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Planck Mass Charged Gravitino Dark Matter

Krzysztof A. Meissner1 and Hermann Nicolai2

Pasteura 5, 02-093 Warsaw, Poland

Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)

Mühlenberg 1, D-14476 Potsdam, Germany

Following up on our earlier work predicting fractionally charged supermassive gravitinos, we

explain their potential relevance as novel candidates for Dark Matter and discuss possible signatures and ways to detect them.

I. INTRODUCTION. motivated by inﬂationary cosmology, the mass of the DM

constituents, though very large, is usually still assumed to be well below the Planck scale, but instead on the

In very recent work we have raised the possibil-

order of the scale of inﬂation . 1016 GeV [8–12]. By ity that, very unconventionally, dark matter (DM) could contrast, the present model combines Planck mass with consist at least in part of an extremely dilute gas of very fractional electric charges and strong interactions of Stan- massive stable gravitinos, which are furthermore frac- dard Model (SM) type in a way that is completely new tionally charged and possibly strongly interacting. In to the best of our knowledge , where, however, only

this article we wish to further investigate this possibility, the non-strongly interacting gravitinos would contribute and to discuss possible observable signatures and ways to signiﬁcantly to DM. This is a main distinctive feature search for them. A scenario based on such large mass DM that sets the present proposal apart from earlier work on candidates is obviously very diﬀerent from conventional

SHDM.

models where the masses of putative DM constituents usually range from fractions of an eV (for axion-like DM) Perhaps even more importantly, the present scenario to the TeV scale (for WIMP-like DM); for supersymmet- is based on a fundamental ansatz that also aims for an ric DM candidates there is a particularly large variety explanation of the fermion content of the SM, and that of mass ranges, owing to the large number of diﬀerent draws its inspiration from the huge duality symmetry

models. With large mass a crucial issue is that of sta- E10 that has been conjectured to underlie M theory . bility because superheavy particles participating in stan- More speciﬁcally, and as explained in , our proposal dard interactions can be expected to simply decay at a relies on an attempt to embed the SM fermions into an very early stage in the evolution of the Universe, un- M theoretic framework extending N = 8 supergravity, less a special mechanism is found that guarantees their which exploits the fact that after complete breaking of

survival to the present epoch. The crucial new ingre- supersymmetry the remaining 48 spin- 21 fermions of this dient ensuring stability here is the fractional charge of theory can be put in precise correspondence with the 3 × the DM candidates, together with their peculiar SU(3)c 16 quarks and leptons of the SM (including right-chiral charge assignments, cf. (1) below. We note that inte- neutrinos), following an insight originally due to , see

grally charged DM candidates (‘CHAMPs’) have already also . We stress that the present version of this pro- been discussed in the literature ; likewise, and more posal does not necessarily require supersymmetry, but exotically, DM candidates with very tiny (unquantized) rather relies on K(E10 ), an inﬁnite-dimensional extension charges have been considered [3, 4]. However, the latter of the usual R symmetries of extended supergravities, and

proposals all concerned sub-Planck mass particles. on the fact that the degrees of freedom corresponding to Although perhaps not so well known, there is already a a combination of eight massive gravitinos and 48 spin- 12 substantial literature on the possibility of DM consisting fermions at a given spatial point (obtained after appropri- of superheavy particles (SHDM), which is now receiving ate decomposition of the D = 11 gravitino components)

renewed attention in the light of the ‘no-show’ of low en- constitute an irreducible unfaithful spinorial representa- ergy supersymmetry at LHC and failed WIMP searches. tion of K(E10 ) [16, 17]. The unaccustomed feature here Early work in this direction includes [5–7] where the DM is that – in contradistinction to accepted model building constituents are assumed to be subject to gravitational wisdom (as e.g. for GUT-type scenarios) – the symmetry

interactions only. Later work incorporates inﬂationary can be so enormously enlarged without increasing the size cosmology into the picture [8, 9], for instance by study- of the fermion multiplet. This interpretation hinges cru- ing production of SHDM in the context of (large ﬁeld) cially on the assumption of emergent spacetime in as inﬂationary models; for more recent work, see also [10– there appears to be no way to achieve this in the frame-

