vacuum without violating graceful exit, and the monotonicity requirement — hence the bound — is relaxed. If Γ/H^4 ≪ 1 for all allowed Mt, the bound is robust.

from the skeptic's reading

How the review went

4 readings by deepseek-v4.1-flash · 12 Nov 2026

  1. Reader holds up, with conditions confidence high
  2. Skeptic agrees 4 min 4 s · 24,506 tokens read, 13,532 written
  3. Editor wrote the verdict above 28 s · 25,375 tokens read, 1,588 written
  4. Referee major revision: 3 major objections, 8 minor 2 min 43 s · 24,700 tokens read, 8,742 written

Not run on this paper: the simulated authors' defence.

Pith did not check this review's objections against the paper.

The review in full

The review in brief, machine-written

The thing worth your time here is the bound, not the model. Hamada, Kawai and Oda take the SM at face value up to a cutoff Λ, run the two-loop RGEs, and ask when the Higgs can inflate without the ξ ~ 104 Ricci coupling. The answer: V_SM(Λ) has to sit below the CMB amplitude ceiling V_max, and the potential has to keep rising, which pushes Λ below roughly 5×1017 GeV and the top pole mass toward 171 GeV. Fig. 3 turns that into an exclusion plot in the Λ–Mt plane, with projected r < 10−2 and 10−3 lines drawn in. That plot is the useful artifact. It is a clean, checkable statement and it will get cited by people working on vacuum stability and Higgs inflation. The RGE running and the bare-mass computation behind it are careful, and the authors are upfront that the digits of Mt at the saddle point should not be taken literally (their Eq. 25 caveat). Good practice, and rarer than it should be. The log-potential section is where I would push back. The abstract calls ns = 0.977–0.983 'consistent with the current observation'; Planck+WMAP gives 0.9603 ± 0.0073, so that is 2–3σ high, not consistent in any comfortable sense. The authors know it. Section 4.2 says outright that matching the observed ns needs N_* ~ 40 while their own reheating estimate (Fig. 9) gives N_* ≳ 60, and then bridges the gap with hand-picked c1 = 0.1, c2 = −0.01 in Eq. (40). That is a template, not a fit, and the abstract should say so. On the stress-test note: the monotonicity premise is stated in the body (§4.1, Eq. 26) and motivated by graceful exit, so it is not hidden. But 'no matter how we extrapolate' in the abstract reads as unconditional, and it is not — a barrier with a plateau above Λ is not obviously excluded by their argument. That is a wording problem more than a physics problem, but it is the sentence people will quote. Worth a referee. Send it out, and ask the referee to make them fix the abstract.

The strongest objection

The central bound (abstract:s3) rests on requiring the SM Higgs potential to be monotonically increasing from the electroweak scale through Λ and above (Eq. 26 and §4.1). This is motivated by the graceful exit problem but is not derived; the paper's dismissal of first-order transitions ('bubbles can hardly collide') is a heuristic. If a barrier is allowed — e.g., the MPP two-vacuum configuration (green line, Fig. 2) with a flat plateau above Λ — the field could in principle start beyond the barrier and inflate on a higher plateau, evading V_SM(Λ) < V_max. The paper's claim that the bound holds 'no matter how we extrapolate' is therefore conditional on the graceful-exit argument being correct in all cases. This is a real but moderate concern: the monotonicity requirement is physically motivated, and for any scenario where the field must roll down to the electroweak vacuum, it is necessary. The concern is that the paper presents the bound as unconditional when it is not.

The reader correctly identifies the monotonicity requirement as the load-bearing assumption for the central bound. The bound V_SM(Λ) < V_max (Eq. 27) follows from requiring the potential to increase monotonically to the inflationary plateau, and the top-mass constraint (Mt ≲ 171 GeV) follows from requiring monotonicity below Λ (Eq. 26). Both rest on the graceful-exit argument, which is physically motivated but heuristic. The reader's rationale also flags the specific model's ns tension (0.977-0.983 vs Planck 0.9603 ± 0.0073, a 2.3-3.1σ tension) and the hand-tuned corrections (Eq. 40), which are separate issues about the specific model rather than the central bound. The reader's CONDITIONAL verdict is appropriate: the central bound is defensible given the monotonicity assumption, but the abstract's 'no matter how we extrapolate' and 'consistent with the current observation' overstate what is shown. I would not change the verdict.

