PHYSICAL REVIEW D 100, 015028 (2019)
Cosmic neutrino background search experiments as decaying dark matter detectors
David McKeen* TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T 2A3, Canada
(Received 1 April 2019; published 18 July 2019)
We investigate the possibility that particles that are long-lived on cosmological scales, making up part or all of the dark matter, decay to neutrinos that have present-day energies around an eV. The neutrinos from these decays can potentially be visible at experiments that hope to directly observe the cosmic neutrino background through neutrino capture on tritium, such as PTOLEMY. In the context of a simple model that can realize such decays, we discuss the allowed signatures at a PTOLEMY-like experiment given current cosmological constraints.
DOI: 10.1103/PhysRevD.100.015028
I. INTRODUCTION enormous density, scattering of CνB neutrinos is highly suppressed since their energies are minuscule and they Particles with lifetimes on cosmological scales that couple to matter only via the weak interaction. Further- decay to neutrinos arise in a number of new physics more, the tiny energies involved make distinguishing from contexts, such as lepton number violation and the gener- backgrounds very troublesome. Both of these facts mean ation of neutrino masses [1], and can even comprise some that detecting the CνB is extremely challenging. The most or all of the dark matter of the Universe [2–5]. The present- promising technique to detect the very low energy CνB— day energy of the neutrinos from these decays can span a − neutrino capture on β-decaying nuclei, ν þðA; ZÞ → e þ wide range, making them accessible at, e.g., existing dark ðA; Z þ 1Þ, where a nucleus, ðA; ZÞ, is labeled by its mass matter direct detection and neutrino experiments [4–6]. number, A, and atomic number, Z—was first proposed by In this paper we will consider the decays of long-lived Weinberg in 1962 [9] and more recently studied in [10,11]. particles to neutrinos that carry very little energy today, in This process benefits from the lack of a threshold energy the neighborhood of an eV. These neutrinos are slightly and its signature is the production of an electron with more energetic than the standard cosmic neutrino back- energy above the end point of natural β decay, ðA; ZÞ → ground (CνB)—the thermal relic neutrinos that decoupled − ν¯ þ e þðA; Z þ 1Þ. For a neutrino of mass mν and energy from the plasma when the Universe had a temperature of a Eν, the shift above the end point is ∼mν þ Eν. In the case of few MeV. The temperature of the CνBis∼10−4 eV today, nonrelativistic CνB neutrinos, this shift is roughly 2mν.Of less than the scale of the atmospheric and solar neutrino course, extremely good resolution on the e− energy is mass splittings, and therefore at least two mass eigenstates required to resolve this gap given the relatively large rate ν in the C B are now nonrelativistic; the most energetic of of β decay compared to capture of CνB neutrinos. ≃ ≳ 0 05 these neutrinos have energy ECνB mν . eV. There is Recently, the PTOLEMY experiment has proposed [12] an upper limit on the neutrino masses, hence on the energy to tackle these difficulties using a target of 100 g of tritium ν of the C B, from observations of the cosmic microwave (i.e., A ¼ 3, Z ¼ 1 in the expressions above) implanted on Pbackground (CMB) and baryon acoustic oscillations of a graphene substrate along with MAC-E (Magnetic 0 12 mν< . eV at 95% confidence level [7]. Terrestrial Adiabatic Collimation with Electrostatic) filtering, radio experiments, in comparison, limit the neutrino mass at frequency monitoring, and advanced calorimetry to mea- 95% confidence level to less than 2.8 eV [8]. sure the e− energy. Tritium has a relatively small rate for β The present-day number density of CνB neutrinos is very −1 decay, Γβ ≃ ð17 yrÞ and implanting it on graphene serves ≃ 330 −3 large, with a cosmic average nCνB cm . Despite this to reduce intrinsic broadening of the e− energy from molecular effects. This could potentially allow for energy *[email protected] resolution as small as 0.1 eV, which is needed to success- fully probe the CνB. Published by the American Physical Society under the terms of This paper is organized as follows. In Sec. II, we describe the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to a simple model containing a long-lived particle that the author(s) and the published article’s title, journal citation, decays to neutrinos, and discuss the number density and and DOI. Funded by SCOAP3. energy distribution of neutrinos allowed by cosmological
2470-0010=2019=100(1)=015028(8) 015028-1 Published by the American Physical Society DAVID MCKEEN PHYS. REV. D 100, 015028 (2019) observations. We see that decays that take place after matter, and h ≃ 0.68 is the Hubble constant today in units 100 Ω Ω recombination, when photons decouple, are the most prom- of km=s=Mpc. J= dm is the fraction of dark matter ising to be probed at experiments sensitive to eV-scale that J particles would comprise today if they did not decay, neutrinos, such as PTOLEMY. We discuss the signature of which we normalize here to 5%. In what follows, we will this scenario at a PTOLEMY-like experiment in detail in suppress the argument of the scale factor and set its value Sec. III, considering both the diffuse and local contributions today to unity, a0 ¼ aðt0Þ¼1. We will also require that to the flux, and compare the reach to that of cosmological the J’s and their decay products do not grossly disturb observations. In Sec. IV, we conclude. the evolution of the Universe from the standard cosmology, with radiation domination at redshifts z ¼ a−1 − 1≳ ≃ 3300 II. DENSITIES AND DISTRIBUTIONS zeq , followed by matter domination, then more recently vacuum energy domination. The simple model we consider involves only a long- The number density of neutrinos produced in J decays lived, real scalar particle J with mass mJ. It couples to the simply follows from Eq. (3), light neutrinos ν through an interaction of the form − τ 2Ω ρ 1 − t= J g ˜ ð Þ¼ J cr;0 e L ¼ − νν þ ð Þ nν t 3 int J H:c: 1 m a 2 J − τ 130 Ω Ω 1 − t= J J= dm eV e In this expression, ν is a two-component, left-chiral spinor ¼ ; ð4Þ cm3 0.05 m a3 field, and the interaction is gauge invariant if, e.g., it comes J from a sterile admixture of the light neutrinos. This → νν where we use a tilde to distinguish this population from the coupling leads to the decay J . Assuming that this standard neutrinos. is the only J decay mode at tree level, its lifetime is There are essentially three qualitatively different regimes 32π 10−15 2 for the J lifetime in terms of its cosmological effects: 9 eV τ ≃ 0 2 τ ¼ ¼ 2 × 10 yr : ð2Þ (i) before neutrino decoupling, J 015028-2 COSMIC NEUTRINO BACKGROUND SEARCH EXPERIMENTS AS … PHYS. REV. D 100, 015028 (2019) dρ˜ν mJnJ (∼0.28=15 ≃ 2% or less) goes into relativistic d.o.f. in þ 4Hρ˜ν ¼ : ð6Þ dt τJ each J decay. This could be the case, e.g., in neutrino portal dark matter models [13] with a small splitting in the dark −4 Using the fact that photons redshift like radiation, ργ ∝ a , sector between a fermion, χ and a scalar ϕ. These interact we can reexpress this equation as with neutrinos via the effective operator ϕχ¯HL=Λ → ðv=ΛÞϕχν¯ where H and L are the Higgs and lepton ðρ˜ ρ Þ d ν= γ mJnJ ΩJ a − τ doublets respectively. The heavier state in the dark sector, ¼ ¼ t= J ð Þ e ; 7 ϕ for instance, could be long-lived and decay through this dt ργτJ Ωγ τJ operator, ϕ → χν where the neutrino has energy ∼mϕ − mχ −5 −2 in the ϕ rest frame. where Ωγ ¼ 2.47 × 10 h is the present-day contribution of the CMB to the critical density. Assuming that the