### One SM gauge singlet scalar for dark matter and the inflaton? Ask Xenon1T!

**How physics might be simpler after LHC1 and Planck results**

The most studied proposal is that dark matter (DM) is a thermal relic weakly-interacting massive particle (WIMP). WIMPs typically have annihilation cross-sections comparable to the value required to reproduce the observed density of DM, the so-called “WIMP miracle”. Nevertheless, the non-observation of any new weak-scale particles at the LHC beyond the Standard Model (SM) places strong constraints on many models for WIMPs, such as in supersymmetric extensions of the SM.The absence of new particles may indeed indicate that any extension of the SM to include WIMP DM should be rather minimal. In the present work we therefore focus on a particularly simple extension of the SM, namely an additional gauge singlet scalar, which is arguably one of the most minimal models of DM[2–4].

A similar issue arises from recent constraints on inflation. In fact,the non-observation of non-Gaussianity by Planck [5] suggests that the inflation model should also be minimal, in the sense of being due to a single scalar field. The absence of evidence for new physics then raises the question of whether the inflaton scalar can be part of the SM or a minimal extension of the SM. The former possibility is realized by Higgs Inflation [6], which is a version of the non-minimally coupled scalar field inflation model of Salopek, Bond and Bardeen (SBB) [7]with the scalar field identified with the Higgs boson.A good example for the latter option are gauge singlet scalar extensions of the SM, because the DM particle can also provide a well-motivated candidate for the scalar of the SBB model. In other words, in these models the same scalar particle drives inflation and later freezes out to become cold DM.

The resulting gauge singlet inflation model was first considered in [8], where it was called S-inflation (see also [9]).[The case of singlet DM added to Higgs Inflation was considered in [10]] All non-minimally coupled scalar field inflation models based on the SBB model are identical at the classical levelbut differ once quantum corrections to the inflaton potential are included. These result in characteristic deviations of the spectral index from its classical value, which have been extensively studied in both Higgs Inflation [6, 11–15] and S-inflation [16]. Since the original studies were performed, the mass of the Higgs boson [17] and the Planck results for the inflation observables [1] have become known. In addition, direct DM detection experiments, such as LUX [18], have imposed stronger bounds on gauge singlet scalar DM [19–25]. This new data has important implications for these models, in particular for S-inflation, which can be tested in Higgs physics and DM searches.The main objective of the present paper is to compare the S-inflation model with the latest results from CMB observations and direct DM detection experiments. We will demonstrate that — in spite of its simplicity — the model still has a large viable parameter space, where the predictions for inflation are consistent with all current constraints and the observed DM relic abundance can be reproduced. In addition, we observe that this model can solve the potential problem that the electroweak vacuum may be metastable, because the singlet gives a positive contribution to the running of the quartic Higgs coupling.Intriguingly, the relevant parameter range can be almost completely tested by XENON1T.

Another important aspect of our study is perturbative unitarity-violation, which may be a significant problem for Higgs Inflation. Since Higgs boson scattering via graviton exchange violates unitarity at high energies [26, 27], one might be worried that the theory is either incomplete or that perturbation theory breaks down so that unitarity is only conserved non-perturbatively [28–31]. In both cases there can be important modification of the inflaton potential due to new physics or strong-coupling effects. Indeed, in conventional Higgs Inflation, the unitarity-violation scale is of the same magnitude as the Higgs field during inflation [14, 32], placing in doubt the predictions of the model or even its viability. In contrast, we will show that S-inflation has sufficient freedom to evade this problem, provided that the DM scalar is specifically a real singlet. By choosing suitable values for the non-minimal couplings at the Planck scale, it is possible for the unitarity-violation scale to be much larger than the inflaton field throughout inflation, so that the predictions of the model are robust. Therefore,in addition to providing a minimal candidate for WIMP DM, the extension of the SM by a non-minimally coupled real gauge singlet scalar can also account for inflation while having a consistent scale of unitarity-violation...

We find two distinct mass regions where the model is consistent with experimental constraints from LUX, LHC searches for invisible Higgs decays and Fermi-LAT: the low-mass region, 53 GeV <ms< 62.4 GeV, where DM annihilation via Higgs exchange receives a resonant enhancement, and the high-mass region, ms > 93 GeV, where a large number of annihilation channels are allowed. In both mass regions it is possible without problems to fix the non-minimal couplings ξs and ξh in such a way that inflation proceeds in agreement with all present constraints. In particular, the tensor-to-scalar ratio and the running of the spectral index are expected to be unobservably small. On the other hand,radiative corrections to the spectral index typically lead to a value of ns slightly larger than the classical estimate, i.e. ns > 0.965. This effect is largest for large values of ms and λhs and current Planck constraints already require ms<2 TeV. The entire high-mass region compatible with Planck constraints will therefore be tested by XENON1T, which can constrain gauge singlet scalar DM up to ms ∼ 4 TeV

Felix Kahlhoefer (DESY), John McDonald (Lancaster University)(Submitted on 13 Jul 2015 (v1), last revised 14 Oct 2015 (this version, v2))

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