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REVIEW 2 major objections 5 minor 51 references

DESI and Planck push pure Starobinsky inflation past 60 e-folds, while free α prefers a broader plateau at 1σ.

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2026-07-13 18:02 UTC pith:5U6FSQBA

load-bearing objection Clean new joint posteriors on α-Starobinsky with DESI DR2; the N*>60 “breakdown” language is overstated without reheating, but the numerical result and 1σ preference for α>1 stand. the 2 major comments →

arxiv 2603.25721 v2 pith:5U6FSQBA submitted 2026-03-26 astro-ph.CO

Bayesian analysis of α-Starobinsky model with Planck, ACT and DESI data

Karim Carrion , Francisco X. Linares Cede\~no , Gabriel Germ\'an , Juan Carlos Hidalgo This is my paper
classification astro-ph.CO
keywords α-Starobinsky inflationBayesian cosmologyPlanckDESI BAOACT DR6 lensinge-folds N*slow-roll consistency relations
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests whether the classic Starobinsky inflation model still fits modern cosmology once DESI BAO and ACT lensing are added to Planck. Pure Starobinsky is rigid: the higher spectral index preferred by the joint data forces the number of e-folds after horizon exit above 60, outside the usual theoretical window. Allowing a single deformation parameter α that widens the inflationary plateau removes that tension and yields a clear 1σ preference for log10 α > 0 across every dataset combination. The authors reach this conclusion with a new sampling trick: they place priors on the observable quantities As, ns and r, map them analytically to the potential parameters, then evolve the exact field equations numerically so that the final posteriors are free of slow-roll approximations. ACT lensing adds almost no extra pull; the shift is driven by Planck plus DESI.

Core claim

When Planck is combined with DESI DR2 (and optionally ACT DR6), the pure Starobinsky limit α = 1 requires a mean N* ≈ 63.4, exceeding the canonical 50–60 e-fold window because of the upward shift in ns. Freeing the deformation parameter α produces a consistent 1σ preference for log10 α > 0, which widens the plateau, raises r at fixed N, and brings N* back near 61 while still matching the higher ns.

What carries the argument

Slow-roll parameterization of the priors: analytical consistency relations that map sampled (As, ns, r) onto (V0, α, N*), after which a modified CLASS code integrates the exact inflationary dynamics so that reported posteriors are free of the slow-roll approximation.

Load-bearing premise

That N* greater than 60 is automatically a sign the pure model is breaking down, even though reheating physics that could absorb the extra e-folds is left free and unsampled.

What would settle it

A joint Bayesian analysis that samples reheating parameters together with α and shows that the pure Starobinsky limit can recover N* inside 50–60 while still fitting the same Planck+DESI ns, or a future CMB-S4 measurement of r that lies outside the α > 1 tracks preferred here.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper performs a joint Bayesian MCMC analysis of the α-Starobinsky (E-model) inflationary potential using Planck 2018 primary CMB, ACT DR6 lensing, and DESI DR2 BAO. Its methodological contribution is a slow-roll-parameterized prior on the observables {A_s^α, n_s^α, r^α} that is analytically inverted via consistency relations (Eqs. 2.16–2.20) to obtain the potential parameters {V_0, α, N_*}; these are then evolved with a modified CLASS that solves the exact background and perturbation equations, so that the reported posteriors on A_s, n_s, r are free of the slow-roll approximation. For the rigid Starobinsky limit α=1 the full data set shifts the posterior mean to N_*≈63.4 (outside the conventional 50–60 window) because of an upward pull on n_s; when α is free the same data yield a 1σ preference for log_{10} α>0 across all combinations, while ACT lensing adds negligible extra constraining power on the inflationary subspace.

