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The Planck 95% CL upper limit on the tensor-to-scalar ratio, $r_{0.002}<0.10$, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain $r_{0.002}<0.056$. In the framework of single-field inflationary models with Einstein gravity, these results imply that: (a) slow-roll models with a concave potential, $V\" (\\phi) < 0,$ are increasingly favoured by the data; and (b) two different methods for reconstructing the inflaton potential find no evidence for dynamics beyond slow roll. Non-parametric reconstructions of the primordial power spectrum consistently confirm a pure power law. A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectrum, a result further strengthened for certain oscillatory models by a new combined analysis that includes Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadrupolar modulation of the primordial fluctuations. However, the polarization data do not confirm physical models for a scale-dependent dipolar modulation.","external_url":"https://arxiv.org/abs/1807.06211","cited_by_count":2186,"metadata_source":"pith","metadata_fetched_at":"2026-07-04T08:39:41.649110+00:00","pith_arxiv_id":"1807.06211","created_at":"2026-05-08T18:39:00.218059+00:00","updated_at":"2026-07-04T08:39:41.649110+00:00","title_quality_ok":true,"display_title":"Planck 2018 results. X. Constraints on inflation","render_title":"Planck 2018 results. X. Constraints on inflation"},"hub":{"state":{"work_id":"ac5d2133-b998-4b22-878d-b78fb5623e08","tier":"super_hub","tier_reason":"100+ Pith inbound or 10,000+ external citations","pith_inbound_count":150,"external_cited_by_count":2186,"distinct_field_count":8,"first_pith_cited_at":"2018-07-17T04:05:07+00:00","last_pith_cited_at":"2026-07-01T17:08:22+00:00","author_build_status":"needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-07-04T14:56:47.168130+00:00","tier_text":"super_hub"},"tier":"super_hub","role_counts":[{"context_role":"background","n":46},{"context_role":"dataset","n":10},{"context_role":"baseline","n":2}],"polarity_counts":[{"context_polarity":"background","n":42},{"context_polarity":"use_dataset","n":10},{"context_polarity":"unclear","n":4},{"context_polarity":"baseline","n":2}],"runs":{"ask_index":{"job_type":"ask_index","status":"succeeded","result":{"title":"Planck 2018 results. 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Also displayed are the monochromatic evaporation [16-23, 25-29] and microlensing [30-38] constraints, compiled using the repository [114]. 103 104 105 106 107 mb [GeV] 103 104 105 106 107 mf [GeV] ns = 0.99 fPBH ≃ 1 5 10 15 20 25 Rmax FIG. 3. Maximum enhancement of the PBH mass f","claim_type":"dataset","confidence":0.95,"evidence_strength":"citation_context"},{"claim_text":"added up to the already known tensions of the Λ-Cold-Dark-Matter model [26-31]. But ACT offered another perspective that is in tension with the Planck data [32], and specifically the spectral index was found to be, nS = 0.9743±0.0034,(1.1) which is in 2σtension with the Planck data. The tensor-to-scalar ratio is constrained by the Planck and BICEP experiments to be [33], r <0.036 (1.2) at 95% confidence. Although the 2σis not a statistically confident result, it is statistically non-ignorable. T","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"- 14 - where an average over the radial oscillations is understood, and we will define ε, mS in the following. During inflation the field value S of the radial mode can be far larger than its minimum today of vσ. If the effective mass of S given by mS(S) ≃ p 3λσS (3.21) is below the approximately constant Hubble rate during inflation HI < 6 × 1013 GeV [148], then diffusion due to stochastic quantum fluctuations can push the field value to [149] Si ≃ \u0012 1 8π2 \u0013 1 4 HI λ 1 4 σ , (3.22) and due to i","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"2 E QUATION -OF-STATE PARAMETERS . . . . . . . . . . . . . . . . . . . . . . . . . 