2.5 Scattering cross sections

We now move towards discussing the particulate aspects of dark matter, starting with a discussion on the scattering cross-sections of dark matter. At present, many physical properties of the dark matter particle remain highly uncertain. Prospects for studying the scattering of dark matter with each of the three major constituents of the universe – itself, baryons, and dark energy – are outlined below.

2.5.1 Dark matter–dark matter interactions

Self-interacting dark matter (SIDM) was first postulated by [853], in an attempt to explain the apparent paucity of low-mass haloes within the Local Group. The key characteristic of this model is that CDM particles possess a large scattering cross-section, yet with negligible annihilation or dissipation. The process of elastic scattering erases small substructures and cuspy cores, whilst preserving the density profile of the haloes.

However, as highlighted by [399], cross-sections large enough to alleviate the structure formation issues would also allow significant heat transfer from particles within a large halo to the cooler sub-haloes. This effect is most prominent close to the centers of clusters. As the sub-halo evaporates, the galaxy residing within the halo would be disrupted. Limiting this rate of evaporation to exceed the Hubble time allows an upper bound to be placed on the scattering cross-section of approximately 2 − 1 σp∕mp ≲ 0.3 cm g (neglecting any velocity dependence). Note the dependence on particle mass – a more massive CDM particle would be associated with a lower number density, thereby reducing the frequency of collisions.

[658] have performed ray-tracing through N-body simulations, and have discovered that the ability for galaxy clusters to generate giant arcs from strong lensing is compromized if the dark matter is subject to just a few collisions per particle. This constraint translates to an upper bound 2 −1 σp ∕mp ≲ 0.1 cm g. Furthermore, more recent analyses of SIDM models [629, 750Jump To The Next Citation Point] utilize data from the Bullet Cluster to provide another independent limit on the scattering cross section, though the upper bound remains unchanged. [643] have proposed that the tendency for baryonic and dark matter to become separated within dynamical systems, as seen in the Bullet Cluster, could be studied in greater detail if the analysis were to be extended over the full sky in Euclid. This concept is explored in further detail in the following section.

How do these cosmological constraints relate to the values anticipated by particle physics? WIMPs are expected to fall in the range of 10 GeV to a few TeV. The aforementioned values would then correspond to around σp ≲ 10− 24 cm2, at least twenty order of magnitudes greater than what one might expect to achieve from neutral current interactions. Therefore in a cosmological context WIMPs are essentially collisionless, as are axions, since they exhibit an even smaller cross section. Any cosmological detection of SIDM would thus point towards the more exotic candidates postulated by particle physicists, particularly those which are not point particles but instead comprise of extended objects such as Q-balls. A measurement of the scattering cross-section would also place an upper bound on the mass of the dark matter particle, since unitarity of the scattering matrix forbids extremely large cross sections [463], i.e.,

( ) ( ) − 17 2 GeV 2 10km s−1 2 σtot ≤ 1.76 × 10 cm ----- ---------- (2.5.1 ) m χ vrel

2.5.2 Dark matter–baryonic interactions

Currently, a number of efforts are underway to directly detect WIMPs via the recoil of atomic nuclei. The underground experiments such as CDMS, CRESST, XENON, EDELWEISS and ZEPLIN have pushed observational limits for the spin-independent WIMP-nucleon cross-section down to the − 43 2 σ ≲ 10 cm régime.14 A collection of the latest constraints can be found at External Linkhttp://dmtools.brown.edu.

Another opportunity to unearth the dark matter particle lies in accelerators such as the LHC. By 2018 it is possible these experiments will have yielded mass estimates for dark matter candidates, provided its mass is lighter than a few hundred GeV. However, the discovery of more detailed properties of the particle, which are essential to confirm the link to cosmological dark matter, would have to wait until the International Linear Collider is constructed.

2.5.3 Dark matter–dark energy interactions

Interactions in the dark sector have provided a popular topic for exploration, with a view to building models which alleviate the coincidence and fine-tuning issues associated with dark energy (see Section 1.4.4). The great uncertainty surrounding the physical nature of dark energy leaves plenty of scope for non-gravitational physics to play a rôle. These models are discussed at length in other sections of this review (1.4 and 2.11). Here, we only mention that [837] have explored the phenomenology associated with dark matter scattering elastically with dark energy. The growth rate of large-scale structures is artificially slowed, allowing a modest constraint of

σp∕mp ≲ --10-- cm2 g− 1. (2.5.2 ) 1 + w

It is clear that such dark sector interactions do not arise in the simplest models of dark matter and dark energy. However a rigorous refutation of GR will require not only a robust measure of the growth of cosmic structures, but confirmation that the anomalous dynamics are not simply due to physics within the dark sector.

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