Large Scale Structure and Supersymmetric Inflation without Fine Tuning

G. Dvali; Q. Shafi; R. Schaefer

REVIEW

Large Scale Structure and Supersymmetric Inflation without Fine Tuning

G. Dvali, Q. Shafi, R. Schaefer

High Energy Physics - Phenomenology · Submitted 15 Jun 1994 · 19 references

Pith's verdict: The (M_X/M_P)^2 amplitude in an R-symmetric SU(3)^3 hybrid inflation model is the durable result; the 'realistic GUT' embedding is sketched and deferred to unpublished work, and the 'no fine tuning' headline is doing more work than the text supports.

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arXiv IDhep-ph/9406319 (version 1)

Pith IDMW7I6T36, Pith's permanent record of this paper and its review

CitationG. Dvali, Q. Shafi, R. Schaefer. "Large Scale Structure and Supersymmetric Inflation without Fine Tuning." arXiv:hep-ph/9406319 (1994). https://pith.science/paper/MW7I6T36

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Editor's note

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Two things here are worth your time, and one gap you should know about before you cite it. The durable result is the amplitude: in this R-symmetric hybrid inflation setup the primordial fluctuation amplitude comes out proportional to (M_X/M_P)^2, with n = 1 - 1/N_Q ≈ 0.98. That is a clean, checkable statement, it needs no tiny dimensionless couplings (κ ~ 10^-2 at x_Q ~ 10), and it is the reason this paper gets cited. The one-loop Coleman-Weinberg potential and the slow-roll analysis are standard and properly attributed to Liddle-Lyth and Coleman-Weinberg. The large-scale-structure half is an extension of the authors' own ref [1] to larger n and different h; the χ² procedure with fitted normalization and IRAS bias is stated clearly enough to follow, and the 99% bound 0.80 < n[H_0/50]^{1/2} < 1.15 is a real, quotable number. Credit where due: the model building is genuinely new relative to Linde's hybrid inflation, and the amplitude coincidence with the GUT scale is a nice observation. The hierarchy resolution and proton stability are cited to Dvali-Shafi, Phys. Lett. B 326 (1994) — published, so that is fine, not a soft spot. I'd push back on the reader's circularity worry: fitting M_X to COBE and then noting it lands near the GUT scale is a consistency check, standard practice, not circular. But the paper should not sell it as 'no fine tuning' without saying which fine tuning it means — the coupling one, not the scale one. The abstract's 'provided the dark matter is a mixture' also overstates: their own limit is composition-independent and n = 1 works for all mixes. The real gap is the one the stress test names, and it is in the paper's own text: the λ'-λ̄' breaking scale v' is never computed, and the embedding is explicitly deferred — 'Without going into the details, which will be published elsewhere, we briefly summarize how things work out.' For the monopoles to be inflated away, v' must exceed μ ≈ 4×10^14 GeV, and nothing in the text shows that. So the 'realistic SUSY GUT' claim rests on unpublished work. Read it for the amplitude formula and the LSS contours; treat the GUT embedding as a promise. Worth a referee, with that gap flagged.

Referee report

Significance

If the central result holds, it is a genuinely attractive outcome: the amplitude of primordial fluctuations is fixed by M_X alone, with the coupling kappa dropping out, so no unnaturally small dimensionless coupling is required, and the predicted n approximately 0.98 is a sharp, falsifiable statement that sits comfortably inside the quoted large-scale structure contours. The R-charge assignment in Eq. (14) is internally consistent, and the higher-dimension operator lambda^3 (lambdabar' lambda')^3 / M^6 does yield a TeV-scale mu-term for the stated vev ratio. I also want to record that the circularity concern raised in the reader's report does not survive scrutiny: Eq. (12) is not a fit to COBE but follows directly from the e-folding integral, as I explain in the second major comment, so the (M_X/M_P)^2 scaling is a real prediction rather than a rewriting of the data. The weaknesses are elsewhere: the grand-unified embedding is asserted rather than demonstrated, and the reheating and gravitino discussion is a single sentence.

