Searches for the Supersymmetric Partner of the Top Quark, Dark Matter and Dark Energy at the ATLAS Experiment

Astrophysical observations suggest the existence of physics beyond the Standard Model (SM) of particle physics to explain the composition and evolution of the universe. Supersymmetry (SUSY) is one of the most favoured theoretical frameworks answering the majority of the shortcomings of the SM. In particular, the postulation of supersymmetric particles with differing spin nicely suppresses the unnatural radiative corrections of the Higgs boson mass, and the lightest supersymmetric particle is an ideal Dark Matter candidate. The former, commonly referred to as the Hierarchy problem, predicts the supersymmetric partner of the SM top quark, the so-called top squark, in the TeV mass range. This mass allows for its direct production at the Large Hadron Collider (LHC) at CERN. This thesis describes the search for direct production of top squark pairs decaying into signatures with jets and missing transverse energy with the ATLAS detector at the LHC. No hint for the existence of top squarks, charginos and neutralinos was found in 36.1 fb$^{-1}$ of proton-proton collision data recorded by the ATLAS experiment in 2015 and 2016 at a centre-of-mass energy of $\sqrt{s}=$13 TeV. Top squark masses up to 1 TeV are excluded at 95% confidence level (CL) depending on the neutralino mass. Sensitivity studies for the full LHC Run 2 dataset which are performed exploiting Boosted Decision Trees and Artificial Neural Networks show that the analysis presented in this thesis has reached almost the maximum achievable sensitivity. The same experimental signature as in the search for the top squark is also predicted by more generic extensions of the SM explaining Dark Matter. Some of these introduce additional spin-0 mediator particles, allowing for the production of Weakly Interacting Massive Particles (WIMPs). Mediator masses below 50 GeV can be excluded at 95% CL, assuming a WIMP mass of 1 GeV and a uniform coupling of the mediator to SM particles and WIMPs. For scalar mediators, the exclusion limits are translated into limits on the spin-independent Dark Matter-nucleon scattering cross section which are compared to the results of direct-detection experiments. The origin of the accelerated expansion of the universe is one of the most intriguing questions of modern cosmology. The exclusion limits on direct top squark production can be reinterpreted in the context of the production of a scalar particle predicted by a modification of general relativity to explain the origin of Dark Energy. The results obtained in this thesis are the first collider-based constraints on couplings of Dark Energy to SM matter. Muons are key to some of the most important physics results published by the ATLAS experiment including the discovery of the Higgs boson and the measurement of its properties. In a separated part of this thesis, the efficiency of the muon reconstruction and identification is estimated and the performance of high-precision Monitored Drift Tube muon chambers under background rates similar to the ones expected for the High Luminosity-LHC is studied based on 4.0 fb$^{-1}$ of proton-proton collision data recorded by the ATLAS experiment in 2016 and 2017 at a centre-of-mass energy of $\sqrt{s}=$13 TeV.