{"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/h-0-tension-phantom-dark-energy-and","title":"$H_0$ Tension, Phantom Dark Energy and Cosmological Parameter Degeneracies","arxiv_id":"2004.08363","date":"2020-04-17","proceeding":null,"authors":["G. Alestas","L. Kazantzidis","L. Perivolaropoulos"],"abstract":"Phantom dark energy can produce amplified cosmic acceleration at late times, thus increasing the value of $H_0$ favored by CMB data and releasing the tension with local measurements of $H_0$. We show that the best fit value of $H_0$ in the context of the CMB power spectrum is degenerate with a constant equation of state parameter $w$, in accordance with the approximate effective linear equation $H_0 + 30.93\\; w - 36.47 = 0$ ($H_0$ in $km \\; sec^{-1} \\; Mpc^{-1}$). This equation is derived by assuming that both $\\Omega_{0 \\rm m}h^2$ and $d_A=\\int_0^{z_{rec}}\\frac{dz}{H(z)}$ remain constant (for invariant CMB spectrum) and equal to their best fit Planck/$\\Lambda$CDM values as $H_0$, $\\Omega_{0 \\rm m}$ and $w$ vary. For $w=-1$, this linear degeneracy equation leads to the best fit $H_0=67.4 \\; km \\; sec^{-1} \\; Mpc^{-1}$ as expected. For $w=-1.22$ the corresponding predicted CMB best fit Hubble constant is $H_0=74 \\; km \\; sec^{-1} \\; Mpc^{-1}$ which is identical with the value obtained by local distance ladder measurements while the best fit matter density parameter is predicted to decrease since $\\Omega_{0 \\rm m}h^2$ is fixed. We verify the above $H_0-w$ degeneracy equation by fitting a $w$CDM model with fixed values of $w$ to the Planck TT spectrum showing also that the quality of fit ($\\chi^2$) is similar to that of $\\Lambda$CDM. However, when including SnIa, BAO or growth data the quality of fit becomes worse than $\\Lambda$CDM when $w< -1$. Finally, we generalize the $H_0-w(z)$ degeneracy equation for $w(z)=w_0+w_1\\; z/(1+z)$ and identify analytically the full $w_0-w_1$ parameter region that leads to a best fit $H_0=74\\; km \\; sec^{-1} \\; Mpc^{-1}$ in the context of the Planck CMB spectrum. This exploitation of $H_0-w(z)$ degeneracy can lead to immediate identification of all parameter values of a given $w(z)$ parametrization that can potentially resolve the $H_0$ tension.","url_abs":"https://arxiv.org/abs/2004.08363v3","url_pdf":"https://arxiv.org/pdf/2004.08363v3.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":"h-0-tension-phantom-dark-energy-and","repo_url":"https://github.com/GeorgeAlestas/H0_Tension_Data","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}