Significance. If the numerical pipeline and the mild preference for a broader plateau hold under scrutiny, the work supplies a timely, data-driven update of α-attractors with the latest DESI BAO and ACT lensing releases, together with a reusable sampling strategy that anchors priors to observables rather than abstract potential scales. Strengths that should be credited include the public modified CLASS repository, the explicit validation of the consistency relations against full numerical spectra (Appendix A: sub-0.1σ agreement on n_s and r), the Gelman–Rubin R−1<0.01 convergence criterion, and the transparent reporting of both 1σ intervals and 95% upper limits on r. These elements make the analysis reproducible and useful for future model-comparison studies once reheating is jointly sampled.

major comments (2)
  1. Abstract, §4.1 and Table 2: the claim that pure Starobinsky (α=1) “shows signs of breaking down” or faces an “apparent discrepancy” solely because the posterior mean shifts to N_*=63.4^{+5.5}_{-8.2} treats the textbook window 50<N_*<60 as a hard consistency cut. In single-field inflation N_* is not fixed by the potential alone; it depends on the post-inflationary equation of state and reheating temperature. The manuscript leaves reheating free (flagged only as future work in §5) and therefore cannot yet convert a mild upward shift in n_s into a genuine model breakdown. The language should be softened to “tension with the instantaneous-reheating expectation” and a short quantitative discussion of how w_reh>1/3 can accommodate N_*∼65 should be added, or the claim should be deferred until reheating parameters are sampled.
  2. Appendix A and the sampling description in §3: the slow-roll seeds produce a systematic ∼0.94σ offset in log(10^{10} A_s) relative to the exact CLASS solution (while n_s and r agree to ≪0.1σ). Although the final reported observables are taken from the numerical pipeline, the offset is large enough that the prior volume itself is slightly mis-centered. Either a next-to-leading-order correction (Stewart–Lyth) should be inserted into the mapping, or an explicit statement that the A_s prior is only approximate and that the posterior is re-weighted by the exact CLASS likelihood should be added so that readers can judge residual bias.
minor comments (5)
  1. Abstract and §1: minor grammatical slips (“through using analytical”, “the pure Starobinsky model au faces an apparent discrepancy”) should be cleaned for readability.
  2. Figure 2 caption and §3: the pivot scale is quoted both as k_*=0.05 Mpc^{-1} and as 1.3128×10^{-58} M_Pl; a single consistent statement would avoid confusion.
  3. Table 1 and Eq. (3.1): the prior ranges on the seed observables are taken from “validated observational pipelines,” but the precise references (or the exact Planck prior tables) are not cited; a short footnote would improve reproducibility.
  4. Figure 5: the large-N slow-roll tracks (n_s≃1−2/N, r≃12α/N^{2}) are useful, yet the caption should note that the numerical CLASS points (not the analytic tracks) are what enter the likelihood.
  5. §2.1: the supergravity motivation is clear, but the statement that the generalized Kähler potential “requires a more sophisticated superpotential” could briefly cite the explicit form used in Ellis et al. (2019) so that the geometric interpretation of α is self-contained.

Circularity Check

0 steps flagged

No load-bearing circularity: slow-roll relations are used only as sampling seeds; final posteriors come from exact numerical CLASS integration and are data-driven.

full rationale

The paper’s central pipeline places flat priors on the observables (A_s^α, n_s^α, r^α), maps them once via the analytic slow-roll consistency relations (Eqs. 2.16, 2.17, 2.20) to the potential parameters (V_0, α, N_*), then evolves the exact background and perturbation equations inside a modified CLASS. The reported posteriors (Tables 2–3, Figs. 3–6, 8) are taken exclusively from that numerical output, not from the slow-roll seeds. Appendix A quantifies the residual mismatch (≲0.05σ for n_s and r, ∼1σ for A_s) and treats the mapping as an efficient prior only. The 1σ preference for log_10 α > 0 and the upward shift of N_* under DESI are therefore ordinary Bayesian updates driven by the likelihoods (Planck + DESI BAO), not forced by construction. Self-citations ([29], [45]) supply background reheating formulae or earlier consistency checks; none is invoked as a uniqueness theorem or as the sole justification of the main claim. The interpretive language that α = 1 “breaks down” for N_* > 60 rests on an external theoretical window, not on a circular reduction inside the derivation. Hence the score remains at the minor-self-citation floor.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The analysis rests on standard single-field slow-roll seeds for prior mapping, the α-Starobinsky potential derived from no-scale supergravity, and the usual flat ΛCDM late-time cosmology. Free parameters are the usual cosmological set plus the three inflationary seeds; no new particles or forces are invented. The only paper-specific modeling choice is the decision to treat N*≳60 as theoretically disfavored without sampling reheating.