J’sdo Lastly, looking at Eq. (9), we might naively think that we J not come to dominate the energy budget of the Universe at can arrange for a number density of neutrinos from decays before recombination that is much larger than that of this time, the energy density is dominated by radiation and 2 the CνB neutrinos. This could be the case if the J’s were the scale factor depends on the time as t ¼ t2a with ¼ 7 6 1011 very light and cold so that their energy density is sup- t2 . × yr. We can then integrate Eq. (7) to find pressed while their number density is large—this relies on pffiffiffi rffiffiffiffiffi ’ ν ρ˜ π Ω τ the J s remaining unthermalized with the C B neutrinos. ν ¼ J J This requirement can be used to set an upper limit on the ρ 2 Ω γ t≫τ γ t2 strength of the J − ν interaction or, equivalently, a lower J rffiffiffiffiffiffiffiffiffiffiffiffiffi Ω τ limit on τJ. Production of J’s through νν → J happens most ¼ 0.15 J J : ð8Þ ∼ Ω 103 readily at Tν mJ and the rate for this is roughly dm yr 2 g Tν ∼ 1=τJ. To keep the J’s out of equilibrium, we require that this is less than the Hubble rate at Tν ∼ m which is Using Eqs. (4), (5), and (8), we can reexpress n˜ ν today in J ∼ 2 ≃1019 terms of ΔN , mJ=MPl with MPl GeV the Planck mass. This eff 2 ≲ τ ≳ 105 ð Þ2 implies that g mJ=MPl or J yr eV=mJ . sffiffiffiffiffiffiffiffiffiffiffiffiffi 1 0 103 Δ 103 Using this in Eq. (9) one obtains an upper bound on the . × Neff eV yr n˜ νðt0Þ¼ : ð9Þ present-day density of neutrinos from J decays roughly 3 0 28 τ −3 cm . mJ J comparable to that in the CνB, Oð100 cm Þ. The energy distribution of such neutrinos today would be indistin- An additional constraint comes from the fact that J guishable from that of the CνB; i.e., they would also be particles redshift like matter before their decay so that their nonrelativistic. energy density can come to exceed that in radiation, Similar situations where nonthermally produced neutri- causing an early period of matter domination. This would nos, such as the right-chiral component of light Dirac conflict with the usual picture of radiation domination from neutrinos, evade constraints on light d.o.f. and lead to an primordial nucleosynthesis until matter-radiation equality enhancement of the CνB signal have already been explored ∼ Ω τ ≲ ∼ at teq trec; we can use this to limit J for J teq trec. in, e.g., [14]. Dark matter that comes into thermal equi- The ratio of the energy density in J’s to that in radiation librium with neutrinos after neutrino decoupling but before during this era is recombination has been studied extensively in [15]. ρJ 2 mJnJ 2 ΩJ − τ τ t ¼ ¼ t= J B. Decays after recombination ( J > rec) ρ ρ Ω ae r g γ g γ ’ rffiffiffiffi Nonrelativistic J s that decay to neutrinos after recombi- 2 ΩJ t − τ nation act as a decaying component of the dark matter. This ¼ e t= J ; ð10Þ g Ωγ t2 alters the expansion history of the Universe between last scattering and today which can change the precise pattern with g ¼ 3.36. Requiring that this ratio is less than unity of CMB angular anisotropies as well as the growth of gives the constraint structure. These effects have been analyzed in detail in Refs. [3,16,17] and even proposed as an explanation of sffiffiffiffiffiffiffiffiffiffiffiffiffi tensions in cosmological data [18]. This limits τ and the Ω 103 J J 23 yr ð Þ energy density in J’s and, consequently, the number density Ω < τ : 11 dm J of neutrinos produced in J decay. For lifetimes short compared to the age of the Universe Note that this is equivalent to a rather weak limit on the (but long compared to trec), Ref. [16] obtains a bound using Ω Ω number of relativistic d.o.f. from CMB observations CMB observables on the J energy density of J= dm < Δ 15 of Neff < . However, it can become an important 0.038 at 95% confidence level. For longer lifetimes, the Ω