12] and references therein. A recurring feature of these work of space-time based quantum ﬁeld theory. studies is that the SHDM particles are still assumed to Apart from the intrinsic interest of incorporating in- have only weak (or even superweak) interactions with ﬁnite dimensional duality symmetries into uniﬁcation in SM matter, whence they are commonly referred to as entirely novel ways, the main motivation for our proposal ‘WIMPZILLAs’. Since these considerations are mainly comes from the fact that, as far as the fermionic sector

is concerned, it can make do with the particle content of unconﬁned) fractionally charged ﬁnal states in the the SM, that is, the observed three generations of quarks SM into which they could decay in a way compat- and leptons (including right-chiral neutrinos). This is in ible with SU(3)c × U(1)em . Being stable all these accord with indications from LHC that there may not particles should be around us, though in extremely be much in terms of new physics beyond the electroweak low abundance since the only processes changing

scale, and increasing evidence that the SM might survive the gravitino number are annihilations of graviti- up to the Planck scale more or less as is, contrary to nu- nos with anti-gravitinos and these are expected to merous still popular scenarios postulating a plethora of be extremely rare over the whole history of the Uni- new particles at the TeV scale or just beyond. The possi- verse after the Planck era, see below. bility that the present framework also oﬀers new options

for DM is an extra incentive for further study. 4. The color non-singlet gravitinos should form bound states with quarks so as to avoid colored ﬁnal states for temperatures T < ΛQCD . Importantly, since

II. MAIN NEW FEATURES. colored gravitinos have electromagnetic charge + 31

and anti-colored ones − 13 , with the known SU(3)c Our proposal implies a number of highly unusual fea- assignments of the SM quarks there is no way to tures for the DM gravitinos. We caution readers that combine gravitinos with quarks or antiquarks to these features rely on a number of assumptions that are build color singlet states that are neutral or inte- contingent on the proposal of according to which the grally charged. Of course, an important open ques-

full conjectured E10 symmetry and its compact subgroup tion here concerns the strong interaction dynam- K(E10 ) manifest themselves only in a “near singularity ics of these superheavy ’meso-gravitinos’ or ’baryo- limit” where space-time is assumed to de-emerge. With gravitinos’. We here appeal to heavy quark the- this reservation in mind let us list the special properties: ory (see e.g. ), where the conﬁnement scale is set by the diﬀerence between the mass of the

1. All gravitinos are assumed to be extremely mas- bound state meson and the mass of the heavier con-

sive with masses m ∼ MPl , or not too far from this stituent, which is usually of the order of ΛQCD . scale. This high mass value is a consequence of the assumption that supersymmetry – if at all present 5. Independently of whether they are in bound states – is broken already at the Planck scale, leaving no or not, the gravitinos do not interact in any way room for low energy supersymmetry (with a single with the CMB despite their electric charges. This

Majorana gravitino which would manifest itself in follows immediately from the Thomson formula, ac-

completely diﬀerent ways). In fact, as we already cording to which the total cross section (for low emphasized in , supersymmetry might actually energy photons) is proportional to the square of never be realized at any energy as a bona fide sym- Compton wave length of the scatterer (see e.g. metry in the framework of space-time based quan- ). In our case, the relevant scale is the Planck tum ﬁeld theory. length, hence the cross section is suppressed by a

huge factor, and thus completely negligible.

2. The eight massive gravitinos split as

6. By contrast, interactions with charged non-strongly 1 1 2 2 3, ⊕ 3̄ , − ⊕ 1, ⊕ 1, − (1) interacting matter are governed by the Rutherford 3 3 3 3 formula, and therefore much like ordinary charged under SU(3) × U(1). Identifying this SU(3) with particle interactions. Being essentially at rest w.r.t. SU(3)c as in , a complex triplet of gravitinos the cosmic frame (see below) the gravitinos would

would thus be subject to strong interactions (the al- merely ‘stir’ the surrounding charged light matter ternative option of identifying SU(3) with the fam- particles but not aﬀect their thermalization. Unlike ily symmetry SU(3)f is disfavored for the reasons common DM candidates with masses . O(1 TeV) given in ). Furthermore, as explained in , they would thus not produce any signiﬁcant dissi- the U(1) in (1) is identiﬁed with U(1)em whence pative eﬀects in the evolution of the universe, ex-

all gravitinos carry fractional electric charges. As cept possibly in the very earliest moments after the we will see, the SU(3)c assignments in (1) lead to Planck era. distinct and well separated physical consequences:

7. The color singlet gravitinos in (1) (which do not

while the color singlets would mainly contribute to participate in strong interactions) are never in ther-

DM, the strongly interacting color triplet graviti-

mal equilibrium during the evolution of the Uni- nos could play a key role in explaining ultra-high verse after the Planck era, so common astrophysi- energy cosmic rays (UHECR) . cal wisdom (see e.g. [22, 23]) does not apply. This

