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Decaying Superheavy Dark Matter and Subgalactic Structure of the Universe Physics Letters B 594 (2004) 1–7 www.elsevier.com/locate/physletb Decaying superheavy dark matter and subgalactic structure of the Universe Chung-Hsien Chou, Kin-Wang Ng Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan, ROC Received 11 December 2003; received in revised form 20 April 2004; accepted 29 April 2004 Available online 9 June 2004 Editor: J. Frieman Abstract The collisionless cold dark matter (CCDM) model predicts overly dense cores in dark matter halos and overly abundant subhalos. We show that the idea that CDM are decaying superheavy particles which produce ultra-high energy cosmic rays with energies beyond the Greisen–Zatsepin–Kuzmin cutoff may simultaneously solve the problem of subgalactic structure formation in CCDM model. In particular, the Kuzmin–Rubakov’s decaying superheavy CDM model may give an explanation to the smallness of the cosmological constant and a new thought to the CDM experimental search. 2004 Elsevier B.V. All rights reserved. PACS: 95.35.+d; 98.62.Gq; 98.70.Sa; 98.80.Cq 1. Introduction teracting particles. However, there exist serious dis- crepancies between observations and numerical simu- Recent cosmological observations such as dynam- lations of CDM halos in collisionless cold dark matter ical mass, Type Ia supernovae, gravitational lensing, (CCDM) models [3–5], which predict too much power and cosmic microwave background anisotropies, con- on small scales, manifested as cuspy CDM cores in cordantly predict a spatially flat universe containing a dwarf galaxies [6], galaxies like the Milky Way [7], mixture of 5% baryons, 25% cold dark matter (CDM), and central regions of galaxy clusters [8] as well as and 70% vacuum-like dark energy [1,2],termedasthe a large excess of CDM subhalos or dwarf galaxies standard CDM model. The identities and the nature within the Local Group [5]. of dark matter and dark energy are among some of the To alleviate the discrepancies, among many other biggest puzzles in contemporary physics. attempts, models of non-standard interacting CDM Although the nature of CDM is yet unknown, it have been proposed. They include self-interactions [9], is successfully treated in many aspects as weakly in- annihilations [10], and decaying cold dark matter (DCDM) [11,12]. Although these models involve dif- ferent interactions, almost all interactions result in E-mail addresses: [email protected] (C.-H. Chou), an adiabatic expansion of the cuspy halo that lowers [email protected] (K.-W. Ng). the core density and reduces the number of subhalos. 0370-2693/$ – see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physletb.2004.04.082 2 C.-H. Chou, K.-W. Ng / Physics Letters B 594 (2004) 1–7 However, both self-interacting and annihilating CDM phenomenological implications and suggest that some models require embarrassing large interaction cross- on-going experiments could test this scenario. sections that have made the models less appealing. Al- though DCDM models are viable, possible underlying particle physics has been ignored. 2. Kuzmin–Rubakov model Another big puzzle in astrophysics is the origin of the ultra-high energy cosmic rays (UHECR). One may Here we will concentrate on a specific scenario expect that UHECR should originate from some un- proposed by Kuzmin and Rubakov (KR) [19] and known astrophysical sources at extragalactic scales. show how the KR scenario for producing UHECR is Greisen, Zatsepin, and Kuzmin (GZK) [13] observed related to the subgalactic structure of the Universe. that due to inverse Compton scatterings of the relic KR [19] considered an extended standard model photons the UHECR energy spectrum produced at cos- with a new SU(2)X gauge interaction and two left- mological distances should steepen abruptly at en- handed SU(2)X fermionic doublets X and Y and four ergy ∼ 1010 GeV. However, a number of cosmic ray right-handed singlets. Here at least two doublets are events with energies beyond the GZK cutoff have introduced because the SU(2)X anomaly prevents the been observed by Fly’s Eye [14] and AGASA [15]. number of SU(2)X doublets from being odd. All new A simple solution to this impasse is to invoke new particles are singlets of the standard model, while physics in which UHECR can be produced in a cos- some conventional quarks and leptons may carry non- mologically local part of the Universe. Ideas such trivial SU(2)X quantum numbers. The SU(2)X gauge as long-lived metastable superheavy particles that are symmetry is assumed to be broken at certain high en- decaying at the present epoch [16–20], annihilations ergy scale, giving large masses mX,Y to all X and Y of stable supermassive particles in halos [21],and particles. Furthermore, X and Y are