The referee's report

If correct, the scenario is an attractive bottom-up connection between the SM, the perturbative string scale, and inflation, with falsifiable predictions (r ∼ 0.01, n_s ∼ 0.98, top mass near 171 GeV). The Λ bound is a genuine constraint that is independent of the unknown UV completion, given the monotonicity premise, and the log-potential analysis is a concrete, reproducible slow-roll calculation. The paper is explicit about its assumptions and does not introduce hidden free parameters beyond the shape of the potential above Λ.

Pith's reading of the paper (a machine's summary, not the authors')

The paper asks whether the Higgs field of the Standard Model can do the job of the inflaton — the field whose slow roll stretches the early universe — without the enormous coupling to spacetime curvature (of order $10^4$) that the standard Higgs-inflation proposal requires. The authors assume the Standard Model remains valid up to a cutoff $Λ$ just below the Planck scale, and that above $Λ$ the Higgs potential turns nearly flat, so the field can roll slowly there. Because the low-energy part of the potential is fixed by measured couplings, the observed size of the cosmic microwave background fluctuations translates into a ceiling on how high the cutoff can be: $Λ$ must be below roughly $5×10^{17}$ GeV, independent of how the potential is continued above $Λ$. That number lands on the scale where the Higgs quartic coupling and its $\beta$ function nearly vanish, and near the perturbative string scale, which is the paper's motivating coincidence. A workable version also pins the top quark mass near 171 GeV and, with a log-shaped potential above the cutoff, gives a spectral index $n_s$ between 0.977 and 0.983 and a tensor-to-scalar ratio $r$ below 0.012.

What carries the argument. The machinery is the renormalization-group-improved Standard Model Higgs potential $V_{SM}(φ) = λ(φ)φ^4/4$, together with the fact that $λ$ and its $\beta$ function $β_λ$ both become tiny near $10^{17}$ GeV. That near-vanishing is what makes the potential flat enough to inflate and what ties the cutoff bound to a specific top Yukawa coupling. Two derived conditions carry the weight: monotonicity, $d V_{SM}/dφ > 0$ below $Λ$, and the amplitude ceiling $V_{SM}(Λ) < V_{max} = 3π^2 A_s r_{max} M_P^4/2$. For the explicit continuation above the cutoff, the slow-roll parameters of the log potential, $ϵ_V = (M_P/φ)^2/[2(C + ln(φ/M_P))^2]$ and $η_V = -(M_P/φ)^2/[C + ln(φ/M_P)]$, are fixed by a single constant $C$, which is itself set by the end-of-inflation field value through the Lambert $W$ function.

Core claim. The central claim is a bound, not a model: if the Higgs is to be the inflaton and the Standard Model is unmodified below a cutoff $Λ$, then $Λ ≲ 5×10^{17}$ GeV. The argument runs through two requirements. First, the potential must rise monotonically everywhere below and above $Λ$, since a barrier would make the end of inflation a first-order transition and create a graceful-exit problem; this is the condition $d V_{SM}/dφ = (β_λ + 4λ)φ^3/4 > 0$ for $φ<Λ$. Second, the height of the Standard-Model potential at the cutoff must sit below the energy scale fixed by the observed amplitude $A_s$ and the tensor-to-scalar ratio, $V_{SM}(Λ) < V_{max}$. Running the two-loop Standard Model renormalization group equations turns both conditions into a curve in the $Λ$–$M_t$ plane, and the surviving region requires $M_t ≲ 171$ GeV for $Λ$ to reach $10^{17}$ GeV. The authors are explicit that the precise top mass value that produces a saddle point depends on the Higgs mass and on RGE details, and should be read as an indication of how finely the top mass must be tuned rather than as a prediction to the last digit. As a concrete continuation above $Λ$ they propose $V(φ) = V_1(C + ln(φ/M_P))$, motivated by a Coleman-Weinberg potential with a momentum cutoff, and show that for $N_* = 50$–$60$ it yields $n_s = 0.977$–$0.983$, $0 < r < 0.012$–$0.010$, together with consistent values for $dn_s/dln k$, $n_t$, and their derivatives. The authors also flag an internal tension: directly matching the log potential onto the Standard Model at $Λ$ prefers $N_* ∼ 40$ and $φ_{end} ≲ 0.5 M_P$, whereas the large-field reheating calculation gives $N_* ≳ 60$; they offer two ways out, loosening the matching condition or adding small corrections to the log.

