TUM-HEP-142022 Decaying Dark Matter and Lyman- forest constraints

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TUM-HEP-1420/22

Decaying Dark Matter and Lyman-α

forest constraints

Lea Fuß, Mathias Garny

Physik Department T31,

James-Franck-Str. 1, Technische Universit¨at M¨unchen,

D-85748 Garching, Germany

E-mail: lea.fuss@tum.de,mathias.garny@tum.de

Abstract. Decaying Cold Dark Matter (DCDM) is a model that is currently under inves-

tigation regarding primarily the S8tension between cosmic microwave background (CMB)

and certain large-scale structure measurements. The decay into one massive and one (or

more) massless daughter particle(s) leads to a suppression of the power spectrum in the late

universe that depends on the relative mass splitting = (1 −m2/M2)/2 between the mother

and massive daughter particle as well as the lifetime τ. In this work we investigate the im-

pact of the BOSS DR14 one-dimensional Lyman-αforest ﬂux power spectrum on the DCDM

model using a conservative eﬀective model approach to account for astrophysical uncertain-

ties. Since the suppression of the power spectrum due to decay builds up at low redshift, we

ﬁnd that regions in parameter space that address the S8tension can be well compatible with

the Lyman-αforest. Nevertheless, for values of the degeneracy parameter ∼0.1−0.5%, for

which the power suppression occurs within the scales probed by BOSS Lyman-αdata, we ﬁnd

improved constraints compared to previous CMB and galaxy clustering analyses, obtaining

τ&18 Gyrs for small mass splitting. Furthermore, our analysis of the BOSS Lyman-αﬂux

power spectrum allows for values τ∼102Gyrs, ∼1%, that have been found to be preferred

by a combination of Planck and galaxy clustering data with a KiDS prior on S8, and we even

ﬁnd a marginal preference within this regime.

arXiv:2210.06117v1 [astro-ph.CO] 12 Oct 2022

Contents

1 Introduction 1

2 Decaying Cold Dark Matter 4

2.1 Formalism 4

2.2 The DCDM power spectrum 7

3 Lyman-αforest data and model 11

3.1 Data 11

3.2 Eﬀective model 11

3.3 Fitting procedure 15

4 Results 16

4.1 Exclusion bounds 16

4.2 Allowed region and comparison with CMB and BAO data 18

5 Three-body decay 20

6 Conclusion 25

1 Introduction

The standard model of cosmology known as ΛCDM is a very successful model in explaining

the large scale structure (LSS) of the universe. Cold dark matter (CDM) sits at the heart

of this model, causing the typical hierarchical bottom-up structure formation we observe in

the LSS by being non-relativistic during the clustering process. Despite the success of CDM,

there are still unresolved issues that are hinting that there may be more [1]. This sparks

interest in diﬀerent cosmological models that are able to address these issues. Moreover,

comparing the process of structure formation within extended cosmological models with LSS

observations allows us to constrain fundamental properties of the two large unknowns, dark

energy and dark matter, such as the equation-of-state, or the lifetime.

One of the open questions is the so-called σ8tension, where σ8is a measure of the

amplitude of matter ﬂuctuations at a scale of 8 Mpc/h. More speciﬁcally, it is convenient to

use the parameter S8=σ8pΩm/0.3 that also includes the matter density parameter Ωm.

The tension arises between early universe cosmological data preferring larger values of S8,

and local, low redshift measurements tending towards lower values when interpreted within

the ΛCDM model, with a typical signiﬁcance of the order of 2−3σ[1,2]. Measurements of the

cosmic microwave background (CMB) temperature and polarization anisotropies by Planck

yield S8= 0.834 ±0.016 [3] which, in this respect, is in agreement with other CMB data like

from ACT [4]. On the other hand, weak gravitational lensing surveys provide constraints

via cosmic shear, e.g. S8= 0.759+0.024

−0.021 from the Kilo-Degree Survey KiDS-1000 [5] and

S8= 0.780+0.030

−0.033 from HSC [6]. The combination from shear and galaxy clustering from three-

year data of DES yields S8= 0.776+0.017

−0.017 [7] and a combination of shear, clustering and galaxy

abundance from KiDS-1000 S8= 0.773+0.028

−0.030 [8], while galaxy cluster counts from SPT-SZ

report S8= 0.766 ±0.025 [9] and eROSITA results favour S8= 0.791+0.028

−0.031 [10]. Individual

– 1 –

measurements might not produce as large deviations, but show a trend being signiﬁcantly

lower compared to CMB data. To account for this, and leaving aside the possibility of

a statistical ﬂuctuation, there either needs to be some unaccounted systematic error (see

e.g. [11]) or an alternative to ΛCDM featuring a suppression of the matter power spectrum

in the k∼0.1−1h/Mpc regime.