22 A.3 N UMBER OF E -F OLDINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1 I NTRODUCTION The Data Release 6 (DR6) from the Atacama Cosmology Telescope (ACT) [1, 2] favors a slightly higher scalar spectral index, ns, than the one indicated from the Planck data [3] prompting renewed interest in inflationary models that can accommodate such a s hift [4-58] - for a review see Ref. [59]. Indeed, the","claim_type":"dataset","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"matter era as independent of the specific microphysics of the inflationary sector, provided the correct initial perturbation spectrum is generated. This standard assumption of the vanishing inflaton relies on a specific, often implicit, premise: that the inflaton remains heavy or decouples completely from the thermal bath after reheating ends. In the simplest chaotic inflation model [16], such as the one governed by a quadratic po- tentialV(ϕ) = 1 2 m2 ϕϕ2, the inflaton massm ϕ is a constant fun","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"be hidden around and within experimental search in present and future particle colliders, while there are strong theoretical reasons that it should be part of the underlying fundamental theory of gravity , such as string theory , and may play important an role at higher energy scales and particularly in cosmology [1, 2]. In this context, the Starobinsky model of inflation [3], which is very attractive because of its simplicity and very good description of the observational data [4, 5, 6], is kno","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"}],"why_cited":"Pith tracks Planck 2018 results. X. Constraints on inflation because it crossed a citation-hub threshold. 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Also displayed are the monochromatic evaporation [16-23, 25-29] and microlensing [30-38] constraints, compiled using the repository [114]. 103 104 105 106 107 mb [GeV] 103 104 105 106 107 mf [GeV] ns = 0.99 fPBH ≃ 1 5 10 15 20 25 Rmax FIG. 3. Maximum enhancement of the PBH mass f","claim_type":"dataset","confidence":0.95,"evidence_strength":"citation_context"},{"claim_text":"added up to the already known tensions of the Λ-Cold-Dark-Matter model [26-31]. But ACT offered another perspective that is in tension with the Planck data [32], and specifically the spectral index was found to be, nS = 0.9743±0.0034,(1.1) which is in 2σtension with the Planck data. The tensor-to-scalar ratio is constrained by the Planck and BICEP experiments to be [33], r <0.036 (1.2) at 95% confidence. Although the 2σis not a statistically confident result, it is statistically non-ignorable. T","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"- 14 - where an average over the radial oscillations is understood, and we will define ε, mS in the following. During inflation the field value S of the radial mode can be far larger than its minimum today of vσ. If the effective mass of S given by mS(S) ≃ p 3λσS (3.21) is below the approximately constant Hubble rate during inflation HI < 6 × 1013 GeV [148], then diffusion due to stochastic quantum fluctuations can push the field value to [149] Si ≃ \u0012 1 8π2 \u0013 1 4 HI λ 1 4 σ , (3.22) and due to i","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"2 E QUATION -OF-STATE PARAMETERS . . . . . . . . . . . . . . . . . . . . . . . . . 22 A.3 N UMBER OF E -F OLDINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1 I NTRODUCTION The Data Release 6 (DR6) from the Atacama Cosmology Telescope (ACT) [1, 2] favors a slightly higher scalar spectral index, ns, than the one indicated from the Planck data [3] prompting renewed interest in inflationary models that can accommodate such a s hift [4-58] - for a review see Ref. [59]. Indeed, the","claim_type":"dataset","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"matter era as independent of the specific microphysics of the inflationary sector, provided the correct initial perturbation spectrum is generated. This standard assumption of the vanishing inflaton relies on a specific, often implicit, premise: that the inflaton remains heavy or decouples completely from the thermal bath after reheating ends. In the simplest chaotic inflation model [16], such as the one governed by a quadratic po- tentialV(ϕ) = 1 2 m2 ϕϕ2, the inflaton massm ϕ is a constant fun","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"be hidden around and within experimental search in present and future particle colliders, while there are strong theoretical reasons that it should be part of the underlying fundamental theory of gravity , such as string theory , and may play important an role at higher energy scales and particularly in cosmology [1, 2]. In this context, the Starobinsky model of inflation [3], which is very attractive because of its simplicity and very good description of the observational data [4, 5, 6], is kno","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"}],"why_cited":"Pith tracks Planck 2018 results. X. Constraints on inflation because it crossed a citation-hub threshold. 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