The premise it rests on. The bound depends on requiring the Higgs potential to rise monotonically everywhere, with no barrier, so that inflation cannot end in a first-order phase transition; if a barrier with workable reheating were allowed, the excluded two-vacuum case would return and the ceiling on the cutoff would weaken.

If the paper is right (Pith's inferences, not the authors')

If the Higgs is the inflaton, the Standard Model must break down below about $5×10^{17}$ GeV, so the cutoff of the theory is tied to a cosmological observable rather than to collider data.

The scenario survives only for a top quark pole mass near 171 GeV; a heavier top pushes the cutoff below the string scale and closes the window.

The log-type continuation makes sharp, checkable predictions for the tensor-to-scalar ratio, $0 < r < 0.012$–$0.010$, within reach of proposed dedicated polarization experiments.

The coincidence of the cutoff bound with the scale where $λ$ and $β_λ$ vanish, and with the perturbative string scale, would suggest the Standard Model is directly connected to string theory.

Because the same running also suppresses the bare Higgs mass at that scale, the Higgs could be a massless state of the ultraviolet theory rather than a tuned light field.

The bound is a statement about the shape of the potential at a scale no collider can reach, so its practical value is as a consistency test: any independent determination of the top Yukawa that lands well above 171 GeV would retire the scenario without any cosmological measurement.

The monotonicity requirement is doing more work than the amplitude bound; if a first-order exit with viable reheating were shown to be acceptable, the excluded two-vacuum configuration would return and the cutoff ceiling would relax, which is the most likely place for the argument to give way.

The acknowledged mismatch between the $N_* ∼ 40$ preferred by matching the log potential to the Standard Model and the $N_* ≳ 60$ preferred by reheating is a symptom of the matching procedure rather than of the log potential itself; a ultraviolet completion that fixes the matching scale would remove the ambiguity and sharpen the $n_s$ prediction.

A useful cross-check would be to run the same two-condition analysis with a Higgs-portal singlet added, since the extra scalar raises $λ$ at high scales and would shift the allowed $Λ$–$M_t$ region in a direction the paper only notes qualitatively.

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The paper

Abstract

We consider a possibility that the Higgs field in the Standard Model (SM) serves as an inflaton when its value is around the Planck scale. We assume that the SM is valid up to an ultraviolet cutoff scale \Lambda, which is slightly below the Planck scale, and that the Higgs potential becomes almost flat above \Lambda. Contrary to the ordinary Higgs inflation scenario, we do not assume the huge non-minimal coupling, of O(10^4), of the Higgs field to the Ricci scalar. We find that \Lambda must be less than 5*10^17GeV in order to explain the observed fluctuation of the cosmic microwave background, no matter how we extrapolate the Higgs potential above \Lambda. The scale 10^17GeV coincides with the perturbative string scale, which suggests that the SM is directly connected with the string theory. For this to be true, the top quark mass is restricted to around 171GeV, with which \Lambda can exceed 10^17GeV. As a concrete example of the potential above \Lambda, we propose a simple log type potential. The predictions of this specific model for the e-foldings N_*=50–60 are consistent with the current observation, namely, the scalar spectral index is n_s=0.977–0.983 and the tensor to scalar ratio 0<r<0.012–0.010. Other parameters, dn_s/dlnk, n_t, and their derivatives, are also consistent.

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. No sentence in this record was written by a model.

abstract compiled · 2026-09-23

The authors' main claim, as the classifier picked it out 0.94

“We find that \Lambda must be less than 5*10^{17}GeV in order to explain the observed fluctuation of the cosmic microwave background, no matter how we extrapolate the Higgs potential above \Lambda.”

How the main claim is stated: asserted 1.00

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.85 · human participants 0.01 · controlled comparison 0.11 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.84 · mentions code or data availability 0.01

The abstract, sentence by sentence

This table labels the abstract only (arXiv listing abstract v3). The number is the probability the classifier gave the label.