Major objections (4)

[p. 11, paragraph beginning 'The superpotential (14) is the generalization of (1)', and Eqs. (14)-(16)] The claim that the mechanism is realized in a realistic SU(3)^3 grand unified theory is the headline of the abstract, but the embedding is sketched rather than shown. The lambdabar'-lambda' sector is said to break G to SU(3)_c x SU(2)_L x SU(2)'_R x U(1) 'prior to inflation' so that the monopoles are inflated away, yet the breaking scale v' is never computed: W_lambda' in Eq. (14) contains only b lambda'^3 + c lambdabar'^3 with b and c unspecified, and the non-renormalizable couplings that would fix v' are not written down. For the scenario to work, v' must exceed the false-vacuum scale mu = sqrt(kappa) M_X, which with the paper's own numbers (kappa approximately 10^-2, M_X approximately 10^15.5 GeV) is about 4 x 10^14 GeV; this inequality is nowhere checked. The paper also does not say whether the subsequent lambda-lambdabar breaking at M_X produces monopoles of its own, which is exactly the issue that ruled out SU(5) two paragraphs earlier. The text defers all of this with 'Without going into the details, which will be published elsewhere, we briefly summarize how things work out.' Since the deferred work is not published, the 'realistic' claim cannot be assessed from this manuscript, and at minimum the authors should compute v' and verify v' > mu here.
[Eqs. (10) and (12)] The logical status of the amplitude formula needs to be stated explicitly, because as written it invites a reading that would undercut the naturalness claim. The sentence 'Using (10), we can estimate the fundamental parameter M_X to be on the order of 10^15.5 GeV' makes it sound as though M_X is fitted to COBE and then its proximity to the unification scale is presented as a success. In fact Eq. (12) is not a COBE fit: it follows from the e-folding integral N_Q approximately (8 pi / M_P^2) integral (V/V') dS, which with V/V' = 16 pi^2 S / kappa^2 gives N_Q approximately (64 pi^3 / kappa^2)(x_Q^2 - 1)(M_X/M_P)^2, and hence kappa/x_Q approximately 8 pi^{3/2} M_X / (sqrt(N_Q) M_P) for x_Q >> 1, which is exactly Eq. (12). Substituting this into Eq. (10) makes kappa cancel and leaves (Delta T/T)_Q approximately (8 pi N_Q)^{1/2} (M_X/M_P)^2, so the amplitude depends on M_X alone. That is the real content of the paper and it is a strong result. The authors should add these three lines, since without them a careful reader will suspect the naturalness argument is circular when it is not.
[pp. 11-12, paragraph beginning 'An inflationary scenario is incomplete'] The reheating and dark matter discussion is too compressed for the claims it carries. The reheat temperature is stated to be about 10^14 GeV, but no estimate is given, and the gravitino problem is dismissed with 'the gravitino mass must be large in order that the primordial gravitino problem is avoided' and 'precisely how this works out would depend on how local supersymmetry is broken.' At T_R approximately 10^14 GeV the thermal gravitino abundance is a severe constraint in gravity-mediated scenarios, and the reader needs at least an order-of-magnitude statement of the required gravitino mass and the resulting upper bound on T_R. Similarly, the baryon asymmetry is said to be generated at the electroweak scale, but with the LSP quoted at 200-350 GeV the strength of the electroweak phase transition is not obviously adequate, and no argument is offered. Since the model is presented as realistic, these two points need more than one sentence each.
[Figure 1 and the paragraph beginning 'The data are then analyzed in the following way'] The statistical treatment should be described more completely, because the n approximately 1 result is headlined in the abstract. Two of the constraints are one-sided: delta M/M (8 h^-1 Mpc) < 0.8 and delta M/M (0.6 h^-1 Mpc) >= 1.1 +/- 0.2. It is not stated how a one-sided bound is incorporated into a chi-squared statistic, nor whether the quoted 68, 95, and 99 percent contours in Figure 1 are computed with the two fitted parameters (normalization and bias b_I) subtracted from the degrees of freedom. The degeneracy between b_I and Omega_HDM is also not discussed, and since the IRAS galaxies may not trace mass, a shift in b_I could trade against the hot component. Finally, the abstract quotes Omega_HDM approximately 0.15-0.30, but the body gives no confidence level for that range; the only quantitative statement in the text is the n bound. The Omega_HDM range should be given with its confidence level, or removed from the abstract.

Minor objections (6)

