SuperWIMP Solutions to Small Scale Structure Problems

Short version: this is a four-page letter that takes Kaplinghat's general argument and evaluates it for gravitino superWIMPs with sneutrino or photino NLSPs. The new content is Figs. 1 and 2 — the mapping onto the (m_SWIMP, Δm) plane showing that weak-scale masses land in the preferred Q and λ_FS windows. That is a real, useful result, and the paper credits Kaplinghat up front rather than burying it in a footnote. The novelty is properly scoped as a model-specific application, not a new mechanism, and the abstract says so (abstract:s3). I'd rather see that than an inflated claim of priority. What it does well: Eqs. (1)–(4) are correctly assembled from Hogan–Dalcanton and Lin et al., the lifetime formulas are quoted from the authors' earlier work, and the logic is clean — compute from particle physics, compare to an external observational target. No fitting to the small-scale data. The BBN discussion is brief but honest about where the constraints bite: three-body decays, small branching ratios, fine above roughly 10⁶ s. The soft spot worth your attention: Q and λ_FS are not independent. Eqs. (1) and (4) make both functions of u_X τ_X^1/2, so Q λ_FS³ is pinned at Q0 × (1 Mpc)³ up to the log factor. The paper says this explicitly — 'Q and λFS are both functions of u_X τ^1/2_X, and so are correlated' — so it is not hidden. But it means the 'simultaneous' satisfaction is one numerical coincidence, and a tight one: λ_FS = 1.0 Mpc gives Q = Q0, and λ_FS = 0.63 Mpc already gives Q = 4Q0. The overlap of the two preferred windows is narrow, and the O(1) corrections from the exponential production-time distribution are deferred to Ref. [28], which is in preparation. That is the piece I would want before believing the shaded overlap survives. The 'Remarkably' in the text is a bit more than the arithmetic supports. Second, the preferred windows themselves are imported with no error bars and no independent test here. The paper is upfront that this is a plausibility argument, not a demonstration — no N-body, 'helps resolve' rather than 'resolves.' That is the right hedge, and I would not hold it against them. Who it is for: anyone working on superWIMP cosmology or non-thermal dark matter and small-scale structure. It is the standard citation for that specific claim. Recommendation: worth a referee. It is a legitimate, well-scoped letter; the referees should push on the robustness of the window overlap and on how much of the quantitative case rests on Ref. [28].

The central claim (abstract:s3) is that superWIMPs have both 'sufficiently large free-streaming lengths and low phase space densities.' Eqs. (1) and (4) show these are not two conditions but one: Q ∝ u_X^{-3} τ_X^{-3/2} and λ_FS ∝ u_X τ_X^{1/2} (up to the mild log factor), so both depend only on w ≡ u_X τ_X^{1/2}. The paper acknowledges this ('Q and λFS are both functions of u_X τ_X^{1/2}, and so are correlated'), and notes the degeneracy is broken only for u_X ≲ 1, deferring that regime to Ref. [28], which is in preparation. What remains unresolved is the robustness of the coincidence: the paper does not state the invariant combination Q λ_FS^3 (fixed by Q0, Ω h², and the log factor, independent of u_X and τ_X) and check it against the preferred windows, nor does it show that the O(1) corrections from the exponential distribution of production times — explicitly deferred to [28] — leave the shaded overlap in Fig. 1 intact. If those corrections move the overlap out of Q0 < Q < 4Q0 or 0.4 < λ_FS < 1.0 Mpc, the 'simultaneous' claim fails for all decay parameters, not just the plotted ones. The paper's own framing ('Remarkably, preferred values of Q and λFS are simultaneously realized') overstates the independence of the two successes.

The paper is a short, honest letter. Eqs. (1)-(4) are standard and internally consistent: I checked the normalization of Eq. (1) against Q0 = 1.0e-27 GeV^4 and the scaling of Eq. (4) against R_EQ ≈ 93 Mpc and t_EQ ≈ 2.2e12 s, and both reproduce the quoted 1.0 Mpc at τ_X = 10^6 s, u_X = 1. The physics is standard superWIMP cosmology, and the relic-density inheritance is correctly stated. The reader's CONDITIONAL verdict is appropriate, and I agree the imported windows (Refs. [15], [16], [26], [27]) are a soft spot. But I would sharpen the weakest assumption: the paper's rhetorical force comes from presenting two virtues, and the reader treats them as two. They are one. The paper acknowledges the degeneracy in a single sentence but does not draw out the consequence — that the simultaneous satisfaction is a single numerical coincidence fixed by Q0 and the λ_FS normalization, and that the escape hatch (u_X ≲ 1) is in an unpublished reference. This is not a correctness error; it is a scoping issue that the paper's own 'Remarkably' sentence papers over. The concrete test above would settle whether the coincidence is robust. If it is, the paper's claim stands as a plausibility argument, which is all it claims to be. I would not change the verdict: CONDITIONAL remains right, because the central claim is a plausibility argument whose quantitative support partly rests on an in-preparation reference.

If it holds, the result is a genuinely attractive unification: the same late-decay kinematics fixed by M_Pl and M_W that gives superWIMPs the correct relic density also gives them phase-space densities and free-streaming lengths in the ranges that small-scale structure observations seem to favor. The prediction is parameter-free in the relevant sense — Q and λ_FS follow from the gravitino and NLSP masses with no fitting to the small-scale data — and it is falsifiable, as the authors note, through the reionization epoch and Lyman-alpha constraints. The paper also gives appropriate credit to Ref. [25] rather than overclaiming novelty, and the numerical values in Eq. (1) and the Q0 conversion check out dimensionally. The main caveat is that the 'preferred' windows are imported from Refs. [15], [16], [26], [27] rather than derived here, so the significance is contingent on those windows surviving scrutiny.

