REVIEW
Chaotic Inflation and Baryogenesis in Supergravity
High Energy Physics - Phenomenology · Submitted 21 Nov 1993 · 31 references
Pith's verdict: The Kähler potential is a real, checkable construction; the soft spot is that η-tracking during inflation is asserted rather than shown, though a quick estimate suggests it holds.
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Referee report
The paper
The paper claims
The paper proposes a Kähler potential for supergravity, $G = (3/8)|ln η + η^2 + ln|W|^2$ with $η = z + z^* + φ_i^*φ_i$, whose scalar potential has a zero-cosmological-constant minimum at $η = 3/4$ where it reduces exactly to the global-sup
The reading
What carries the argument
The load-bearing object is the Kähler potential $G = (3/8)|ln η + η^2 + ln|W(φ)|^2$ built from $η = z + z^* + φ_i^*φ_i$, where $z$ is the field whose fermion partner is the goldstino. It does three jobs at once: its kinetic term has the correct signature only for $|η| > √{3/4}$, which is why the authors must assume the universe starts in that domain; its potential, $V = η^{3/8} e^{η^2} { [8η/(16η^2+3)] |W_i|^2 + [(16η^2-9)^2/(8(16η^2-3))] |W|^2 }$, has its minimum at $η = 3/4$ with $W_i = 0$ and zero vacuum energy; and at that minimum the potential collapses to the global-SUSY expression, which is what allows ordinary chaotic inflation to proceed. The gravitino mass $m_{3/2}^2 = η^{3/8} e^{η^2} |W|^2$ is set by the constant term in $W$ alone, and the gaugino mass is fixed by the same constant through the kinetic function $h(z)$, evaluated at $z = 3/8$.
Extended reading notes
Core claim
The central claim is that a single change of Kähler potential makes chaotic inflation compatible with supergravity. With $G = (3/8)|ln η + η^2 + ln|W(φ)|^2$ and $η = z + z^* + φ_i^*φ_i$, the resulting scalar potential has a minimum at $η = 3/4$ where the cosmological constant vanishes and the potential takes precisely its global-SUSY form, so a flat direction such as $W = (1/2)Mφ^2$ can drive inflation with $φ$ starting near $1/√M$. Because supersymmetry breaking is introduced by a constant in the superpotential that does not feed soft masses to squarks and sleptons, the gravitino can be made heavy — above $10^{11}$ GeV — so it decays before electroweak breaking and neither the gravitino problem nor the entropy crisis from the goldstino partner's late oscillation arises. Identifying $φ$ with the right-handed sneutrino at $M ≃ 10^{13}$ GeV then ties the COBE normalization, the MSW neutrino mass window, and leptogenesis-induced baryogenesis to one parameter.
Load-bearing premise
The scenario assumes without derivation that the universe begins in the domain $η > √{3/4}$ with order-one fluctuations of $η$, and that $η$ then settles quickly to its minimum so that the potential really becomes the global-supersymmetry one during inflation.
Editorial extensions
If this is right
- Any inflation model that works in global supersymmetry can be promoted to supergravity by adopting this Kähler potential, since the potential at $η = 3/4$ is the global one.
- The gravitino mass can be taken above $10^{11}$ GeV while squark and slepton masses stay near the TeV scale, because the constant added to the superpotential generates no soft masses for the matter fields.
- The entropy crisis is avoided provided the $η$ oscillation decays with $Γ_η ≳ 10^{-3}$ GeV, which makes the dilution factor from $η$ of order one rather than the $10^{15}$ of minimal supergravity.
- Baryogenesis proceeds through the formula $Y_B = 0.35 ε (3T_{RH}/4M) exp[-0.012 G_F^2 m_{ν_τ}^2 M_{Pl} T_{RH}/\sin^4 β]$, and with an order-one CP phase, $T_{RH} ∼ 10^9$ GeV and $m_{ν_τ} ≃ 10$ eV it reproduces the observed asymmetry.
- Flat directions do not grow past the Planck scale during inflation, since the expansion rate satisfies $H ≲ √M$ and the quantum spread $⟨χ^2⟩ = (H^3/4π^2)t_e$ stays below $1/(4√3π)$.
- The matter content preferred by the baryogenesis estimate — a $10$ eV $τ$-neutrino plus a lightest-supersymmetric-particle cold component — is the mixed dark matter scenario.
Reading between the lines
- Because the potential reduces to the global form at the minimum, the model's density-perturbation predictions are those of a simple $M^2φ^2$ chaotic model; the Kähler potential adds no separate signature in the scalar tilt or tensor amplitude, so its distinctive tests must come from the reheating and $η$ sectors rather than from the power spectrum.