[Eqs. (4) and (6)] The overall normalization of the one-loop potential should be rechecked against the helicity sum in Eq. (4). With four real scalars in phi and phibar (masses squared kappa^2 S^2 +/- kappa mu^2) and two Weyl fermions (mass kappa S), the sum over helicity states gives a coefficient of the logarithm that appears to be twice the one quoted in Eq. (6); if so, Eq. (12) shifts by a factor sqrt(2). Please show the multiplicity counting explicitly.
[Eq. (9) and the following paragraph] The text notes that eta diverges as x approaches 1 and concludes that inflation ends 'as x approaches 1 (from above)', but slow roll actually fails when |eta| reaches order unity at some x_end > 1. Since N_Q depends on x_end, the value of x_end should be given, and the approximation x_end approximately 1 used in deriving Eq. (12) should be justified.
[Abstract and p. 5] The abstract says n = 0.98 is in excellent agreement 'provided the dark matter is a mixture of cold and hot components', whereas the body states that the n bound is 'independent of the dark matter composition'. These should be reconciled, since the abstract implies a preference for a mixed dark matter that the quoted 99 percent bound does not support.
[p. 8, paragraph following Eq. (10)] The estimate M_X approximately 10^15.5 GeV should be compared quantitatively with the unification scale of about 10^16 GeV quoted on p. 2. A factor of three is within the uncertainties, but the reader would benefit from seeing the numerical coefficient in Eq. (10) evaluated for N_Q = 50 and 60, so that the residual tension is visible rather than glossed as 'on the order of'.
[p. 5, paragraph following Eq. (2)] The assertion that the R-symmetry 'is the only symmetry which can eliminate all of the undesirable self-couplings of the (inflation) S, while allowing the linear term in the superpotential' is a uniqueness claim that is not proved. Either sketch the argument or soften the wording.
[References] Reference [7] lists 'S. Mollenrach', which should presumably read Mollerach, and cites 'E.J. Copeland et al., Phys. Rev. D, in press' as unpublished; reference [17] has the typo 'Atrophys. J.'. Please also confirm that the two-year COBE analysis of ref. [9] is cited consistently with the hexadecupole value used in the text.

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The paper

The paper claims

A supersymmetric grand unified model is claimed to deliver hybrid inflation with no fine-tuned parameters, and to predict a spectral index of 0.98 together with a mixed cold-plus-hot dark matter sector that matches large-scale structure.

The reading

The paper has two halves that are meant to lock together. First, the authors fit a family of cosmological models to a battery of large-scale observations — the COBE quadrupole, the IRAS galaxy power spectrum, bulk peculiar velocities, cluster abundances and the quasar-era fluctuation floor — and report that the data prefer a spectral index $n$ close to 1 and a hot (light neutrino) dark matter fraction of roughly $0.15$ to $0.30$ for Hubble constants between 40 and 60 km s$^{-1}$ Mpc$^{-1}$. Second, they construct an inflationary model inside a realistic supersymmetric grand unified theory based on $SU(3)_c$ times $SU(3)_L$ times $SU(3)_R$, and argue that it needs no small dimensionless couplings, no adjustment of the inflaton mass, and no special treatment of the gauge hierarchy. The payoff they advertise is that the size of the primordial density fluctuations comes out proportional to $(M_X/M_P)^2$ — the square of the ratio of the unification scale to the Planck scale — with no extra dial to turn, and the spectral index comes out at $n = 0.98$. If the argument holds, the same superpotential that fixes the grand unified scale also fixes the amplitude of structure in the universe, which is the kind of link between particle physics and cosmology the programme was built to find.

What carries the argument

The load-bearing object is the R-symmetric superpotential $W = kappa S$ times $ar{varphi} varphi - mu^2 S$ together with its one-loop effective potential along the inflationary trajectory $|S| > S_c = mu/sqrt{kappa}$, with $varphi = ar{varphi} = 0$. The R-symmetry is doing two jobs at once: it is what makes the linear $mu^2 S$ term allowed while all unwanted cubic and quartic self-couplings of the inflaton are forbidden, and in the grand unified version it is what keeps the electroweak doublet pair massless at tree level and blocks baryon-number-violating operators. The one-loop Coleman-Weinberg correction, fed by the mass splitting $kappa mu^2$ inside the $varphi$ and $ar{varphi}$ supermultiplets, supplies the slope that ends inflation. The amplitude formula $(Delta T/T)_Q$ approximately $(8pi N_Q)^{1/2}(M_X/M_P)^2$ is the punchline: the fluctuation size is set by the ratio of the unification scale to the Planck scale, the same scaling that appears in the cosmic-string scenario, and the slow-roll parameters $epsilon$ and $eta$ expressed in the variable $x = S/S_c$ show inflation terminating as $x$ approaches 1.