assumed to carry collapses of cosmic topological defects [22] have different global symmetries, so there is no mixing be- been proposed. In most of the models the super- tween them. As such, both the lightest of X and the heavy objects can simultaneously be viable candidates lightest of Y, which we call X and Y respectively, for DM. are perturbatively stable. However, SU(2)X instantons In this Letter, we try to address these issues at the induce effective interactions violating global symme- same time within a single theoretical framework. We tries of X and Y . Assume mX >mY , then the instanton pursue the DCDM scenario, suggesting that the CDM effects lead to the decay is decaying weakly interacting superheavy particles X → Y + quarks + leptons (1) with mass of the grand unification scale. In our ∼ −1 × scenario, not only the decay would produce much with a long lifetime roughly estimated as τX mX 4π/α less concentrated cores in CDM halos, but also the e X ,whereαX is the SU(2)X gauge coupling con- 13 decay products contain highly energetic quarks and stant. With the choices mX 10 GeV and αX 0.1, leptons which lead to the production of ultra-high τX 10 Gyr and X particles are decaying at the energy cosmic rays (UHECR) with energies beyond present epoch. There have been many discussions on the Greisen–Zatsepin–Kuzmin cutoff. Moreover, the the production of X particles in the early Universe. longevity of the superheavy particles may shed new X particles may be produced thermally during re- light on the origin of the observed small value of the heating after inflation with the produced energy den- cosmological constant. sity comparable to the critical energy density of the The Letter is organized as follows. In Section 2 Universe [19] (see also Refs. [18,25]). Also, it was we illustrate our idea by using the Kuzmin–Rubakov realized in the same or different context that super- model. After briefly reviewing this model, we show heavy particles can be efficiently generated from vac- in Section 3 how this model can be naturally fitted uum quantum fluctuations during inflation [26] or cou- into the scenario of DCDM. We show how this model plings to the inflaton field during preheating [27]. solves the cuspy halo problem, and find out the The particles X and Y are good dark matter parameter space which allow us to solve the origin candidates. According to KR, there are two possible of UHECR as well. In Section 4 we discuss some outcomes after X particles have decayed. If Y particles C.-H. Chou, K.-W. Ng / Physics Letters B 594 (2004) 1–7 3 are perturbatively stable, they are also stable against low we will simply study the effect of DCDM to the instanton-induced interactions in virtue of energy original NFW profile with α = 1 [3] in Eq. (2).Defin- conservation and instanton selection rules. In addition, ing x = r/r200, it gives the halo mass profile M(x)= if mX mY , an approximately equal amount of Y M200F(x)that is the mass within x and the associated 1/2 particles is produced in the early Universe. Therefore, rotational velocity V(x) = V200[F(x)/x] ,where the decay products would contain stable supermassive M200 = M(x = 1), V200 = V(x= 1),and Y particles that constitute a dominant fraction of ln(1 + cx) − cx/(1 + cx) the CDM with a small admixture of X particles F(x)= . (3) ln(1 + c) − c/(1 + c) as well as highly energetic quark jets and leptons that subsequently produce UHECR. Alternatively, the Suppose a CDM halo gas composed of X particles Higgs sector and its interactions with fermions may be is formed at some high redshift with the NFW profile organized in such a way that Y particles are in fact and a velocity dispersion perturbatively unstable. As such, Y particles would vX = GM ,X/2r ,X, instantly decay into relativistic particles and leave 200 200 metastable X particles being the CDM. where M200,X is the mass of X particles within Intriguingly, it has been recently pointed out that the radius r200,X. The observed velocity dispersion if the longevity of the superheavy particles in the typically ranges from 10 to 1000 km/s for dwarf KR model is due to instanton-induced decays, the halo to cluster halo. In X’s rest frame, the decay (1) observed small but finite cosmological constant can be produces a Y with a recoiling velocity γrcvrc = δ(1 − − = − 2 = − explained by instantons or vacuum tunnelling effects δ/2)/(1 δ),whereγrc 1/ 1 vrc and δ (mX in a theory with degenerate vacua [23].Insucha mY )/mX, and highly relativistic quarks and leptons theory, the vacuum energy density of the true ground of energy Eq,l = γrcvrcmX(1 − δ).Thevalueofδ state is smaller than that in one of the degenerate vacua depends on the detail dynamics of the high energy where we live now by an exponentially small amount model.
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