SentenceRoleThe authors' own workStates the main conclusionStrength
We consider a possibility that the Higgs field in the Standard Model (SM) serves as an inflaton when its value is around the Planck scale. contribution 0.91 0.34 0.08 hedged possibility 0.96
We assume that the SM is valid up to an ultraviolet cutoff scale \Lambda, which is slightly below the Planck scale, and that the Higgs potential becomes almost flat above \Lambda. method 0.87 0.35 0.04 asserted 0.79
Contrary to the ordinary Higgs inflation scenario, we do not assume the huge non-minimal coupling, of O(10^4), of the Higgs field to the Ricci scalar. contribution 0.67 0.56 0.05 asserted 0.99
We find that \Lambda must be less than 5*10^{17}GeV in order to explain the observed fluctuation of the cosmic microwave background, no matter how we extrapolate the Higgs potential above \Lambda. result 1.00 0.95 0.60 asserted 1.00
The scale 10^{17}GeV coincides with the perturbative string scale, which suggests that the SM is directly connected with the string theory. interpretation 0.99 0.41 0.15 hedged possibility 0.97
For this to be true, the top quark mass is restricted to around 171GeV, with which \Lambda can exceed 10^{17}GeV. result 0.85 0.63 0.08 asserted 0.85
As a concrete example of the potential above \Lambda, we propose a simple log type potential. method 0.70 0.88 0.03 asserted 0.83
The predictions of this specific model for the e-foldings N_*=50--60 are consistent with the current observation, namely, the scalar spectral index is n_s=0.977--0.983 and the tensor to scalar ratio 0<r<0.012--0.010. result 1.00 0.89 0.17 hedged possibility 0.61
Other parameters, dn_s/dlnk, n_t, and their derivatives, are also consistent. result 1.00 0.82 0.06 asserted 0.82

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.89

What was examined, and what was not

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Levels run

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  • T body sentences
  • C citations
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How the labels were made

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,126 input tokens, $0.0003 reported.

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON

Figures (11)
Figure 1 of the paper
Figure 1. Left: MS running couplings. The 95% confidence intervals are given for m2 B /I1, yt(µ), λ(µ), and 10βλ(µ); see text for more details. The intervals for the gauge couplings gY , g2, and g3 are too small to be seen. Right: Enlarged view around the horizontal axis of Left. Darker bands are the 95% confidence intervals under the (theoretically unjustified) assumption that the Tevatron mass (14) can be identified with the top pole mass Mt . 1.96σ variation of Mt (15), where αs(Mz) and MH are fixed to their central values. Similarly, we plot the bare Higgs mass-squared m2 B , divided by
Figure 2 of the paper
Figure 2. RGE improved Higgs potential (23), with MH = 125.6 GeV and αs = 0.1184. The Solid and dashed lines are the SM Higgs potential (23). Beyond the UV cutoff Λ, which we have taken in this figure to be 4.5 × 1017 GeV as an illustration, we assume that the potential becomes flat as depicted by the dot-dashed lines. 3.3 Higgs inflation? We have seen in
Figure 3 of the paper
Figure 3. Left: Excluded region by Eq. (27) (red, left) and by Eq. (26) (blue, right) in
Figure 4 of the paper
Figure 4. Slow roll parameters V ∗, ηV ∗, ξ 2 V ∗ and $3 V ∗ as functions of ϕend/MP within the range 0.01 < ϕend/MP < 1.57. The dotted, dashed, and solid lines correspond to N∗ = 40, 50, and 60, respectively. The e-folding becomes N∗ = 2C − 1 4 ϕ 2 ∗ − ϕ 2 end M2 P + ϕ 2 ∗ 2M2 P ln ϕ∗ MP − ϕ 2 end 2M2 P ln ϕend MP = ϕ 2 ∗ 2M2 P ln ϕ∗ ϕend − ϕ 2 ∗ − ϕ 2 end 4M2 P × ( 1 − √ 2MP /ϕend for ϕend ≥ √ 2MP ,
Figure 5 of the paper
Figure 5. ns, dns d ln k , d 2ns d ln k 2 , r, nt , and dnt d ln k as functions of ϕend/MP . of k∗; see Ref. [71] for related discussions. When we vary N∗ and ϕend within the ranges 50 ≤ N∗ ≤ 60 and 0 < ϕend < 1.57MP , we get 0.980–0.984 > ns > 0.974–0.979, 0 < r < 0.029–0.024, −(4.0–2.7) × 10−4> dns d ln k >−(5.3–3.7) × 10−4 , 0 > nt > −(3.7–3.0) × 10−3 , −(1.6–0.9) × 10−5 > d 2ns d ln k 2 > −(2.2–1.2) × 10−5 , 0 < dnt d ln k < (8.2–5.6) × 10−5 , (34) where the order of the inequality corresponds to that of 0 < ϕend < 1.57MP ; the range of numbers denoted by the en-dash “–” corresponds to…
Figure 6 of the paper
Figure 6. Left: ϕ∗/MP as a function of ϕend/MP . Right: Potential values, V∗ = V(ϕ∗) and Vend = V(ϕend), as functions of ϕend/MP . The larger (smaller) values correspond to V∗/M4 P (Vend/M4 P ). We indicate N∗ the same as in
Figure 7 of the paper
Figure 7. Three blue curves are high energy potential (58) for
Figure 8 of the paper
Figure 8. At upper-left, upper-right, lower-left, and lower-right, respectively, we have plotted 2
Figure 9 of the paper
Figure 9. The e-foldings N∗ as a function of ϕend/MP corresponding to the pivot scale k∗ = 0.002 Mpc−1 in the instantaneous decay approximation; see text. where g∗ ' 106.75 is the effective number of degrees of freedom in the SM; the resultant reheating temperature is Treh ' 4 × 1015 GeV for ϕend = 0.5MP . Then the e-folding number, corresponding to the pivot scale k∗ = 0.002 Mpc−1 and the Hubble parameter H0 = 67.3 km s−1Mpc−1 , is given by [37]: N∗ ' 69 + 1 4 ln V∗ M4 P + 1 4 ln V∗ Vend . (39) Using the value of V∗ and Vend as depicted in
Figure 10 of the paper
Figure 10. Log potential (29) plus the correction (40) as a function of ϕ is drawn in the log￾log plot as the solid line in the right, which is the modification of the line for ϕend = 0.5MP in
Figure 11 of the paper
Figure 11. Running of the beta function b2 at the scale Λ0 of vanishing beta function as a function of top pole mass Mt . to the string scale in the conventional perturbative superstring scenario.15 This fact may suggest that the physics of the SM, string theory, and the universe are all directly connected. There are possibilities that realizes the flatness from the gauge symmetry as in the gauge-Higgs unification scenario [31, 32, 33, 34, 35]. See also Refs. [29, 30] for other stringy attempts. Furthermore, Ref. [72, 73] derives the log potential of the type (58). It would be interesting to…