3. Despite their strong and electromagnetic interac- can be seen as follows. The inverse collision time is

tions with ordinary matter, the Planck mass grav- given by the standard formula Γ ∼ hnσvi where n itinos would be stable. This is due to their frac- is the particle number density and σ the annihila- tional charges since there are simply no (conﬁned or tion cross section. For the annihilation of a charged

gravitino-antigravitino pair of mass M and charge N ≥ 2, but for these one cannot have chiral gauge inter- e into a pair of spin- 12 fermions the cross section actions with non-composite gauge bosons). Depending behaves as σv ∝ α2 /M 2 , where v is the veloc- on their mass, such neutral gravitinos would either de- ity of the incoming particles (which is small) and cay into lighter supersymmetric particles (neutralinos) α ≡ α(M ) = e(M )2 /4π. Thermal equilibrium re- via the Noether interaction present in any supergrav-

quires Γ & H ∼ T 2 /MPl , so with the general ity Lagrangian, or themselves contribute to DM if they formula n = g(µT /(2π))3/2 e−µ/T for particles of cannot decay. Either of these scenarios diﬀers from the mass µ (g = 4 for each massive gravitino species) present one since our gravitino DM candidates do par- this constraint translates into an approximate con- ticipate in SM interactions, but cannot decay because of dition the absence of suitable fractionally charged ﬁnal states

µ 21 in the SM, despite their interactions with SM matter. µ So it is precisely the exotic gravitino charge assignments e−µ/T & (2)

T α(µ)2 MPl that can make our Planck mass gravitinos survive to the

present epoch. which for µ ∼ MPl and T < MPl can never be satis- ﬁed (note that α(µ) . O(0.1) for all SM gauge cou- plings over the whole range of µ from the weak scale III. SOME PROPERTIES OF SUPERHEAVY up to MPl ). In other words, the non-strongly inter- GRAVITINO DARK MATTER acting Planck mass DM gravitinos would be frozen out from the very beginning. Their abundance thus cannot be estimated from thermal equilibrium but As we said, the possibility of DM carrying SM charges

requires a “pre-Planckian” explanation. The rapid has already been considered in the literature, although decrease of the annihilation cross section ∝ MPl −2 not very prominently because DM is usually assumed to of color singlet gravitinos, together with their ex- interact only very weakly with SM matter, apart from treme dilution, also shows that they have no eﬀect their gravitational interactions . The relevant analy- on the CMB or UHECR processes. ses are obviously very model dependent, see e.g. , and

usually apply only for much lighter DM constituents, so

8. By contrast, the strongly interacting (color triplet) accepted cosmological bounds may be invalid for the case

gravitinos can reach thermal equilibrium, due to of masses of the order of MPl considered here. In fact, their strong interactions and the fact that the rel- at least in more conventional DM scenarios, electrically evant cross section does not decrease with energy charged DM is already very strongly constrained by ex- , unlike for the color singlet gravitinos, thus al- isting data: it is either completely diluted, or otherwise lowing for an estimate of the color triplet gravitino the electric charges of putative DM particles must be ex-

density. This density turns out to be too small for tremely small. Indeed, the most stringent cosmological the strongly interacting gravitinos to contribute in bound on the charge of DM particles of mass m is [25–27] any signiﬁcant way to DM, unlike the color singlet m 21 gravitinos. However, they could play a key role in |q| . 7.6 · 10−10 (3) explaining UHECR events . 1 TeV

9. If any signals originating from DM gravitinos were with 90% conﬁdence limit. For the DM candidates usu-

to be found they would provide direct access to ally discussed (axion-like or WIMP-like, or any kind of Planck scale physics. We also note that for a Planck new particle associated with low energy supersymmetry) mass particle the Compton wavelength coincides which are assumed to have masses . O(1 TeV) this im- with the Schwarzschild radius (both are thus nearly plies that the allowed charges are . O(10−10 ). This com- equal to the Planck length). When viewed as mini pletely excludes charged DM of any conventional type

black holes our gravitinos are very close to, but (a possible way out here would be to invoke new U(1) strictly below extremality (because 23 < 1 !). As gauge interactions but there is neither observational ev- a result the attractive force for oppositely charged idence nor any compelling theoretical reason for them). gravitinos is almost doubled, while for charges of Remarkably, however, if we assume the DM particle to the same sign we are very close to a ‘force-free’ have Planck scale mass, then the admissible charge comes

BPS-type situation. Possible consequences of this out to be of order unity: for m ∼ 1019 GeV the above fact for cosmological issues (such as structure for- formula gives mation) remain to be explored, however. |q| . 7.6 · 10−2 (4)

Let us emphasize that the present scenario is com-

pletely diﬀerent from earlier proposals with light neu- Taking into account the theoretical uncertainties and tral (Majorana) gravitinos as DM candidates. In con- model dependencies, this value is quite compatible with ventional scenarios of low energy supersymmetry and charges of order one! supergravity, gravitinos do not carry SM charges (this The assumed large mass of the DM gravitinos has an- would require N -extended supergravities with at least other important consequence: it is a well known result in

general relativity that in the course of the expansion of is usually given as the Universe any peculiar motion w.r.t. the cosmic frame of a massive particle out of equilibrium decreases as the ρDM ∼ 0.3 · 106 GeV·m−3 . (7) inverse of the scale factor. So whatever the initial velocity distribution was shortly after the Planck era, it is reduced If DM is made out of Planck mass particles, this means by a factor of aPL /anow ∼ 10−30 , despite occasio

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