free parameters (3)
  • log(10^10 A_s^α), n_s^α, r^α
    Sampled with flat priors (Table 1) that seed the mapping to V0, α, N*; final values are re-computed by CLASS.
  • log10 α, log10 V0, N*
    Derived parameters whose posteriors are the main scientific output; α is free only in the second analysis.
  • ω_b, ω_cdm, τ_reio, 100 θ_s
    Standard cosmological parameters with broad flat priors, jointly sampled.
axioms (4)
  • domain assumption First-order slow-roll consistency relations (Eqs. 2.15–2.20) are accurate enough to map priors even though final spectra are exact.
    Invoked in §2.2 and §3; validated a posteriori in Appendix A but still used as the sampling engine.
  • domain assumption Single-field canonical inflation with the α-Starobinsky potential (Eq. 2.4) and no additional degrees of freedom during inflation.
    Core model assumption throughout §§2–4.
  • ad hoc to paper The theoretically preferred window 50 < N* < 60 remains a meaningful consistency test when reheating is left free.
    Used to interpret the α=1 posterior as ‘breaking down’ (abstract, §4.1); reheating is deferred to future work.
  • domain assumption Standard flat ΛCDM late-time cosmology and public Planck/ACT/DESI likelihoods are adequate.
    Assumed in the Cobaya pipeline (§3).

pith-pipeline@v1.1.0-grok45 · 21889 in / 2722 out tokens · 37025 ms · 2026-07-13T18:02:35.176967+00:00 · methodology

0 comments
read the original abstract

We present a joint Bayesian analysis to impose constraints on the generalized $\alpha$-Starobinsky inflationary model using the high-precision cosmological datasets: Planck, CMB lensing from ACT DR6, and Baryon Acoustic Oscillations (BAO) from DESI DR2. For the parameter inference, we introduce an alternative sampling approach. Rather than imposing priors on the cosmological parameters of the inflationary potential $(V_0, \, \alpha, \, N_*)$, we place priors directly on the primordial physical observables $(A_s,\, n_s,\, r)$ through analytical slow-roll consistency relations. Our pipeline internally maps these sampled observables to the corresponding $\alpha$-Starobinsky parameters. These values are then passed to a modified version of $\tt{CLASS}$, which solves the exact inflationary dynamics numerically. This pipeline ensures that the final reported posteriors for the observables are computed exactly, completely free from the slow-roll approximation. Applying this methodology, we explore the viability of the $\alpha$-Starobinsky model. We show that, when the full combined dataset is considered, the pure Starobinsky model (i.e., the canonical limit $\alpha = 1$) shows signs of breaking down, since it requires a large number of $e$-folds of inflation after horizon crossing ($N_* > 60$) due to the shift in the scalar spectral index, $n_s$. In contrast, allowing the deformation parameter $\alpha$ as a free parameter yields a clear $1\sigma$ preference for $\log_{10} \alpha > 0$, present across all datasets. Notably, we also show that the addition of ACT DR6 lensing data introduces no significant impact on these primordial constraints, confirming that our robust posteriors are primarily driven by Planck and DESI measurements.

discussion (0)

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Reference graph

Works this paper leans on

51 extracted references · 42 linked inside Pith

  1. [1]

    Linde,REVIEW ARTICLE: The inflationary Universe,Reports on Progress in Physics 47(1984) 925

    A.D. Linde,REVIEW ARTICLE: The inflationary Universe,Reports on Progress in Physics 47(1984) 925

    1984

  2. [2]

    Lyth and A.A

    D.H.D.H. Lyth and A.A. Riotto,Particle physics models of inflation and the cosmological density perturbation,Phys. Rept.314(1999) 1 [hep-ph/9807278]

    Pith/arXiv arXiv 1999

  3. [3]

    Baumann,TASI Lectures on Inflation,arXiv e-prints(2009) arXiv:0907.5424 [0907.5424]

    D. Baumann,TASI Lectures on Inflation,arXiv e-prints(2009) arXiv:0907.5424 [0907.5424]

    Pith/arXiv arXiv 2009

  4. [4]

    Martin, C

    J. Martin, C. Ringeval and V. Vennin,Encyclopaedia Inflationaris,arXiv e-prints(2013) arXiv:1303.3787 [1303.3787]

    Pith/arXiv arXiv 2013

  5. [5]

    Brandenberger,Initial conditions for inflation — A short review,International Journal of Modern Physics D26(2017) 1740002 [1601.01918]