Cold dark matter made of weakly-interacting massive particles explains structure on large scales but predicts too much power on scales below about a megapace: halos come out too cuspy, cores too dense, and satellite galaxies too numerous. This paper argues that a variant called superWIMP dark matter fixes those small-scale problems for free. In a superWIMP scenario the WIMP freezes out as usual and then decays, at times of $10^5$ to $10^8$ s, into a stable particle that interacts only gravitationally, so the dark matter is born late and fast. That late, energetic birth lowers the phase-space density of the dark matter and lets it stream out of overdense regions before matter-radiation equality, which is exactly the pair of effects needed to soften cusps and damp small-scale power. The appeal is that the relic density is inherited from the decaying WIMP rather than tuned, so the same particle physics that motivates WIMPs survives intact.

What carries the argument. Two quantities carry the argument. The first is the phase-space density $Q = 1.0/1.0^3$, the dark matter mass per unit of six-dimensional phase space, whose fine-grained value is conserved for a collisionless, dissipationless gas and whose coarse-grained value can only decrease. Observed galaxies sit near $Q_0 = 1.0$-$4.0$ times $Q_0$, so a viable model must not start below that floor, and values close to it are the ones that tame cusps. The second is the free-streaming length, the distance the dark matter travels from its production time until matter-radiation equality, computed by integrating $v(t)/a(t)$ and reducing, in the relativistic-at-production case, to about $1.0$ Mpc times $u_X$ times the square root of $1.0^2$ s divided by the lifetime, with a mild logarithmic correction. Because both $Q$ and the free-streaming length depend on $u_X$ times the square root of the lifetime, they are correlated as they are for warm dark matter, except when $u_X$ is at or below one, where the correlation breaks and new parameter space opens.

Core claim. The paper's claim is that superWIMP dark matter naturally lands in the two windows that small-scale structure observations seem to prefer. Using $Q = 1.0$-$4.0$ times $Q_0$ with $Q_0 = 1.0^{-27}$ GeV$^4$ as the phase-space-density target, and roughly $0.4$ Mpc to $1.0$ Mpc as the free-streaming target, the authors derive $Q$ and $Q_0$ in terms of the superWIMP velocity at production $u_X$, the WIMP lifetime $1.0^6$ s, and the relic density. For gravitino superWIMPs with either a sneutrino or a photino as the next-to-lightest supersymmetric particle, they plot the preferred bands in the plane of superWIMP mass and mass splitting and find that both bands are crossed simultaneously for weak-scale masses, with the sneutrino case requiring the next-to-lightest particle to be heavier than about 500 GeV. They also check that Big Bang nucleosynthesis and cosmic microwave background constraints do not close the relevant lifetime range, since the hadronic branching ratios for sneutrino and photino decays are of order $10^{-3}$ and hadrons appear only in three-body modes.

The premise it rests on. The argument rests on the claim that the observed-preferred windows, phase-space density between one and four times $1.0^{-27}$ GeV$^4$ and a free-streaming length between about $0.4$ and $1.0$ Mpc, are the ranges that actually cure the small-scale problems, and those windows are taken from other papers rather than derived or simulated here.

Gravitino superWIMPs with weak-scale masses and a sneutrino or photino next-to-lightest particle fall in both preferred bands at once, so no new tuning of masses or couplings is needed beyond what supersymmetry already supplies.

The dark matter relic density is inherited from the decaying WIMP rather than set by the superWIMP itself, so the successful WIMP relic-density prediction is preserved.

Cuspy cores, dense cores, and the excess of dwarf-galaxy subhalos should be softened relative to cold dark matter, and the disk angular-momentum problem should be eased, because power is reduced on scales below about a megapace.

Big Bang nucleosynthesis and cosmic microwave background spectral distortions do not exclude the scenario for lifetimes above about $10^6$ s, because hadrons appear only in three-body decays with branching ratios near $10^{-3}$.

If the decaying particle is a charged slepton rather than a neutral one, the dominant effect on the power spectrum is not free streaming but the acoustic oscillation of the slepton-baryon-photon fluid before it decouples, which can damp power more strongly than free streaming does.

The same machinery predicts a correlation between the core size of a dwarf galaxy and its abundance: if superWIMPs set both $Q$ and the free-streaming length through one combination of velocity and lifetime, then the halos that are least cuspy should also be the ones missing from the subhalo count, which is a joint test rather than two separate ones.

A charged-slepton next-to-lightest particle would leave a distinct imprint in the acoustic peaks of the matter power spectrum, so the damping mechanism itself could be read off from the shape of the small-scale spectrum rather than only from its cutoff.

Because the free-streaming window is narrow, a modest tightening of the Lyman-alpha bound would push the natural gravitino mass range below the weak scale, which would turn a virtue of the scenario into a pressure point on the supersymmetric mass spectrum.

The epoch of reionization is the cheapest existing handle on this scenario: earlier reionization requires higher phase-space density, so a confirmed redshift of reionization well above six would squeeze the same region of parameter space that the cusp solution needs.

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