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Most of the extensions of the Standard Model proposes introduction of new particles and interactions. However we cannot predict the properties of this particles from the models themselves. So for example the masses of the particles might be arbitrary, much too big for us to measure them in particle accelerators. Hence narrowing down the possible parameters to a single value or small interval would be a huge advantage in the search for new particles. On the other hand we know that gravity isn’t perturbatively renormalisable. There were various solutions proposed. Steven Weinberg hypothesised that gravity possesses a UV interacting fixed point, which will allow us to treat it as fundamental theory. Moreover such hypothesis has significant influence on particle physics, since one can calculate the allowed coupling constants values in the low energy physics. We apply the hypothesis of asymptotic safety of gravity to the extensions of the Standard Model to make specific, experimental predictions for these particles properties. We apply our analysis to the models extended only by one additional scalar field (and possibly some fermionic or vector particles) called Higgs portal models, with the focus on the Conformal Standard Model, which is one of those. This assumptions will let us calculate the allowed self-coupling parameters (from which we can calculate masses, because the Higgs mass and vacuum expectation value are known experimentally). We expect to obtain the exactly one value satisfying the conditions originating from this assumptions. Such an analysis was never done in context of Higgs portal models with gauge fields or for the CSM. The Higgs portal models are of high importance and attract a lot of attention, because they can deal, in principle, with the problems of the Standard Model, which cannot be solved just by asymptotic safety assumption. The results would be generic for all Higgs portal models. They could be used in the context of non-minimally coupled inflationary models including Higgs portal term, since the non-minimal gravitational couplings are in the direct relation with the self-couplings. In my talk I will outline the asymptotic safety hypothesis, discuss its implications in the particle physics. I will also briefly describe the Conformal Standard Model and show our preliminary results for the values of self couplings in the CSM.

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In the recent years many extensions of the Standard Model (SM) have been developed, which deal with high energy behaviour of SM, such as hierarchy problem. One of those is the Conformal SM (CSM) proposed by Krzysztof Meissner and Hermann Nicolai (https://arxiv.org/abs/1507.01755) with softly broken conformal symmetry mechanism, which stabilises hierarchy and, with proper choice of parameters, is valid up to the Planck scale. That model consists, in comparison to the SM, of additional right-chiral neutrinos and a complex scalar sextet which, in distinction to the Higgs boson, is not coupled to the SM particles.
 On the other hand Planck data favours inflation scenarios of Starobinsky type. Fedor Bezrukov and Mikhail Shaposhnikov proposed a model in which Higgs particle coupled to gravity can serve as an Inflaton in the Starobinsky framework. 
We proposed Inflation with CSM lagragian in Bezrukov-Shaposhinkov manner, doi: 10.5506/APhysPolB.49.115. The inflation is driven by two non-minimally coupled fields. One of those is the SU(2) Higgs-like doublet and the second is associated with the trace of the sextet. These two fields are related to the Higgs particle and “shadow”, heavier Higgs via the mass mixing matrix. Since these type of models, with non-minimal coupling(s), can match the observational data related to inflation, they are of high interest. We calculated spectral tilt, tensor-scalar ratio and estimated a range of coupling to gravity constants for this model. We proposed a natural extension of CSM, which helps to preserve unitarity of the model. Since then our derivation can provide a consistent (up to Planck scale) fundamental theory for both elementary particles (CSM) and Cosmology (Inflation and dark matter candidates predicted by CSM).

 On my poster talk I will outline CSM and Bezrukov-Shaposhnikov model features, then present our model and finally present our progress in the field and plans for the future.

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