One model to achieve such a suppression is the Decaying Cold Dark Matter (DCDM)

model. It is based on the hypothesis that dark matter can decay on cosmological time-

scales into secondary dark sector particles. The decay products are assumed to be eﬀectively

stable on cosmological scales and, like the dark matter itself, suﬃciently weakly coupled to

visible matter to escape (in-)direct detection. However, the kinetic energy released in the

decay process counteracts the growth of structures and leads to a suppression of the power

spectrum. The model has been mainly investigated in two variants: a decay into massless

secondaries that act as dark radiation (DR), or into a massless and a massive daughter.

Depending on the mass splitting between mother and massive daughter particles, the latter

acts as warm dark matter (WDM) being gradually produced in the decay process in the

late universe. For both variants, the evolution in the early universe is identical to ΛCDM,

thereby preserving its success in explaining the CMB and LSS on very large scales. Both

models were studied regarding the S8and also the Hubble tension [12], taking CMB, BAO

and recently also galaxy clustering data into account. The decay into massless secondaries

was investigated e.g. in [13–23], allowing also the possibility that only a fraction fof the

dark matter decays. It was found that the decay into purely DR will most likely not be

able to solve cosmological tensions and requires minimum lifetimes of around ∼200 Gyrs for

f= 1. The latest works [22,23] for this model conﬁrm this even more while also providing

tight constraints. For lifetimes shorter than the age of the universe, [22] ﬁnds f < 2.16%

and for f→1 a lower bound of τ > 250 Gyrs [22,23]. As a further variant, also the decay

of warm dark matter mother particles into massless dark radiation has been considered [24],

but similar to the decay of CDM into massless daughters, this setup was found to neither

solve the H0nor S8tensions [25].

The model with a decay of CDM into WDM and DR, on which we mainly focus in this

work, is apart from the lifetime τdescribed by the mass splitting parameter

=1

21−m2

M2,(1.1)

involving the mass of the mother (M) and the massive daughter (m) particle. The results

regarding the Hubble tension are similar compared to the massless case, implying that it is

probably not to be resolved with DCDM [26–28] (see also [29,30] for earlier work). The

situation for the S8tension is however not so clear. While [28] suggests that this tension can

also not be addressed, [31], which includes an improved treatment of perturbations, ﬁnds that

it actually can be lessened for τ∼55 Gyrs and ∼0.7% based on Planck CMB, BAO, RSD

and SN Ia data. In two follow-up works a newly developed code for much faster computation

of the DCDM power spectra is used. This allows for a more in depth analysis, like in [32],

where a mild preference for DCDM is found depending on the priors for S8. The latest

work [22] also includes full-shape information from BOSS DR12 galaxy clustering, and ﬁnds

that DCDM can ease the S8tension even though it is not performing signiﬁcantly better than

ΛCDM when disregarding KiDS data. However, when including KiDS, DCDM is preferred,

and the best-ﬁt model occurs for a lifetime of τ∼120 Gyrs and ∼1.2%.

– 2 –

Another possibility to study DCDM is via galaxy and halo properties with more regards

towards the small scale issues (see e.g. [33]) like the cusp-core problem of DM halos [34].

For DCDM with a massive and a massless daughter particle, [35] connects the model to

the observed population of Milky Way satellites. Combining numerical and semi-analytic

methods, they ﬁnd constraints at τ&30 Gyrs for 20 .vk.200km/s. Here vkis the so-

called kick-velocity which is transferred to the daughter particles during the decay, being

related to via vk∼c for 0.5. The analysis [36] builds up on this work and uses

Milky Way satellite galaxies observed by DES, excluding τ < 18 Gyrs for vk= 20 km/s. This

probe is extremely sensitive to the low regime which still aﬀects the halo distribution and

substructure due to the low virial velocities in dwarf galaxies.

Even when not considering cosmological tensions, it is still interesting to constrain

fundamental properties of dark matter like its lifetime via diﬀerent complementary probes,

regarding how little we know about the actual particle nature, and the fact that very few

particles are naturally stable [13]. Therefore, the degree to which DCDM is compatible with

various cosmological and astrophysical observations is worth studying.