- The same $M ≃ 10^{13}$ GeV number is fixed by COBE, sets the seesaw neutrino mass, and controls the reheat temperature that enters the baryon asymmetry, so independent tightening of the neutrino mass scale and of $Y_B$ becomes a cross-check on a single parameter rather than on three.
- The construction is generic in the sense that any sufficiently flat singlet direction can be plugged in as $W$, which means the framework's content lies mostly in the $η$ sector and in the decay rates; a reader looking for a prediction that distinguishes it from ordinary chaotic inflation will not find one in the inflationary era itself.
- The requirement that $η$ begin above $√{3/4}$ is a statement about which patches of the early universe are populated, in a regime where the kinetic term for $η$ is not even positive definite below that value; making the scenario predictive would need an account of why the pre-inflationary distribution lands there.
Original abstract
We propose a K\"ahler potential in supergravity which successfully accommodates chaotic inflation. This model can have a large gravitino mass without giving a large mass to squarks and sleptons, and thus is free from both the gravitino problem and entropy crisis. In this model baryogenesis takes place naturally, identifying the inflaton with a right-handed sneutrino with its mass $M \simeq 10^{13}$GeV, which is consistent with the COBE data and the Mikheyev--Smirnov--Wolfenstein solution to the solar neutrino problem. The model can also accommodate the matter content appropriate for the mixed dark matter scenario.
The compiled record
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. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We propose a K\"ahler potential in supergravity which successfully accommodates chaotic inflation. This model can have a large gravitino mass without giving a large mass to squarks and sleptons, and thus is free from both the gravitino problem and entropy crisis. In this model baryogenesis takes place naturally, identifying the inflaton with a right-handed sneutrino with its mass $M \simeq 10^{13}$GeV, which is consistent with the COBE data and the Mikheyev--Smirnov--Wolfenstein solution to the solar neutrino problem. The model can also accommodate the matter content appropriate for the mixed dark matter scenario.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We propose a K\"ahler potential in supergravity which successfully accommodates chaotic inflation. | contribution 0.99 | 0.91 | 0.41 | asserted 0.97 |
| s1 | This model can have a large gravitino mass without giving a large mass to squarks and sleptons, and thus is free from both the gravitino problem and entropy crisis. | result 0.76 | 0.73 | 0.19 | hedged possibility 0.83 |
| s2 | In this model baryogenesis takes place naturally, identifying the inflaton with a right-handed sneutrino with its mass $M \simeq 10^{13}$GeV, which is consistent with the COBE data and the Mikheyev--Smirnov--Wolfenstein solution to the solar neutrino problem. | result 0.54 | 0.71 | 0.35 | asserted 0.82 |
| s3 | The model can also accommodate the matter content appropriate for the mixed dark matter scenario. | result 0.82 | 0.72 | 0.08 | hedged possibility 0.92 |
What was examined, and what was not
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References
How the literature uses it
50 arXiv papers cite this in 59 sentences
Papers citing it · 33 sentences without a confident label
Contests it 1 paper
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We also note that an early attempt at a chaotic inflation model in no-scale supergravity was made in [ref] , though this model suffers from an instability along the inflationary path [ref] .
Resurrecting Quadratic Inflation in No-Scale Supergravity in Light of BICEP2 · Models with the Kähler Potential fixed dynamically · contest 0.88
Compares with it 2 papers
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It is the quartic coupling that drives sneutrino inflation, in contrast to the early sneutrino inflation models [ref] where the sneutrino mass term is responsible for inflation.
The mu problem and sneutrino inflation · Introduction · 0.91
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The situation is similar to sneutrino inflation [ref] , but no SUSY is required in our setup.
Type II Seesaw Higgs Triplet as the inflaton for Chaotic Inflation and Leptogenesis · Higg Triplet as the inflaton · 0.98
Cites it as support 1 paper
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In this case, the $η$ problem can be avoided [ref] and it is natural, therefore, to consider inflationary models in this context [ref] .
Starobinsky-Like Inflation and Neutrino Masses in a No-Scale SO(10) Model · Introduction · 0.96
Cites it as background 21 papers
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Inflationary Baryogenesis has been widely investigated in the literature [ref] , but with few cases able to simultaneously explain each of the issues named above.[Inflation with Leptogenesis by the right-handed sneutrino has been considered in [ref] .] We present a model herein that represents a simple and well-motivated realization of this idea.
Affleck-Dine Leptogenesis from Higgs Inflation · Introduction · 0.83
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On the other hand inflation with the singlet right-handed sneutrino has been well studied [ref] and in MSSM the Higgs-sneutrino inflation along flat-directions [ref] has also been studied.
Plateau Inflation in $R$-parity Violating MSSM · Introduction · 0.84
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Here we are interested in inflationary models [ref] based on no-scale supergravity .
Two-Field Analysis of No-Scale Supergravity Inflation · Introduction · 0.87
Discussion
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