    R. Brandenberger,Initial conditions for inflation — A short review,International Journal of Modern Physics D26(2017) 1740002 [1601.01918]

    Pith/arXiv arXiv 2017

  6. [6]

    Achúcarro, M

    A. Achúcarro, M. Biagetti, M. Braglia, G. Cabass, R. Caldwell, E. Castorina et al.,Inflation: Theory and Observations,arXiv e-prints(2022) arXiv:2203.08128 [2203.08128]

    Pith/arXiv arXiv 2022

  7. [7]

    Kallosh and A

    R. Kallosh and A. Linde,On the present status of inflationary cosmology,General Relativity and Gravitation57(2025) 135 [2505.13646]

    arXiv 2025

  8. [8]

    Bennett, D

    C.L. Bennett, D. Larson, J.L. Weiland, N. Jarosik, G. Hinshaw, N. Odegard et al.,Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results,APJs 208(2013) 20 [1212.5225]

    Pith/arXiv arXiv 2013

  9. [9]

    Aghanim, Y

    Planck Collaboration, N. Aghanim, Y. Akrami, F. Arroja, M. Ashdown, J. Aumont et al., Planck 2018 results. I. Overview and the cosmological legacy of Planck,AAP641(2020) A1 [1807.06205]

    Pith/arXiv arXiv 2018

  10. [10]

    Coulton, M.S

    W. Coulton, M.S. Madhavacheril, A.J. Duivenvoorden, J.C. Hill, I. Abril-Cabezas, P.A.R. Ade et al.,Atacama Cosmology Telescope: High-resolution component-separated maps across one third of the sky,PRD109(2024) 063530 [2307.01258]

    Pith/arXiv arXiv 2024

  11. [11]

    Balkenhol, D

    L. Balkenhol, D. Dutcher, A. Spurio Mancini, A. Doussot, K. Benabed, S. Galli et al., Measurement of the CMB temperature power spectrum and constraints on cosmology from the SPT-3G 2018 TT, TE, and EE dataset,PRD108(2023) 023510 [2212.05642]

    Pith/arXiv arXiv 2018

  12. [12]

    Aghanim, Y

    Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi et al., Planck 2018 results. VI. Cosmological parameters,AAP641(2020) A6 [1807.06209]

    Pith/arXiv arXiv 2018

  13. [13]

    Akrami, F

    Planck Collaboration, Y. Akrami, F. Arroja, M. Ashdown, J. Aumont, C. Baccigalupi et al., Planck 2018 results. X. Constraints on inflation,AAP641(2020) A10 [1807.06211]

    Pith/arXiv arXiv 2018

  14. [14]

    Martin, C

    J. Martin, C. Ringeval and V. Vennin,Encyclopædia Inflationaris: Opiparous Edition,Physics of the Dark Universe46(2024) 101653

    2024

  15. [15]

    Starobinsky,A new type of isotropic cosmological models without singularity,Physics Letters B91(1980) 99

    A.A. Starobinsky,A new type of isotropic cosmological models without singularity,Physics Letters B91(1980) 99

    1980

  16. [16]

    Kallosh and A

    R. Kallosh and A. Linde,Universality class in conformal inflation,JCAP2013(2013) 002 [1306.5220]

    Pith/arXiv arXiv 2013

  17. [17]

    Ferrara, R

    S. Ferrara, R. Kallosh, A. Linde and M. Porrati,Minimal supergravity models of inflation,PRD 88(2013) 085038 [1307.7696]

    Pith/arXiv arXiv 2013

  18. [18]

    Ellis, D.V

    J. Ellis, D.V. Nanopoulos and K.A. Olive,Starobinsky-like inflationary models as avatars of no-scale supergravity,JCAP2013(2013) 009 [1307.3537]

    Pith/arXiv arXiv 2013

  19. [19]

    Kallosh, A

    R. Kallosh, A. Linde and D. Roest,Superconformal inflationaryα-attractors,Journal of High Energy Physics2013(2013) 198 [1311.0472]

    Pith/arXiv arXiv 2013

  20. [20]

    Ellis, D.V

    J. Ellis, D.V. Nanopoulos, K.A. Olive and S. Verner,Unified no-scale attractors,JCAP2019 (2019) 040 [1906.10176]. – 20 –

    Pith/arXiv arXiv 2019

  21. [21]