Figures are the authors', reproduced from the paper.

References (91)
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How the literature uses it

35 arXiv papers cite this in 46 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 24 sentences without a confident label

Uses its data or values 1 paper
Compares with it 2 papers
  • Unlike critial Higgs inflation [ref] in four dimensions where $r≳0.1$ for the $ξ∼𝒪(1)$, our $r$ can be as small as $10^-12$ safely inside Planck 2015 $TT,TE,EE+lowP$ bound $r≲0.1$ for extra dimension scale around TeV scale.

    Higgs inflation in Gauss-Bonnet braneworld · Tree-Level Results · 0.97

  • The results of [ref] were based on approximating the Higgs potential near the saddle point, whereas we have constructed the entire potential starting from the electroweak scale masses and couplings.

    Higgs inflation at the hilltop · Small field values · 0.81

Cites it as support 4 papers
  • The MPP requires a degenerate vacuum around the Planck scale, which spoils the monotonicity of the Higgs potential which is necessary for a successful inflation [ref] .

    Hillclimbing Higgs inflation · Introduction · 0.96

  • To make matters worse, even renormalization-group improvements do not suffice to make Higgs-like potentials compatible with data [ref] .

    Multi-field inflation from single-field models · Introduction · 0.97

  • This potential is not sufficiently flat to allow a long enough period of inflation with a small enough amplitude of perturbations [ref] .

    Higgs inflation at the hilltop · Introduction · 0.96

Cites it as background 13 papers
  • $∙$ Inflation with non-minimal coupling Our main benchmark model is the quartic potential with a non-minimal coupling $ξϕ^2 R/M_pl^2$ (with dimensionless $ξ>0$) between inflaton and gravity [ref] .

    Low-energy probes of small CMB amplitude in models of radiative Higgs mechanism · Inflation models for interpretation · 0.87

  • Other models include a derivative coupling with the Einstein tensor (new Higgs inflation) [ref] , a galileon-like term (Higgs G-inflation) [ref] , and a non-canonical kinetic term (running kinetic inflation) [ref] , all of which can be treated in a unified manner in the context of generalized G-inflation [ref] as generalized Higgs inflation [ref] [Another Higgs inflation model without any higher derivative couplings was also proposed recently [ref] .].

    Graceful exit from Higgs G-inflation · Introduction · 0.98

  • One interesting attempt is given in the context of the Higgs inflation [ref] - [ref] (see Refs. [ref] - [ref] for recent discussions in the ordinary Higgs inflation and related works after the BICEP2 result).

    Higgs inflation and Higgs portal dark matter with right-handed neutrinos · Introduction · 0.92

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