{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/towards-a-measurement-of-the-spectral","title":"Towards a measurement of the spectral runnings","arxiv_id":"1611.05883","date":"2016-11-17","proceeding":null,"authors":["Julian B. Muñoz","Ely D. Kovetz","Alvise Raccanelli","Marc Kamionkowski","Joseph Silk"],"abstract":"Single-field slow-roll inflation predicts a nearly scale-free power spectrum of perturbations, as observed at the scales accessible to current cosmological experiments. This spectrum is slightly red, showing a tilt $(1-n_s)\\sim 0.04$. A direct consequence of this tilt are nonvanishing runnings $\\alpha_s=\\mathrm d n_s/\\mathrm d\\log k$, and $\\beta_s=\\mathrm d\\alpha_s/\\mathrm d\\log k$, which in the minimal inflationary scenario should reach absolute values of $10^{-3}$ and $10^{-5}$, respectively. In this work we calculate how well future surveys can measure these two runnings. We consider a Stage-4 (S4) CMB experiment and show that it will be able to detect significant deviations from the inflationary prediction for $\\alpha_s$, although not for $\\beta_s$. Adding to the S4 CMB experiment the information from a WFIRST-like or a DESI-like survey improves the sensitivity to the runnings by $\\sim$ 20\\%, and 30\\%, respectively. A spectroscopic survey with a billion objects, such as the SKA, will add enough information to the S4 measurements to allow a detection of $\\alpha_s=10^{-3}$, required to probe the single-field slow-roll inflationary paradigm. We show that only a very-futuristic interferometer targeting the dark ages will be capable of measuring the minimal inflationary prediction for $\\beta_s$. The results of other probes, such as a stochastic background of gravitational waves observable by LIGO, the Ly-$\\alpha$ forest, and spectral distortions, are shown for comparison. Finally, we study the claims that large values of $\\beta_s$, if extrapolated to the smallest scales, can produce primordial black holes of tens of solar masses, which we show to be easily testable by the S4 CMB experiment.","url_abs":"https://arxiv.org/abs/1611.05883v2","url_pdf":"https://arxiv.org/pdf/1611.05883v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"towards-a-measurement-of-the-spectral","repo_url":"https://github.com/misharash/cobaya_mock_cmb","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}