Extended reading notes

Core claim

The central claim is that hybrid inflation — a false-vacuum phase at energy density $mu^4$ that ends when a singlet field $S$ rolls down to a critical value — can be realized inside a realistic supersymmetric grand unified theory rather than bolted on. The superpotential $W = kappa S$ times $ar{varphi} varphi - mu^2 S$ is the most general form allowed by an R-symmetry under which $S$ picks up a phase and $W$ picks up the same phase, and that same symmetry forbids the troublesome self-couplings of $S$ while permitting the linear term that supplies the vacuum energy. Supersymmetry breaking during inflation, through the non-zero $F_S$ term, generates one-loop Coleman-Weinberg corrections that slope the potential and drive $S$ toward its minimum, ending inflation and restoring supersymmetry. The authors embed this in $SU(3)_c$ times $SU(3)_L$ times $SU(3)_R$ with the role of $varphi$ and $ar{varphi}$ played by a conjugate pair of Higgs superfields, and the R-symmetry simultaneously keeps a pair of electroweak doublets light, forbids dimension-four and dimension-five baryon-number-violating operators, and leaves the proton essentially stable. Normalizing to the COBE quadrupole gives $(Delta T/T)_Q$ approximately $(8pi N_Q)^{1/2}(M_X/M_P)^2$, so the observed fluctuation amplitude picks out $M_X$ of order $10^{15.5}$ GeV and a coupling $kappa$ of order $10^{-2}$; the spectral index follows as $n$ approximately $1 - 1/N_Q$, approximately $0.98$.

Load-bearing premise

The naturalness claim rests on the fact that matching the predicted fluctuation amplitude to the observed COBE value yields $M_X$ of order $10^{15.5}$ GeV, a number close to the grand unified scale, but that scale is read off from the data rather than derived, so the argument shows consistency rather than the absence of tuning.

Editorial extensions

If this is right

If the construction is right, the amplitude of primordial density fluctuations is fixed by the grand unified scale alone, so measuring the amplitude is an indirect measurement of $M_X$.
The model predicts $n$ approximately $0.98$ with a tensor contribution suppressed relative to the scalar one by a factor of order $kappa/(8pi sqrt{N_Q})$, that is below $10^{-4}$ of the scalar amplitude, a small but in principle decisive signature.
The scheme prefers a dark matter sector that mixes a stable cold relic (in this model a bino of 200 to 350 GeV) with a few-electron-volt neutrino, matching the hot fraction of $0.15$ to $0.30$ that the data fit selects.
Because the R-symmetry forbids dimension-four and dimension-five baryon-violating operators, proton stability comes for free alongside the inflationary sector rather than being imposed separately.
The reheating temperature is estimated at about $10^{14}$ GeV, which forces the gravitino mass to be large if the primordial gravitino problem is to be avoided.

Reading between the lines

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

The no-fine-tuning claim is partly a statement about the absence of small dimensionless couplings, but the scale $M_X$ is fixed by matching to the observed COBE amplitude rather than predicted; a shift in the normalization would move $M_X$ and with it the apparent coincidence with the grand unified scale.
The amplitude formula being proportional to $(M_X/M_P)^2$ makes this model hard to distinguish from a cosmic-string scenario by amplitude alone, so the discriminator has to be the spectral index, the running, or the tensor fraction rather than the overall size of the fluctuations.
A precise independent determination of the hot dark matter fraction, for instance from neutrino mass constraints or from a sharper weak-lensing plus CMB combination, would test the cosmological half of the paper without touching the particle-physics half, and the two halves could then be checked separately.
The claim that R-symmetry is the unique symmetry able to set up a natural false-vacuum inflationary sector in global supersymmetry is stated rather than proved in the text, and it is the kind of assertion that a broader survey of possible symmetries could unsettle.

Original abstract

We explore constraints on the spectral index $n$ of density fluctuations and the neutrino energy density fraction $\Omega_{HDM}$, employing data from a variety of large scale observations. The best fits occur for $n\approx 1$ and $\Omega_{HDM} \approx 0.15 - 0.30$, over a range of Hubble constants $40-60$ km s$^{-1}$ Mpc$^{-1}$. We present a new class of inflationary models based on realistic supersymmetric grand unified theories which do not have the usual `fine tuning' problems. The amplitude of primordial density fluctuations, in particular, is found to be proportional to $(M_X /M_P)^2$, where $M_X (M_P)$ denote the GUT (Planck) scale, which is reminiscent of cosmic strings! The spectral index $n = 0.98$, in excellent agreement with the observations provided the dark matter is a mixture of `cold' and `hot' components.