Ω 0 09ðτ 15 Þ constraint in a scenario where only a fraction of mJ constraint is roughly J= dm < . J= Gyr . Using 015028-3 DAVID MCKEEN PHYS. REV. D 100, 015028 (2019) these constraints in Eq. (4), the current neutrino number these expressions the characteristic energy of the neutrinos density is then limited to be today is ( 95 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi eV av 1 10−5 τ 103 τ ≲ n˜ νðt0Þ ≲ Eν × J= yr; J trec 3 m ¼ ð15Þ cm J m ½0 04ðτ Þ2=3 0 5 τ ≳ 8 J min . J=Gyr ; . ; J trec; > 1 τ ≲ 12 <> ; J Gyr 2 3ð1 − 2τ Þ 12 ≲ τ ≲ 160 which ignores a slight correction due to the relatively × > . t0= J ; Gyr J Gyr :> recent transition to vacuum energy domination. Therefore, 2.3ð160 Gyr=τ Þ; τ ≳ 160 Gyr: J J obtaining relativistic neutrinos today with Eν ∼ eV requires ≳ 10 ≲ 10 τ ≲ τ ≳ ð12Þ mJ keV (mJ keV) for J trec ( J trec), as we would expect given the redshift of matter-radiation equal- ≃ 3300 We observe that neutrino number densities comparable ity, zeq . to that in the CνB from J decay are possible for τJ larger or In Fig. 1, we show the cosmic average flux of non- smaller than trec without being ruled out by cosmological standard neutrinos as functions of their energy today for ¼ 50 τ ¼ 103 Ω data. We now turn to the question of their energy distri- mJ keV, J yr 015028-4 COSMIC NEUTRINO BACKGROUND SEARCH EXPERIMENTS AS … PHYS. REV. D 100, 015028 (2019) with contributions to the energy density from baryons, 4.52 M fν Ω =Ω ¼ T e J dm Ω ¼ 0 05 Ω ¼ 0 69 Rcos b . ; dark energy, Λ . ; dark matter, yr 100 g 1=2 0.05 Ω ¼ 0 26 Ω ¼ 8 7 10−5 dm . , and (standard) radiation, r . × . eV − τ τ t0= J For J >trec, the dark matter is split up into a decaying × ð1 − e Þ: ð17Þ Ω Ω − Ω mJ component, J, and a nondecaying component, dm J. For comparison, the fluxes of CνB, solar ν [19], and In this expression fν is the fraction of these neutrinos that atmospheric ν [21] neutrinos are plotted in Fig. 1 as well. e We also show the results of the recent computations of the are of electron flavor. While we have thus far not specified low energy thermal component of solar neutrinos [20] and the flavor content of the neutrinos that J couples to, we will the antineutrino flux from the decay of neutrons and tritons discuss this briefly here. produced in primordial nucleosynthesis [22], which extend Note that if J is indeed the Majoron [1] it couples to the into the 0.1–1 eV range but in relatively low numbers. neutrino mass eigenstates with strength proportional to Because the number density is suppressed with increas- their masses, and thus the flavor content of these neutrinos does not oscillate [4]. First, consider the case that the ing mJ, and cosmological limits are strong for small τJ, the P most viable scenario to produce an observable number of neutrinos are light and not degenerate, mν≲0.1 eV. If → ν ν neutrinos with Eν ∼ eV today involves relatively light J’s, the mass hierarchy is normal then J 3 3 is the dominant ≃ 0 03 Γ ≃ of order a few eV, with lifetimes comparable to the age of mode and fνe . . If instead it is inverted, J→ν1ν1 Γ →ν ν and fν ≃ 1=2. If the neutrinos are relatively heavy the Universe. If the light neutrinos are massive, it is J 2 2 e P ’ possible for early decays, before trec, of light J s to lead and degenerate with mν≳0.1 eV the rate into all mass to a population of nonrelativistic neutrinos with present-day ≃ 1 3 eigenstates is comparable and fνe = . Different scenar- energy Eν ∼ mν. The signal of these neutrinos is indistin- ios where J couples to states that are not mass eigenstates guishable from that of the CνB in such a case. Since, as lead to flavor oscillations and can give different values ’ seen in Sec. II A, such neutrinos number density can be at of fν . ν Oð1Þ e most comparable to the C B, they can only lead to an Since we are focusing on τ >t , we can use