    Ballardini,Chasing cosmic inflation: constraints for inflationary models and reheating insights,JCAP2025(2025) 116 [2408.03321]

    M. Ballardini,Chasing cosmic inflation: constraints for inflationary models and reheating insights,JCAP2025(2025) 116 [2408.03321]

    Pith/arXiv arXiv 2025

  22. [22]

    Kallosh, L

    R. Kallosh, L. Kofman, A. Linde and A. Van Proeyen,Superconformal symmetry, supergravity and cosmology,Classical and Quantum Gravity17(2000) 4269 [hep-th/0006179]

    Pith/arXiv arXiv 2000

  23. [23]

    Madhavacheril, F.J

    M.S. Madhavacheril, F.J. Qu, B.D. Sherwin, N. MacCrann, Y. Li, I. Abril-Cabezas et al.,The Atacama Cosmology Telescope: DR6 Gravitational Lensing Map and Cosmological Parameters, APJ962(2024) 113 [2304.05203]

    Pith/arXiv arXiv 2024

  24. [24]

    F.J. Qu, B.D. Sherwin, M.S. Madhavacheril, D. Han, K.T. Crowley, I. Abril-Cabezas et al., The Atacama Cosmology Telescope: A Measurement of the DR6 CMB Lensing Power Spectrum and Its Implications for Structure Growth,APJ962(2024) 112 [2304.05202]

    Pith/arXiv arXiv 2024

  25. [25]

    Abdul Karim, J

    M. Abdul Karim, J. Aguilar, S. Ahlen, S. Alam, L. Allen, C.A. Prieto et al.,DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraints,PRD112(2025) 083515 [2503.14738]

    Pith/arXiv arXiv 2025

  26. [26]

    Calabrese, J.C

    E. Calabrese, J.C. Hill, H.T. Jense, A. La Posta, I. Abril-Cabezas, G.E. Addison et al.,The Atacama Cosmology Telescope: DR6 constraints on extended cosmological models,JCAP2025 (2025) 063 [2503.14454]

    Pith/arXiv arXiv 2025

  27. [27]

    Louis, A

    T. Louis, A. La Posta, Z. Atkins, H.T. Jense, I. Abril-Cabezas, G.E. Addison et al.,The Atacama Cosmology Telescope: DR6 power spectra, likelihoods andΛCDM parameters,JCAP 2025(2025) 062 [2503.14452]

    Pith/arXiv arXiv 2025

  28. [28]

    Motohashi,Consistency relation for Rp inflation,PRD91(2015) 064016 [1411.2972]

    H. Motohashi,Consistency relation for Rp inflation,PRD91(2015) 064016 [1411.2972]

    Pith/arXiv arXiv 2015

  29. [29]

    Garcia, G

    M.A.G. Garcia, G. Germán, R. Gonzalez Quaglia and A.M. Moran Colorado,Reheating constraints and consistency relations of the Starobinsky model and some of its generalizations, JCAP2023(2023) 015 [2306.15831]

    Pith/arXiv arXiv 2023

  30. [30]

    Lesgourgues,The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview,arXiv e-prints(2011) arXiv:1104.2932 [1104.2932]

    J. Lesgourgues,The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview,arXiv e-prints(2011) arXiv:1104.2932 [1104.2932]

    Pith/arXiv arXiv 2011

  31. [31]

    D. Blas, J. Lesgourgues and T. Tram,The Cosmic Linear Anisotropy Solving System (CLASS). Part II: Approximation schemes,JCAP2011(2011) 034 [1104.2933]

    Pith/arXiv arXiv 2011

  32. [32]

    Cremmer, S

    E. Cremmer, S. Ferrara, C. Kounnas and D.V. Nanopoulos,Naturally vanishing cosmological constant in N=1 supergravity,Physics Letters B133(1983) 61

    1983

  33. [33]

    Lahanas and D.V

    A.B. Lahanas and D.V. Nanopoulos,The road to no-scale supergravity,Phys. Rept.145(1987) 1

    1987

  34. [34]

    Ellis, D.V

    J. Ellis, D.V. Nanopoulos and K.A. Olive,No-scale Supergravity Realization of the Starobinsky Model of Inflation,PRL111(2013) 111301 [1305.1247]

    Pith/arXiv arXiv 2013

  35. [35]