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,455 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.42 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We explore constraints on the spectral index $n$ of density fluctuations and the neutrino energy density fraction $\Omega_{HDM}$, employing data from a variety of large scale observations. The best fits occur for $n\approx 1$ and $\Omega_{HDM} \approx 0.15 - 0.30$, over a range of Hubble constants $40-60$ km s$^{-1}$ Mpc$^{-1}$. We present a new class of inflationary models based on realistic supersymmetric grand unified theories which do not have the usual `fine tuning' problems. The amplitude of primordial density fluctuations, in particular, is found to be proportional to $(M_X /M_P)^2$, where $M_X (M_P)$ denote the GUT (Planck) scale, which is reminiscent of cosmic strings! The spectral index $n = 0.98$, in excellent agreement with the observations provided the dark matter is a mixture of `cold' and `hot' components.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We explore constraints on the spectral index $n$ of density fluctuations and the neutrino energy density fraction $\Omega_{HDM}$, employing data from a variety of large scale observations.	contribution 0.78	0.83	0.06	asserted 0.78
s1	The best fits occur for $n\approx 1$ and $\Omega_{HDM} \approx 0.15 - 0.30$, over a range of Hubble constants $40-60$ km s$^{-1}$ Mpc$^{-1}$.	result 1.00	0.81	0.19	asserted 1.00
s2	We present a new class of inflationary models based on realistic supersymmetric grand unified theories which do not have the usual `fine tuning' problems.	contribution 1.00	0.90	0.27	asserted 1.00
s3	The amplitude of primordial density fluctuations, in particular, is found to be proportional to $(M_X /M_P)^2$, where $M_X (M_P)$ denote the GUT (Planck) scale, which is reminiscent of cosmic strings!	result 0.93	0.91	0.19	asserted 1.00
s4	The spectral index $n = 0.98$, in excellent agreement with the observations provided the dark matter is a mixture of `cold' and `hot' components.	result 0.96	0.79	0.30	asserted 0.87

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from analysis of existing data 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** The χ 2 contours (68 %, 95%, and 99% confidence levels) for values of n and Ωhdm implied by the large scale structure data. In the left panel we have the constraints for a Hubble constant of 40 km s−1 Mpc−1 . Similarly we have the constraints for Hubble constants of 50 and 60 km s−1 Mpc−1 in the center and right panels. Values of n ∼ 1 are consistent with all values of the Hubble constant. We note that decreasing the Hubble constant favors larger values of n and smaller ΩHDM. 14

Figures reproduced from arXiv:hep-ph/9406319 by the authors.

References

Works cited (19)

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A.D. Linde, Phys. Lett. B, 259, 38 (1991) and Stanford Preprint 93-17 (1993)

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A.R. Liddle and D.H. Lyth, Phys. Rep. 231, 1 (1993); E.J. Copeland et. al., Phys. Rev. D, in press; S. Mollenrach, S. Matarrese a nd F. Lucchin, CERN Preprint (1993)

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T. P. Walker, et al., Astrophys. J., 376, 51, (1991); M.S. Smith, L. H. Kawano, and R.A. Malaney, Astrophys. J. Suppl. , 85, 219 (1993)

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Feldman, H., Kaiser, N., and Peacock, J.A., Mon. Not. R. Ast. Soc. (1993)

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W. Saunders, M. Rowan-Robinson, and A. Lawrence, Mon. Not. Roy. Ast. Soc. , 258, 134, (1992); K.B. Fisher, et al., Mon. Not. Roy. Ast. Soc., (in press)

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M. G. Haehnelt and M. J. Rees, Mon. Not. Roy. Ast. Soc. , 263 168, (1993). R. K. Schaefer and Q. Shaﬁ, Phys. Rev. D , 47, 1333, (1993); M. G. Haehnelt, Mon. Not. Roy. Ast. Soc. , in press, (1994); A. Nusser and J. Silk, Astrophys. J. Lett. , 411, L1, (1993). 13

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[15]

It has been suggested that the number of ”Lyman alpha clo uds”, ob- jects which are detected by their Lyman series absorption li nes in the continuum emission of quasars, may provide an even more stri ngent bound on the amplitude of galaxy sized density ﬂuctuations. For a re- cent discussion and additional references see A. Klypin et al. , preprint astro-...

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N. Kaiser, 1987, Mon. Not. Roy. Ast. Soc. , 227, 1

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[19]

S. Coleman and E. Weinberg, Phys. Rev., D7, 1888 (1973). 1 Figure Captions Figure 1. The χ2 contours (68 %, 95%, and 99% conﬁdence levels) for values of n and Ω hdm implied by the large scale structure data. In the left panel w e have the constraints for a Hubble constant of 40 km s −1 Mpc−1. Similarly we have the constraints for Hubble constants of 50 an...