the same ν J rec increase in the event rate of massive C B-like neutrinos, limit on Ω as a function of τ from [16] that lead to the ν J J similar to scenarios explored in [14]. The standard C B rate upper limit on n˜ ν in Eq. (12) to limit their capture rate. Oð1Þ can vary by an factor depending on whether the Doing so gives neutrinos are Majorana or Dirac [11] as well as gravita- tional clustering [23] and focusing by the Sun [24].For 3.44 M fν eV these reasons, in what follows we focus on decays of a light R ≲ T e cos yr 100 g 1=2 m J after recombination. Below, we examine the experimental 8 J signature of neutrinos from these decays at experiments > 1 τ ≲ 12 <> ; J Gyr ν searching for the C B such as PTOLEMY. 2 3ð1 − 2τ Þ 12 ≲ τ ≲ 160 × > . t0= J ; Gyr J Gyr :> 2 3ð160 =τ Þ; τ ≳ 160 ; III. OBSERVING THE NEUTRINOS . Gyr J J Gyr FROM DARK MATTER DECAY ð18Þ A. Neutrino capture from diffuse J → νν which, as expected, is comparable to the rates expected We are interested in the detection prospects for neutrinos from the CνB. However, as we see from Eq. (15), the with Eν ∼ eV today which could show up in experiments neutrinos’ energies can be around an eV today without searching for direct evidence of the CνB. The most requiring the neutrino masses to be large. promising technique to detect these neutrinos is neutrino capture on β-decaying nuclei. As a benchmark detector setup, we focus on the recently proposed experiment B. Dark matter decay in the Galaxy PTOLEMY [12], which hopes to use a tritium target of Thus far, we have discussed only the contribution to a ¼ 100 mass MT g and to achieve an energy resolution of neutrino capture signal from diffuse J decays averaged over about 0.1 eV (full width at half maximum) on recoiling the entire Universe. Since the J’s act as dark matter today if electrons near the end point. This could probe neutrinos τJ is comparable to or larger than the age of the Universe, with energies as low as 0.1 eV. their local density in the Milky Way can be greatly ≪ The cross section for an electron neutrino with Eν enhanced over the cosmic average. Using a Navarro- keV to capture on tritium is [11] Frenck-White dark matter profile [25], ρðrÞ ∝ r−1ð1 þ Þ−2 ¼ 24 σ ¼ 3.83 × 10−45 cm2: ð16Þ r=rs with scale radius rs kpc and local dark matter density of 0.3 GeV=cm3 along with the capture cross Using this with Eq. (4) leads to a capture rate on tritium for section on tritium in Eq. (16), we find a rate for capture neutrinos from J decays, averaged over the Universe, of from neutrinos produced in the Milky Way of 015028-5 DAVID MCKEEN PHYS. REV. D 100, 015028 (2019) 5.82 M fν eV R ¼ T e MW yr 100 g 1=2 m J 10 Ω Ω Gyr J= dm − τ × e t0= J : ð19Þ τJ 0.05 This signal is essentially monochromatic with Eν ¼ mJ=2. For τL ≲ 5 Gyr, this rate is negligible but becomes important as τJ is increased, so that for τJ ≳ 100 Gyr it is roughly comparable to that from cosmically averaged J decays, Rcos. In Fig. 2, we show contours for a capture rate on tritium of 1 yr−1ð100 gÞ−1 [10 yr−1ð100 gÞ−1] as solid (dotted) Ω Ω τ curves in the J= dm vs J parameter space, for (from right ¼ 1 3 ¼ 1 2 to left) mJ ; eV. We have chosen fνe = , appro- priate if J were a Majoron decaying to light neutrinos with an inverted mass hierarchy. Note that these are raw signal rates and do not impose a cut to remove background from β decay. In addition, we shade the 2σ exclusion region on a decaying dark matter component from the analysis of CMB data in Ref. [16]. We also point out the two benchmark points in this parameter space whose fluxes were shown FIG. 2. Contours showing capture rates on tritium of in Fig. 1: m ¼ 1 eV, τ ¼ 7 Gyr, Ω =Ω ¼ 0.08 as −1 −1 −1 −1 J J J dm 1 yr ð100 gÞ (solid) and 10 yr ð100 gÞ (dotted) in the a green club and m ¼ 3 eV, τ ¼ 1011 yr, Ω =Ω ¼ 1 J J J dm space of τJ and the J energy density