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The optical depth $\tau$ is the least well determined parameter in the standard model of cosmology, and one whose precise value is important for both understanding reionization and for inferring fundamental physics from cosmological…

Cosmology and Nongalactic Astrophysics · Physics 2022-10-05 Noah Sailer , Shi-Fan Chen , Martin White

We study the possibility of measuring the optical depth at reionization, $\tau$, without relying on large-scale Cosmic Microwave Background (CMB) polarization. Our analysis is driven by the need to obtain competitive measurements that can…

Cosmology and Nongalactic Astrophysics · Physics 2024-05-15 William Giarè , Eleonora Di Valentino , Alessandro Melchiorri

Recently, it was pointed out that invoking a large value of the CMB optical depth, $\tau_{\rm CMB} = 0.09$, could help resolve tensions between DESI DR2 BAO data and the CMB. This is larger than the value of $\tau_{\rm CMB} = 0.058$…

Cosmology and Nongalactic Astrophysics · Physics 2025-05-23 Christopher Cain , Alexander Van Engelen , Kevin S. Croker , Darby Kramer , Anson D'Aloisio , Garett Lopez

Recent studies report a mild discrepancy between baryon acoustic oscillation (BAO) and cosmic microwave background (CMB) measurements within the $\Lambda$CDM framework. This discrepancy could be explained if the optical depth $\tau$…

Cosmology and Nongalactic Astrophysics · Physics 2026-01-15 Yuta Kageura , Masami Ouchi , Fumihiro Naokawa , Hiroya Umeda , Akinori Matsumoto , Yuichi Harikane , Minami Nakane , Tran Thi Thai

We present the first constraints on the electron optical depth to reionization, $\tau_{\mathrm{e}}$, from the Lyman-$\alpha$ forest alone for physically motivated reionization models that match the reionization's end-point, $z_{\rm{end}}$,…

Cosmology and Nongalactic Astrophysics · Physics 2025-10-02 Olga Garcia-Gallego , Vid Iršič , Martin G. Haehnelt , James S. Bolton

Amongst standard model parameters that are constrained by cosmic microwave background (CMB) observations, the optical depth $\tau$ stands out as a nuisance parameter. While $\tau$ provides some crude limits on reionization, it also degrades…

Cosmology and Nongalactic Astrophysics · Physics 2016-02-23 Adrian Liu , Jonathan R. Pritchard , Rupert Allison , Aaron R. Parsons , Uroš Seljak , Blake D. Sherwin

We examine the constraints on the epoch of reionization (redshift z_r) set by recent WMAP-3 observations of tau_e = 0.09 +/- 0.03, the electron-scattering optical depth of the cosmic microwave background (CMB), combined with models of…

Astrophysics · Physics 2007-05-23 Michael Shull , Aparna Venkatesan

The reionization optical depth $\tau_{\rm reio}$ has interesting connections to existing cosmological anomalies. As first studied in the context of the Hubble tension in our previous paper, a larger $\tau_{\rm reio}$, which could be…

Cosmology and Nongalactic Astrophysics · Physics 2025-09-12 Itamar J. Allali , Lingfeng Li , Praniti Singh , JiJi Fan

Based on the work by Mitra, Choudhury & Ferrara (2010), we obtain model-independent constraints on reionization from cosmic microwave background (CMB) and QSO absorption line data by decomposing the function N_{ion}(z) (the number of…

Cosmology and Nongalactic Astrophysics · Physics 2015-05-28 Sourav Mitra , T. Roy Choudhury , Andrea Ferrara

The standard cosmological model, with its six independent parameters, successfully describes our observable Universe. One of these parameters, the optical depth to reionization $\tau_\mathrm{reio}$, represents the scatterings that Cosmic…

Cosmology and Nongalactic Astrophysics · Physics 2024-08-06 Paulo Montero-Camacho , Yin Li , Miles Cranmer

Neutral hydrogen around high-z QSO and an optical depth tau ~ 0.17 can be reconciled if reionization is more complex than a single transition at z ~ 6-8. Tracing its details could shed a new light on the first sources of radiation. Here we…

In light of the recent inference of a high optical depth to Thomson scattering, tau, from the WMAP data we investigate the effects of extended periods of partial ionization and ask if the value of tau inferred by assuming a single sharp…

Astrophysics · Physics 2009-06-15 Gilbert Holder , Zoltan Haiman , Manoj Kaplinghat , Lloyd Knox

The optical depth to reionization, $\tau$, is the least constrained parameter of the cosmological $\Lambda$CDM model. To date, its most precise value is inferred from large-scale polarized CMB power spectra from the ${\it Planck}$…

Cosmology and Nongalactic Astrophysics · Physics 2024-07-10 Kevin Wolz , Nicoletta Krachmalnicoff , Luca Pagano

We introduce a new statistical technique for extracting the inhomogeneous reionization signal from future high-sensitivity measurements of the cosmic microwave background temperature and polarization fields. If reionization is…

Astrophysics · Physics 2009-02-10 Cora Dvorkin , Kendrick M. Smith

Cosmic Reionization imprints its signature on the temperature and polarization anisotropies of the cosmic microwave background (CMB). Advances in CMB telescopes have already placed a significant constraint on the history of reionization. As…

Cosmology and Nongalactic Astrophysics · Physics 2022-05-18 Hina Sakamoto , Kyungjin Ahn , Kiyotomo Ichiki , Hyunjin Moon , Kenji Hasegawa

We examine the constraints on high-redshift star formation, ultraviolet and X-ray pre-ionization, and the epoch of reionization at redshift z_r, inferred from the recent WMAP-5 measurement, tau_e = 0.084 +/- 0.016, of the electron…

Astrophysics · Physics 2009-11-13 J. Michael Shull , Aparna Venkatesan

We study the constraints on reionization from five years of WMAP data, parametrizing the evolution of the average fraction of ionized hydrogen with principal components that provide a complete basis for describing the effects of…

Astrophysics · Physics 2009-11-13 Michael J. Mortonson , Wayne Hu

Patchy reionization leaves a number of imprints on the small-scale cosmic microwave background (CMB) temperature fluctuations, the largest of which is the kinematic Sunyaev-Zel'dovich (kSZ), the Doppler shift of CMB photons scattering off…

Cosmology and Nongalactic Astrophysics · Physics 2018-12-26 Simone Ferraro , Kendrick M. Smith

We assess the uncertainty with which a balloon-borne experiment, nominally called Tau Surveyor ($\tau S$), can measure the optical depth to reionization $\sigma(\tau)$ with given realistic constraints of instrument noise and foreground…

Cosmology and Nongalactic Astrophysics · Physics 2022-11-23 Josquin Errard , Mathieu Remazeilles , Jonathan Aumont , Jacques Delabrouille , Daniel Green , Shaul Hanany , Brandon S. Hensley , Alan Kogut

We study constraints on allowed reionization histories by comparing predictions of a physical semi-numerical model with secondary temperature and polarization anisotropies of the cosmic microwave background (CMB). Our model has four free…

Cosmology and Nongalactic Astrophysics · Physics 2020-12-02 Tirthankar Roy Choudhury , Suvodip Mukherjee , Sourabh Paul
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