View on Pith Pith review arXiv 1973

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Planck 2015 results. XX. Constraints on inflation
astro-ph.CO 2015-02 accept novelty 6.0 of 10

Full-mission Planck data give a scalar spectral index ns = 0.9655 +/- 0.0062 and a tensor-to-scalar bound r < 0.11, disfavouring phi-squared and natural inflation relative to R-squared inflation.
Massive Primordial Black Holes from Hybrid Inflation as Dark Matter and the seeds of Galaxies
astro-ph.CO 2015-01 conditional novelty 6.0 of 10

A mild waterfall phase of hybrid inflation produces a broad primordial black hole mass spectrum that can match the dark matter abundance and seed supermassive black holes, for a narrow window of potential parameters.
D7-Brane Moduli Space in Axion Monodromy and Fluxbrane Inflation
hep-th 2014-05 conditional novelty 6.0 of 10

The paper derives a corrected Type IIB D7-brane superpotential, shows the extended no-scale cancellation survives a light brane modulus, and argues fluxbrane inflation can be made parametrically consistent, though onl...
The importance of being warm (during inflation)
hep-ph 2013-07 conditional novelty 6.0 of 10

Warm inflation with a thermalized inflaton bath at T > H brings the quartic chaotic potential into agreement with Planck and predicts a suppressed tensor-to-scalar ratio, r approximately 8(1 - ns)(H/T).
Planck 2013 results. XXII. Constraints on inflation
astro-ph.CO 2013-03 conditional novelty 6.0 of 10

Planck 2013 measures the scalar spectral index at 0.9603 plus or minus 0.0073 and bounds the tensor-to-scalar ratio below 0.11, ruling out exact scale invariance and disfavouring steep, exponential, and simple hybrid ...
On the Adiabatic Solution to the Polonyi/Moduli Problem
hep-ph 2011-09 conditional novelty 6.0 of 10

The adiabatic suppression mechanism for the Polonyi/moduli problem is incomplete: coherent oscillations are unavoidably generated at the end of inflation, and thermal production of Polonyi particles bounds the reheati...
Hybrid inflation along waterfall trajectories
gr-qc 2010-06 conditional novelty 6.0 of 10

Hybrid inflation can generate more than 60 e-folds during the waterfall phase, producing a red adiabatic spectrum that may be consistent with CMB observations.
Hilltop Inflation
hep-ph 2005-02 conditional novelty 6.0 of 10

Hilltop inflation, starting near a potential maximum, is shown to be generic, to predict r < 0.002, and to arise naturally from F- and D-term models once Planck-suppressed terms are included.
Running cosmological constant in light of recent CMB-BAO data
astro-ph.CO 2026-10 conditional novelty 5.0 of 10

A logarithmically corrected cosmological constant can drive inflation that fits CMB-plus-BAO data with a positive correction and CMB-only data with a regularized negative correction, depending on the size and sign of ...
Supersymmetric Hybrid Inflation with K\"{a}hler-Induced $\mathbf{R}$-Symmetry Breaking
hep-ph 2025-06 conditional novelty 5.0 of 10

Nonrenormalizable R-symmetry breaking in the Kahler potential can tune the spectral index of supersymmetric hybrid inflation into the ACT DR6 window while keeping tensor modes below 1e-5.
Higgs-like inflation under ACTivated mass
hep-ph 2025-05 conditional novelty 5.0 of 10

In metric Higgs-like inflation, a quadratic mass term in the Jordan frame raises the spectral index and can restore compatibility with the ACT+BK+Planck+DESI data.
Simulations of Magnetic Monopole Collisions
hep-th 2025-02 conditional novelty 5.0 of 10

Numerical field-theory simulations reproduce the predicted right-angle, 60-degree, and 45-degree scattering of BPS magnetic monopoles and show tetrahedral and cubic intermediate states.
Analysis of inflationary models in higher-dimensional uniform inflation
hep-ph 2025-01 conditional novelty 5.0 of 10

In (D+4)-dimensional uniform inflation the spectral index and tensor-to-scalar ratio are ns=1-(D+6)ε+2η and r=8(D+2)ε, which excludes D≥2 for the five models studied while allowing D=1 in the b0k >> 1 branch.
No-scale hybrid inflation with R-symmetry breaking
hep-ph 2020-09 conditional novelty 5.0 of 10

A no-scale supergravity hybrid inflation model with maximally broken R-symmetry yields a Starobinsky-like flat plateau and CMB-consistent observables, with new parameter freedom b up to 0.25.
QCD Axion on Hilltop by a Phase Shift of $\pi$
hep-ph 2019-08 conditional novelty 5.0 of 10

A heavy axion inflaton can shift the QCD axion potential by π, placing the QCD axion at the hilltop and allowing f_a ≳ 3×10^9 GeV to explain all dark matter.
Vector dark matter production at the end of inflation
hep-ph 2018-10 conditional novelty 5.0 of 10

Tachyonic production of one transverse dark photon polarization at the end of inflation can reproduce the observed dark matter relic density for masses between microelectronvolts and hundreds of GeV.
The ALP miracle: unified inflaton and dark matter
hep-ph 2017-02 conditional novelty 5.0 of 10