in units of the total dark as a red spade. Ω Ω matter energy density, J= dm (J acts as a decaying dark matter component). mJ has been chosen to be, from right to left, 1 C. Signature (green) and 3 (red) eV. In all cases we have taken the electron neutrino fraction of the J decays to be fν ¼ 1=2. The 2σ Just as is the case with the CνB, detecting the neutrinos e exclusion from CMB data in [16] is the shaded gray region. from J decay is challenging because the signal of an We also show the locations of the two benchmark points which electron above the β-decay end point can be swamped by ¼ 1 τ ¼ 7 Ω Ω ¼ − are plotted in Figs. 1 and 3: mJ eV, J Gyr, J= dm the enormous rate from β decay due to the finite e energy 0 08 ¼ 3 τ ¼ 1011 Ω Ω ¼ 1 . (green club) and mJ eV, J yr, J= dm resolution. To mitigate this background, PTOLEMY aims (red spade). for roughly 0.1 eV resolution on the electron energy to be able to observe the CνB for neutrinos with mν ≳ 0.1 eV. For reference, Dirac (Majorana) CνB neutrinos would lead to a rate of 4ð8Þ yr−1 for 100 g of tritium [11]. We see that J → νν decays at late times can lead to comparable event rates with Eν above threshold and, unlike the CνB, this can even be the case if mν < 0.1 eV. To illustrate the signal, we show the e− kinetic energy distribution for capture on tritium in Fig. 3, assuming a resolution of 0.1 eV as proposed by PTOLEMY, for two benchmark points currently allowed by cosmological ¼ 1 τ ¼ 7 109 Ω Ω ¼ 0 08 data, mJ eV, J × yr, J= dm . (solid, ¼ 3 τ ¼ 1011 Ω Ω ¼ 1 green) and mJ eV, J yr, J= dm (solid, ¼ 1 2 red) taking fνe = as above. These benchmark points are also marked in Fig. 2 and their cosmically averaged fluxes are shown in Fig. 1. Also shown in Fig. 3 is the background from the standard tritium β decay with mν ¼ 0 FIG. 3. Event rates for capture on tritium for neutrinos from as a solid gray line. The rates are shown as functions of the → νν ¼ 1 τ ¼ 7 109 Ω Ω ¼ 0 08 − ¼ 0 J for mJ eV, J × yr, J= dm . (green, e kinetic energy Ke minus the mν end point energy ¼ 3 τ ¼ 1011 Ω Ω ¼ 1 ¼ 1 solid) and mJ eV, J yr, J= dm (red, solid) Kend. The mJ and 3 eV benchmarks here give rates and natural β decay (gray, solid) with an electron energy 7 0 −1ð100 Þ−1 − 0 2 of 4.8 and . yr g for Ke Kend > . eV, resolution of 0.1 eV. For comparison, we plot the total rate for −1 −1 respectively, compared to 0.66 yr ð100 gÞ from the signal plus background for a Majorana CνB signal with mν ¼ β-decay background. As a comparison, we also plot the 0.15 eV (yellow, dashed). 015028-6 COSMIC NEUTRINO BACKGROUND SEARCH EXPERIMENTS AS … PHYS. REV. D 100, 015028 (2019) total rate in the case of a standard CνB signal with an mν ¼ Hubble constant between CMB and local observations and 0.15 eV Majorana neutrino as a dashed yellow curve. the σ8 problem. This signature also does not suffer from the Note that, for the diffuse components of the signals, we same degeneracies that affect the extraction of conclusions used, as in Fig. 1, the energy spectrum from Eq. (13), from cosmological observations. Furthermore, in the event Ω ¼ 0 05 Ω ¼ 0 69 Ω ¼ 0 26 b . , Λ . , dm . with the dark matter of a positive signal, the two distinct sources of neutrinos, split up into a decaying and nondecaying component, ΩJ from J decays averaged over the Universe and those in the Ω − Ω and dm J, respectively. The contribution from J Milky Way could allow for the dark matter distribution of decays within the Milky Way gives bumps with a width the Milky Way to be studied in more detail. Another determined by the detector resolution. These two sources of interesting possibility in the event of a positive signal neutrinos lead to the interesting signature of a peak at Ke − would come from terrestrial searches for light particles ¼ 2 Kend mJ= from local J decays and a shoulder extending coupled to