In this work we confront DCDM with measurements of the one-dimensional Lyman-α

forest ﬂux power spectrum, using data from BOSS DR14 [37]. The Lyman-αforest is an

important probe for dark matter models that lead to a modiﬁcation of the power spectrum

on scales k&1h/Mpc, which is typically the case for models addressing the S8tension.

A pecularity of DCDM is that the suppression of the power spectrum occurs at late red-

shifts, such that it is diﬀerent for weak lensing, galaxy clustering and cluster number count

observations that are sensitive mainly to z.1 as compared to Lyman-αmeasurements at

z∼2−4. Therefore, one expects that a larger amount of power suppression is possible at

low redshift as compared to models where the power suppression is imprinted already in the

early universe, making DCDM a promising model in view of the S8tension and Lyman-α

constraints.

The main challenge in any Lyman-αforest analysis is the extraction of the actual

matter ﬂuctuations from the measured ﬂux power spectrum, requiring a description of the

complex intergalactic medium (IGM). In this work, we make use of an eﬀective model that

was already used to analyse BOSS data and extensively validated against hydrodynamical

simulations for a variety of dark matter models as well as massive neutrino cosmologies in the

past [38,39]. It contains a number of free parameters that account for the IGM behavior as

well as uncertainties from strongly non-linear scales entering via the line-of-sight projection,

while taking advantage of the increased reach of a perturbative treatment of the underlying

three-dimensional matter distribution at the relevant redshifts z∼3. This allows us to

determine robust constraints on the DCDM parameters from the Lyman-αforest on the

relatively large scales measured with a high precision by BOSS.

The possibility to address the S8tension with DCDM raises the question about an

embedding of this scenario in a more complete particle physics framework. We make a ﬁrst

step in this direction by exploring the generalization from two- to three-body decays, that

generically occur in models where the involved particle species are fermions. A small mass

splitting can be realized naturally by a pseudo-Dirac fermion pair in that setup.

The structure of this work is as follows: In Sec. 2, we give an overview of the formalism of

DCDM, the basic background dynamics and the generated power spectrum. Then, in Sec. 3,

we review the data set used in this work as well as the eﬀective model and its input and free

parameters. Afterwards, in Sec. 4we present our results within the DCDM parameter space

of lifetime and mass splitting. We also set them in context with earlier works with emphasis

– 3 –

Figure 1: Background evolution of the DCDM (orange), WDM (green) and DR (red) density

parameter for τ= 40 Gyrs and = 0.006 in comparison to a conventional CDM scenario

without any decay (blue). For large redshifts (corresponding to tτ) the decay is irrelevant,

while subsequently the DCDM density drops below CDM, and WDM as well as DR are

produced. The plateau at low redshift is due to the logarithmic z-axis.

on the S8tension. In Sec. 5we comment on an extension from two- to three-body decays.

Finally, we conclude in Sec. 6.

2 Decaying Cold Dark Matter

2.1 Formalism

The DCDM model we study comprises collisionless cold dark matter particles that are un-

stable and decay into two components,

DCDM →WDM + DR .(2.1)

One is a massive daughter acting as a warm dark matter (WDM) component whereas the

other is massless dark radiation (DR, see Sec. 5for an extension to three-body decays). This

model can be described by introducing two new parameters Γ and . The ﬁrst one, Γ, is the

decay width of the CDM mother particle which we usually replace by the decay time τ= Γ−1.

It determines when the decay sets in. The second parameter deﬁned in (1.1) is related to the

mass splitting between the mother and massive daughter particle, and characterizes the ratio

of energy transformed into DR and WDM. The parameter is also related to the amount of

energy that is transformed from rest mass into kinetic energy, and only depends on the mass

ratio of mother and daughter and not on the absolute mass values. In the case of m→0

corresponding to →0.5, only dark radiation is produced by a decay into two massless

daughters. In the opposite case of m→Mcorresponding to →0, the daughter particle

has almost the same mass as the mother particle and therefore the energy transferred to DR

vanishes. Eﬀectively, the decay becomes irrelevant for = 0, independently of the lifetime.

Therefore, in both the limits of τ→ ∞ as well as →0 one recovers ΛCDM.

– 4 –

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TUM-HEP-1420/22DecayingDarkMatterandLyman-forestconstraintsLeaFu,MathiasGarnyPhysikDepartmentT31,James-Franck-Str.1,TechnischeUniversitatMunchen,D-85748Garching,GermanyE-mail:lea.fuss@tum.de,mathias.garny@tum.deAbstract.DecayingColdDarkMatter(DCDM)isamodelthatiscurrentlyunderinves-tigationregard...

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