Cosmic neutrino background detection in large-neutrino-mass cosmologies

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Cosmic neutrino background detection in large-neutrino-mass cosmologies

James Alvey, Miguel Escudero, Nashwan Sabti, and Thomas Schwetz

Phys. Rev. D 105, 063501 – Published 1 March 2022

Abstract

The cosmic neutrino background (CNB) is a definite prediction of the standard cosmological model and its direct discovery would represent a milestone in cosmology and neutrino physics. In this work, we consider the capture of relic neutrinos on a tritium target as a possible way to detect the CNB, as aimed for by the PTOLEMY project. Crucial parameters for this measurement are the absolute neutrino mass $m_{ν}$ and the local neutrino number density $n_{ν}^{loc}$ . Within the $Λ CDM$ model, cosmology provides a stringent upper limit on the sum of neutrino masses of $\sum m_{ν} < 0.12 eV$ , with further improvements expected soon from galaxy surveys by DESI and EUCLID. This makes the prospects for a CNB detection and a neutrino mass measurement in the laboratory very difficult. In this context, we consider a set of nonstandard cosmological models that allow for large neutrino masses ( $m_{ν} \sim 1 eV$ ), potentially in reach of the KATRIN neutrino mass experiment or upcoming neutrinoless double-beta decay searches. We show that the CNB detection prospects could be much higher in some of these models compared to those in $Λ CDM$ , and discuss the potential for such a detection to discriminate between cosmological scenarios. Moreover, we provide a simple rule to estimate the required values of energy resolution, exposure, and background rate for a PTOLEMY-like experiment to cover a certain region in the $(m_{ν}, n_{ν}^{loc})$ parameter space. Alongside this paper, we publicly release a code to calculate the CNB sensitivity in a given cosmological model.

Received 10 December 2021
Accepted 26 January 2022

DOI:https://doi.org/10.1103/PhysRevD.105.063501

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Cosmology Extrasolar neutrino astronomy Neutrino interactions Particle astrophysics

Neutrino detection

Gravitation, Cosmology & AstrophysicsParticles & Fields

Authors & Affiliations

James Alvey ^1,*, Miguel Escudero ^2,†, Nashwan Sabti ^3,‡, and Thomas Schwetz ^4,§

¹GRAPPA Institute, Institute for Theoretical Physics Amsterdam, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
²Physik-Department, Technische Universität, München, James-Franck-Straße, 85748 Garching, Germany
³Department of Physics, King’s College London, Strand, London WC2R 2LS, United Kingdom
⁴Institut für Astroteilchenphysik, Karlsruher Institut für Technologie (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany

^*j.b.g.alvey@uva.nl
^†miguel.escudero@tum.de
^‡nashwan.sabti@kcl.ac.uk
^§schwetz@kit.edu

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Vol. 105, Iss. 6 — 15 March 2022

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Images

Figure 1
Event spectra expected at PTOLEMY within the fiducial scenario considered in this work for the two cases where the energy resolution is $Δ > m_{lightest}$ (left) and $Δ < m_{lightest}$ (right), see Sec. 3 for details. Note that the sensitivity of a PTOLEMY-like experiment to detect the cosmic neutrino background is governed by both $a$ ) the separation of the CNB signal from the large $β$ -decay background, and $b$ ) the absolute CNB signal rate, specifically as compared to the background. The former is controlled by the relative sizes of $Δ$ and $m_{lightest}$ , while the latter is instead specified by the exposure, local number density $n_{ν}^{loc}$ , and the background rate $Γ_{b}$ .
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Figure 2
Sensitivity of a cosmic neutrino background detection by PTOLEMY at 68%, 95%, and 99.7% C.L. for Dirac neutrinos (left) and Majorana neutrinos (right) as a function of the lightest neutrino mass $m_{lightest}$ and the local neutrino density per helicity state $n_{ν}^{loc}$ . The right vertical axis shows the CNB capture rate per year per 100 g of tritium sample mass. We assume a 1 yr exposure of 100 g tritium with an energy resolution of 100 meV and a background level of $7 \times 10^{- 7} Hz / eV$ . The yellow curve shows the $Λ CDM$ prediction including gravitational clustering in the Milky Way, and the star indicates the current upper bound on $m_{lightest}$ from Planck, see Eq. (11). The purple curve corresponds to the Low- $T_{ν} + DR$ cosmology and the blue curve to the High- $p_{ν}$ scenario, see Sec. 2 for details. Here, the vertically-hatched and horizontally-hatched regions denote exclusion limits from $CMB + BAO$ data in these cosmologies, respectively. We show the KATRIN sensitivity by a red arrow [see Eq. (9)]. In the right panel we include the current limit from neutrinoless double-beta decay experiments, assuming the most conservative nuclear matrix element, see Eq. (13).
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Figure 3
The dependence of the PTOLEMY sensitivity on the energy resolution (top left), background rate (bottom left), sample size (top right), and exposure time (bottom right). For comparison, the dotted curves correspond to the PTOLEMY sensitivity using our default parameters as in the left panel of Fig. 2. Note that, as before, the regions above the purple and blue curves are excluded by $CMB + BAO$ data.
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Figure 4
Possible future experimental scenarios. In the left panel, we assume Dirac neutrinos with normal-mass ordering and a cosmological neutrino mass determination of $(60 \pm 20) meV$ when interpreted within $Λ CDM$ , see Eq. (38). In the right panel, we assume Majorana neutrinos with inverted ordering, an upper bound on the neutrino mass from cosmology corresponding to $\sum m_{ν} < 20 meV$ in $Λ CDM$ [see Eq. (39)], and a positive detection of $m_{β β} \approx 20 meV - 40 meV$ in neutrinoless double-beta decay experiments, corresponding to $100 meV ≲ \sum m_{ν} ≲ 400 meV$ (vertical orange-shaded band). Instead of showing $m_{lightest}$ on the horizontal axes, we are using $\sum m_{ν} / 3$ here. The yellow line corresponds to the $Λ CDM$ case, whilst the purple and blue lines represent the Low- $T_{ν} + DR$ and High- $p_{ν}$ cosmologies, respectively. In the left panel, the shaded bands correspond to allowed regions, and in the right panel the hatched regions are excluded. Note that in this figure we have assumed that KATRIN has reached its final sensitivity (the hatched region to the right of the red, vertical line).
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