{"work":{"id":"183507cb-a874-4670-8d30-a28bb2db86a3","openalex_id":null,"doi":null,"arxiv_id":"1303.5082","raw_key":null,"title":"Planck 2013 results. XXII. Constraints on inflation","authors":null,"authors_text":"Planck Collaboration 2014V Planck Collaboration XXII , Planck","year":2013,"venue":"astro-ph.CO","abstract":"We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to $n_s = 0.9603 \\pm 0.0073$, ruling out exact scale invariance at over 5 $\\sigma$. Planck establishes an upper bound on the tensor-to-scalar ratio of r < 0.11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V\" < 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n > 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining $d n_s/d ln k = -0.0134 \\pm 0.0090$. Several analyses dropping the slow-roll approximation are carried out, including detailed model comparison and inflationary potential reconstruction. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit $\\chi^2$ by ~ 10; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with bounds on $f_\\mathrm{NL}$ measured by Planck. The fractional primordial contribution of CDM isocurvature modes in the curvaton and axion scenarios has upper bounds of 0.25% or 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelation can improve $\\chi^2$ by approximatively 4 as a result of slightly lowering the theoretical prediction for the $\\ell<40$ multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions.","external_url":"https://arxiv.org/abs/1303.5082","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-07-03T03:07:34.683627+00:00","pith_arxiv_id":"1303.5082","created_at":"2026-05-10T14:45:43.836265+00:00","updated_at":"2026-07-03T03:07:34.683627+00:00","title_quality_ok":true,"display_title":"Planck 2013 results. XXII. Constraints on inflation","render_title":"Planck 2013 results. XXII. Constraints on inflation"},"hub":{"state":{"work_id":"183507cb-a874-4670-8d30-a28bb2db86a3","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":13,"external_cited_by_count":null,"distinct_field_count":4,"first_pith_cited_at":"2018-07-17T04:05:07+00:00","last_pith_cited_at":"2026-06-26T15:04:26+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-07-04T06:16:40.990029+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":3}],"polarity_counts":[{"context_polarity":"background","n":3}],"runs":{},"summary":{},"graph":{},"authors":[]}}