    Liddle, P

    A.R. Liddle, P. Parsons and J.D. Barrow,Formalizing the slow-roll approximation in inflation, PRD50(1994) 7222 [astro-ph/9408015]

    Pith/arXiv arXiv 1994

  36. [36]

    Torrado and A

    J. Torrado and A. Lewis,Cobaya: code for Bayesian analysis of hierarchical physical models, JCAP2021(2021) 057 [2005.05290]

    Pith/arXiv arXiv 2021

  37. [37]

    Aghanim, Y

    Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi et al., Planck 2018 results. V. CMB power spectra and likelihoods,AAP641(2020) A5 [1907.12875]

    Pith/arXiv arXiv 2018

  38. [38]

    Lewis and S

    A. Lewis and S. Bridle,Cosmological parameters from CMB and other data: A Monte Carlo approach,PRD66(2002) 103511 [astro-ph/0205436]

    Pith/arXiv arXiv 2002

  39. [39]

    Gelman and D.B

    A. Gelman and D.B. Rubin,Inference from Iterative Simulation Using Multiple Sequences, Statistical Science7(1992) 457

    1992

  40. [40]

    Bezerra-Sobrinho and L.G

    J. Bezerra-Sobrinho and L.G. Medeiros,Starobinsky Inflation and the Latest CMB Data: A Subtle Tension?,arXiv e-prints(2025) arXiv:2511.06640 [2511.06640]. – 21 –

    Pith/arXiv arXiv 2025

  41. [41]

    Abazajian, G

    K. Abazajian, G. Addison, P. Adshead, Z. Ahmed, S.W. Allen, D. Alonso et al.,CMB-S4 Science Case, Reference Design, and Project Plan,arXiv e-prints(2019) arXiv:1907.04473 [1907.04473]

    Pith/arXiv arXiv 2019

  42. [42]

    Abazajian, G.E

    K. Abazajian, G.E. Addison, P. Adshead, Z. Ahmed, D. Akerib, A. Ali et al.,CMB-S4: Forecasting Constraints on Primordial Gravitational Waves,APJ926(2022) 54 [2008.12619]

    Pith/arXiv arXiv 2022

  43. [43]

    L. Dai, M. Kamionkowski and J. Wang,Reheating Constraints to Inflationary Models,PRL 113(2014) 041302 [1404.6704]

    Pith/arXiv arXiv 2014

  44. [44]

    Muñoz and M

    J.B. Muñoz and M. Kamionkowski,Equation-of-state parameter for reheating,PRD91(2015) 043521 [1412.0656]

    Pith/arXiv arXiv 2015

  45. [45]

    Germán, J.C

    G. Germán, J.C. Hidalgo and L.E. Padilla,Inflationary models constrained by reheating, European Physical Journal Plus139(2024) 302 [2310.05221]

    Pith/arXiv arXiv 2024

  46. [46]

    Spurio Mancini, D

    A. Spurio Mancini, D. Piras, J. Alsing, B. Joachimi and M.P. Hobson,COSMOPOWER: emulating cosmological power spectra for accelerated Bayesian inference from next-generation surveys,MNRAS511(2022) 1771 [2106.03846]

    Pith/arXiv arXiv 2022

  47. [47]

    Sørensen, S

    C.T.G. Sørensen, S. Hannestad, A. Nygaard and T. Tram,Calculating Bayesian evidence for inflationary models using CONNECT,JCAP2025(2025) 043 [2406.03968]

    Pith/arXiv arXiv 2025

  48. [48]

    Balkenhol, C

    L. Balkenhol, C. Trendafilova, K. Benabed and S. Galli,candl: cosmic microwave background analysis with a differentiable likelihood,AAP686(2024) A10 [2401.13433]

    Pith/arXiv arXiv 2024

  49. [49]

    Stewart and D.H

    E.D. Stewart and D.H. Lyth,A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation,Physics Letters B302(1993) 171 [gr-qc/9302019]

    Pith/arXiv arXiv 1993

  50. [50]

    Mukhanov, H.A

    V.F. Mukhanov, H.A. Feldman and R.H. Brandenberger,Theory of cosmological perturbations, Phys. Rept.215(1992) 203

    1992

  51. [51]

    Lyth and A.R

    D.H. Lyth and A.R. Liddle,The primordial density perturbation: Cosmology, inflation and the origin of structure, Cambridge university press (2009). – 22 –

    2009