What does Dark matter look like in non-susy SO(10) models?

A theoretical answer: a scalar 16 

The existence of Dark Matter (DM) of the Universe is now established without doubt [1]. However, the fundamental physics behind it is unknown at present. In the most popular new physics scenario containing DM – supersymmetry – discrete R-parity is imposed by hand to prevent phenomenological disasters such as fast proton decay [2]. Similarly, in dedicated DM extensions of the standard model (SM) with new singlet [3], doublet [4] or higher multiplet scalars [5], ad hoc Z2 symmetry must be added to ensure the stability of DM. These phenomenological models cannot answer the two most fundamental questions related to DM: (i) why this particular multiplet or particle constitutes the DM of the Universe?; (ii) what is the origin of the imposed Z2 symmetry? Therefore the underlying physics principles related to the existence of DM remain obscured. In this work we argue that the existence of DM of the Universe can be a consequence of Grand Unification (GUT). The GUT framework not only explains the origin of DM but also determines the type of the DM particle and constrains its properties. In this scenario the existence of DM, non-zero neutrino masses via seesaw [6] and baryon asymmetry of the Universe via leptogenesis [7] all point to the same GUT framework. We show that the Z2 symmetry needed for DM stability could be a discrete remnant of GUT symmetry group, such as SO(10) [8] that we choose to work with in the following. When breaking SO(10) down to the SM gauge group SU(2)L×U(1)Y, the SO(10) embedded U(1)X, where X is orthogonal to the SM hypercharge Y, leaves unbroken Z2 [9, 10]
PX = PM = (−1)3(B−L), (1)
which is the well known matter parity PM. Due to its gauge origin PM is a symmetry of any SM extension including non-SUSY ones. In the latter case group theory predicts uniquely, without any detailed model building, that the only possible Z2-odd multiplet under Eq. (1) is the 16 of SO(10) [11]. As inclusion of the fourth fermion generation 164 to the SM is not supported by experimental data, the non-SUSY SO(10) GUT predicts that the DM is a mixture of SU(2)L×U(1)Y  PM-odd complex scalar singlet S and neutral component of doublet H2 belonging to a new scalar 16 of SO(10). Thus the DM of the Universe corresponds to the scalar analogues of the fermionic neutral matter fields, the right-handed neutrino NR and the left-handed neutrino νL, respectively. Preserving PM requires SO(10) breaking by an order parameter carrying even charge of B − L [910]. Therefore SO(10) breaking also generates heavy Majorana masses which induce the seesaw mechanism as well as leptogenesis. 
To test the proposed DM scenario we study the scalar potential of a minimal SO(10) GUT model containing one scalar 16 for the DM and one scalar 10 for the SM Higgs double...

 DM direct detection cross-section per nucleon vs. MDM. Color shows SM Higgs masses from 115 GeV (red) to 170 GeV (violet). The points shown encompass the whole parameter space allowed by theoretical and experimental constraints. [Since 2009 all the region above Xenon100 has been excluded, see next paragraph]
The direct DM interaction with nuclei occurs via the SM Higgs boson exchange...  If MDM<∼300 GeV, cancellation between different terms in [the DM-Higgs effective coupling] is possible and the spin independent direct detection cross section can be accidentally small, cf. Fig [above]
Based on SO(10) GUT, we have presented a minimal DM model, calculated the full set of its RGEs and studied its predictions. We find that the EWSB occurs radiatively due to SM Higgs boson couplings to the DM, analogously to SUSY models. The thermal relic DM mass is predicted to be MDM<∼O(0.1−1) TeV by the requirement of perturbativity of model parameters up to the GUT scale.
(last revised 14 Dec 2009 (this version, v3))

A phenomenological comment

The red line is the previous best limit from Xenon100. The blue line is the current 90% CL limit from LUX, which puts them at the pole position in the entire mass range above GeV. They are the first to break the 10^-45 cm^2 cross section barrier: the limit goes down to 7.6*10^-46 cm^2 for dark matter mass of 33 GeV. To put it into perspective, the LHC can currently study processes with a cross section down to 10^-39 cm^2 (1 femtobarn). The inlay shows the low mass region where positive signals were claimed by CDMS-Si (green), CoGeNT (orange), CRESST (yellow) and DAMA (grey). All of these regions are now comfortably excluded, at least in the context of simple models of dark matter.

So, the light dark matter signal that has been hanging around for several years is basically dead now. Of course, theorists will try to reconcile the existing positive and negative results, just because it's their job. For example, by playing with the relative couplings of dark matter to protons and neutrons one can cook up xenophobic models where dark matter couples much more strongly to silicon and germanium than to xenon. But seriously, there's now little reason to believe that we are on the verge of a discovery. Next time, maybe.
Fiat LUX, Jester, 30 October 2013

More about the race to detect DM wimps here.

More about scalar dark matter model building
Contrary to what Jester says half kidding, theorists can make their job to escape the direct phenomenological constraints in a little less opportunistic way than just building xenophobic models, but in extending the philosophy developed in the former paragraph in a recent article from 2014 for instance which reads in its conclusion:

We have explored the phenomenology of an inert doublet and complex scalar dark matter model stabilized by ZN symmetries, with explicit investigation of the Z3 and Z4 cases. The new feature of these models as compared to the Z2 case is the possibility of semi-annihilation and dark matter conversion. This has important consequences for all dark matter observables.
In the Z3 model, semi-annihilation processes, e.g. x1x1 → x1h, can give the dominant contribution to the relic abundance through the cubic (µ00 SS3) or quartic (λS12S2H† 1H2) terms in the scalar potential. This means that the λS1 parameter which sets the coupling of DM to the Higgs and thus the direct detection cross section is not uniquely determined by the relic density constraint as occurs in the Z2 model. Large semi-annihilation is therefore associated with suppressed direct detection rate. While the bulk of the points will be testable by ton-scale detectors, it is possible to satisfy the constraints from vacuum stability and globality of the minimum of the potential with very small values of λS1 – hence to escape all future searches, in particular when the DM is near the TeV range. The direct detection limits from LUX almost completely rule out the region where dark matter masses are below 120 GeV since for kinematic reasons the semi-annihilation does not play an important rôle (the Higgs cannot be produced in the final state)... Furthermore we have shown that the model can be perturbative up to the GUT scale even with a large fraction of semi-annihilation. Enlarging the symmetry to Z4 entails two dark sectors, hence two dark matter candidates: a singlet and a doublet. In this case both semi-annihilation and dark matter conversion significantly affects the dark matter phenomenology of the model. While this model shares many characteristics of the inert doublet model especially when interactions between the two dark sectors can be ignored, the presence of the singlet dark matter candidate means that the doublet DM could only contribute to a fraction of the relic density (and vice versa). This means in particular that the doublet DM can have any mass instead of being confined to be at the electroweak scale or heavier than 500 GeV as in the inert doublet model. We found that for the sub-dominant dark matter component, it is possible to have a detectable signal in future direct detection experiments even after taking into account the fraction of each component in the DM density. This occurs in particular when the sub-dominant component is the doublet since it typically has a large direct detection rate. Furthermore in some cases a detectable signal in future ton-scale experiments is predicted for each DM component, opening up the exciting possibility of discovering two DM particles.
(Submitted on 19 Mar 2014)