One axion-like particle with mass of order 0.01 eV and photon coupling of order 10^-11 GeV^-1 can simultaneously drive inflation, reheat the universe, and account for dark matter.
Non-perturbative approach for curvature perturbations in stochastic-$\delta N$ formalism
astro-ph.CO 2014-05 conditional novelty 5.0 of 10

Numerically integrating the stochastic inflaton dynamics reproduces the standard power spectrum in chaotic inflation and yields, for the first time, the full power spectrum through the hybrid inflation waterfall, incl...
The Gravitational Wave Spectrum from Cosmological B-L Breaking
hep-ph 2013-05 conditional novelty 5.0 of 10

In a B-L hybrid inflation model, cosmic strings produce a gravitational wave background five to eight orders of magnitude above the inflationary one, with a spectral kink that encodes the reheating temperature.
The hybrid inflation waterfall and the primordial curvature perturbation
astro-ph.CO 2012-01 conditional novelty 5.0 of 10

The hybrid inflation waterfall generates a peaked, non-gaussian curvature spectrum that is negligible on cosmological scales and only threatens black hole bounds when the waterfall mass is comparable to or below the H...
Non-Gaussianity, Spectral Index and Tensor Modes in Mixed Inflaton and Curvaton Models
astro-ph 2008-02 accept novelty 5.0 of 10

In mixed inflaton-curvaton models, large non-Gaussianity can coexist with an acceptable spectral index and tensor-to-scalar ratio, and a consistency relation links the bispectrum and trispectrum when the curvaton stay...
Direct detection of the inflationary gravitational wave background
astro-ph 2005-06 accept novelty 5.0 of 10

Direct detection of the inflationary gravitational-wave background by BBO or DECIGO is possible in several slow-roll inflation models, but likely only when the signal is also detectable in CMB polarization.
Fine-tunings in radiative $\alpha$-particle capture on $^{12}$C at astrophysical energies
nucl-th 2026-01 unverdicted novelty 4.0 of 10

Astrophysical S-factor data constrain variations in the electromagnetic fine-structure constant to |δ α/α| ≤ 0.0002 in radiative alpha capture on carbon-12.
Split supersymmetry and hybrid inflation in light of Atacama Cosmology Telescope DR6 data
hep-ph 2025-07 conditional novelty 4.0 of 10

An update of mu-term hybrid inflation shows that a tuned soft-SUSY parameter B makes the scalar spectral index match ACT DR6, with tensor-to-scalar ratio of order 10^-3 to 10^-2 and a 2 TeV wino dark matter candidate.
Waterfall phase in supersymmetric hybrid inflation
hep-ph 2025-07 conditional novelty 4.0 of 10

Waterfall-phase e-foldings in R-symmetric SUSY hybrid inflation can produce a PTA-compatible scalar-induced gravitational wave background and, in SU(5), dilute monopoles to observable levels.
Hybrid cosmological attractors
hep-th 2022-04 conditional novelty 4.0 of 10

Uplifting an α-attractor potential with a hybrid-inflation sector produces a second attractor with ns = 1, continuously interpolating to the standard 1 - 2/N as the uplift or critical field shrinks.
Constraints on millicharged particles from Planck
hep-ph 2013-10 conditional novelty 4.0 of 10

Planck CMB data alone bound the present abundance of millicharged particles to Omega_mcp h^2 < 0.001 at 95% confidence, provided those particles remain coupled to the baryon-photon plasma at recombination.
COrE (Cosmic Origins Explorer) A White Paper
astro-ph.CO 2011-02 conditional novelty 4.0 of 10

A 15-band full-sky microwave polarimeter with 10 to 30 times Planck's sensitivity would detect primordial tensor modes at r = 0.001 at 3 sigma and measure the CMB lensing deflection to the cosmic variance limit, provi...
Minimal Inflation
hep-th 2009-12 conditional novelty 4.0 of 10

Identifying the inflaton with the scalar component of the supersymmetry-breaking X superfield yields a toy model with a nearly scale-invariant spectrum, negligible gravitational waves, and a supersymmetry-breaking sca...
Supersymmetric Hybrid Inflation Redux
hep-ph 2009-08 conditional novelty 4.0 of 10

Including a soft supersymmetry-breaking linear term in the inflaton potential lets minimal-Kaehler supersymmetric hybrid inflation produce the WMAP5 spectral index 0.963 instead of the previously predicted 0.985 or higher.
Constraining SUSY GUTs and Inflation with Cosmology
hep-ph 2006-03 conditional novelty 4.0 of 10

In SUSY GUTs, hybrid inflation generically ends by forming cosmic strings, and the WMAP null detection forces the inflation scale below about 3 x 10^15 GeV and the couplings kappa and lambda below about 10^-5.
Supersymmetric Hybrid Inflation in light of Atacama Cosmology Telescope Data Release 6, Planck 2018 and LB-BK18
astro-ph.CO 2025-04 conditional novelty 3.0 of 10