neutrinos, e.g., imprinting spectral features in 2 from mJ= down to the end point from redshifted diffuse the spectrum of tritium β decay [26]. decays, with roughly comparable signal strength in each. Similar models with higher multiplicity of neutrinos in The size of the signal from local J decays is subject to the decay of dark matter χ, e.g., χ → 2J → 4ν, could lead to uncertainty coming from our ignorance of the precise dark larger event rates. However, this would come at the cost of matter distribution of the Milky Way as well as its overall diluting the energy of the neutrinos today, potentially normalization; observation of a nonzero signal could of masking the distinguishing spectral features in the capture course help shed light on this issue. rate. Other models, more complicated than the simple one described here, with potentially more involved cosmologi- IV. CONCLUSIONS cal histories could also lead to larger enhancements. This paper has explored a new physics scenario that Although we have not discussed them in detail, other ν searches for the CνB can impact: light dark matter that proposals to search for the C B, such as using laser decays to neutrinos. While the event rates at a PTOLEMY- interferometers [27], that do not involve looking for like experiment in this scenario are not enormous and the electrons above the β-decay end point could also be impacted by the decay of dark matter to neutrinos. range of mJ accessible is not large, over a spread of several eV, a comparable signal strength to those expected from the While potential signals in such a setup are not likely to CνB is possible. Furthermore, the signal described here is lead to large effects, assessing the sensitivity of new distinct from that of the CνB, and can potentially be techniques in general to the signal described in this paper observable even if the e− energy resolution is poorer than would be interesting. Moreover, other interesting features what is needed for CνB detection given the current upper to consider would be the effects of gravitational clustering bound on mν. of the neutrinos from J decay and potential anisotropies in While a robust statistical analysis of possible signals is the signal from decays in the Milky Way, along the lines beyond the scope of this study, if the electron energy explored in [28]. resolution can be kept to the roughly 0.1 eV level, excesses β beyond the -decay background could potentially be seen. ACKNOWLEDGMENTS Seeing such a signal would of course be tremendously exciting, opening up a world of new physics implications. We thank Nikita Blinov, Andrew Long, David Even providing an upper bound on the rate, however, Morrissey, Ann Nelson, Maxim Pospelov, and Nirmal would constrain part of the parameter space of dark matter Raj for helpful conversations. This work is supported by decaying to neutrinos that is not currently probed by the National Research Council of Canada and was per- cosmological observations. This would be useful informa- formed in part at the Aspen Center for Physics, which is tion, especially in light of nagging tensions in the cosmo- supported by National Science Foundation Grant No. PHY- logical data, such as the discrepancy in the extraction of the 1607611. [1] Y. Chikashige, R. N. Mohapatra, and R. D. Peccei, Phys. Lett. B 318, 360 (1993); M. Lattanzi and J. W. F. Valle, Lett. 98B, 265 (1981); J. Schechter and J. W. F. Valle, Phys. Phys. Rev. Lett. 99, 121301 (2007); F. Bazzocchi, M. Rev. D 25, 774 (1982); K. S. Babu, Phys. Lett. B 203, 132 Lattanzi, S. Riemer-Sorensen, and J. W. F. Valle, J. Cosmol. (1988). Astropart. Phys. 08 (2008) 013; M. Frigerio, T. Hambye, [2] I. Z. Rothstein, K. S. Babu, and D. Seckel, Nucl. Phys. and E. Masso, Phys. Rev. X 1, 021026 (2011); F. S. Queiroz B403, 725 (1993); V. 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