A known supersymmetric hybrid inflation model, with soft supersymmetry-breaking and supergravity terms included, can produce a spectral index n_s in 0.96 to 0.98, consistent with ACT DR6, Planck 2018 and BK18, by choo...
Metastable cosmic strings
hep-ph 2023-07 accept novelty 3.0 of 10

A network of metastable cosmic strings with GUT-scale tension and lifetime parameter sqrt(kappa) around 8 can fit the pulsar-timing gravitational-wave signal at 3 nHz and predict an observable signal at LISA and groun...
Noncanonical Approaches To Inflation
gr-qc 2019-06 unverdicted novelty 3.0 of 10

A review thesis covering Mukhanov parametrization, general scalar-tensor theories, and new slow-roll techniques for canonical and noncanonical inflation observables.
Particle physics models of inflation and curvaton scenarios
hep-ph 2010-01 accept novelty 3.0 of 10

The review argues that inflatons and curvatons built from MSSM flat directions are the class most tightly tied to known particle physics, and therefore the class most likely to be falsified by CMB and collider data.
Non-topological solitons and quasi-solitons
hep-th 2024-11 accept novelty 2.0 of 10

A comprehensive review of non-topological solitons (Q-balls) and quasi-solitons (oscillons), their properties, dynamics, and roles in early-universe physics.
Supergravity based inflation models: a review
astro-ph.CO 2011-01 accept novelty 1.0 of 10

Supergravity can accommodate new, hybrid, chaotic, and topological inflation, and Jordan-frame supergravity can host Higgs inflation, provided the Kähler potential or D-term structure is chosen to avoid the eta problem.

How the literature uses it

125 arXiv papers cite this in 215 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 · 143 sentences without a confident label

Uses its method or tool 1 paper

To achieve this, one can e.g. employ supersymmetric hybrid inflation [ref] at the last intermediate symmetry breaking stage (alternatively, one may utilize tribrid inflation [ref] ).

Explaining PTA Results by Metastable Cosmic Strings from SO(10) GUT · Superpotential · 0.81

Uses its data or values 1 paper

Thus, the observational data of $δT/T∼10^-5$ [ref] determine the spontaneous symmetry breaking scale: $M≈10^15-16$ GeV, which is tantalizingly close to the scale of SUSY grand unified theory (GUT) [ref] .

Spectral Index and Non-Gaussianity in Supersymmetric Hybrid Inflation · Introduction · 0.95

Compares with it 7 papers

This was also accomplished in Refs. [ref] where the energy scale during inflation was associated with a $B - L$ breaking scale.[In previous models in the literature, Refs. [ref] , the energy scale during inflation was also related to a GUT symmetry breaking scale.

A Pati-Salam Version of Subcritical Hybrid Inflation · Introduction · 0.90
This is to be contrasted with the simplest supersymmetric hybrid inflation models in which the corresponding $M_X$ can easily be 1-2 orders of magnitude larger than the scale of vacuum energy during inflation [ref] .

GUT Inflation and Proton Decay after WMAP5 · GUT Inflation with a Coleman-Weinberg (CW) Potential · 1.00
Finally we would like to contrast the results with standard SUSY hybrid inflation [ref] .

Hybrid inflation with moduli stabilization and low scale supersymmetry breaking · Discussion · 1.00

Cites it as support 1 paper

This problem will eliminate if radiative corrections are taken into account because, these corrections drive the system towards the global minimum by lifting the potential in the $Φ$ direction [ref] .

Supersymmetric hybrid inflation with non-minimal coupling to gravity · The Model · 0.98

Cites it as background 54 papers

In the standard version of SUSY hybrid inflation [ref] GUT symmetry is broken at the end of inflation whereas in the shifted [ref] and the smooth [ref] versions of the model it is broken during inflation.

Simplified Smooth Hybrid Inflation in Supersymmetric SU(5) · Introduction · 0.92
The hybrid model [ref] results from the globally supersymmetric renormalizable superpotential [equation] where $Ψ_1, Ψ_2$ are chiral superfields,

Gravitational Waves and Primordial Black Holes from Supersymmetric Hybrid Inflation · The Hybrid Model · 0.84
The SUSY hybrid inflation model is defined as the following superpotential [ref] ; [equation] where $ϕ$ and $ϕ$ are a conjugate pair of superfields carrying gauge and/or global charges.

Spectral Index and Non-Gaussianity in Supersymmetric Hybrid Inflation · Modification of Hybrid Inflation · 0.86

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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