Constraining electroweak baryogenesis and dark matter models with searches for new Higgs bosons in the ATLAS experiment

The Standard Model (SM) of particle physics has been fundamental in understanding particles and their interactions, yet several mysteries remain unresolved. This dissertation explores two of the open questions in particle physics: the origin of the Universe's matter-antimatter asymmetry and the nature of dark matter (DM). This is achieved through extensions of the SM, namely the Two-Higgs-Doublet Model (2HDM) and its interface with DM in 2HDM+$a$. The 2HDM extends the SM by introducing a second Higgs doublet, resulting in five Higgs bosons, pivotal for electroweak baryogenesis. The 2HDM+$a$ additionally introduces a pseudoscalar DM mediator and a fermionic DM particle, offering a comprehensive framework for DM searches. The question of matter-antimatter asymmetry is explored with the search for a heavy $CP$-odd Higgs boson, $A$, decaying into a heavy $CP$-even Higgs boson, $H$, and a $Z$ boson, specifically the $A \to ZH \to \vvbb$ channel, using data collected by the ATLAS detector during the Run 2 of the LHC operation (2015-2018). This analysis constitutes the first search for $b\bar{b}$ resonances with a mass higher than 125 GeV produced in association with missing transverse energy \met. The highest excess over the SM background is observed for the signal hypothesis of ($m_A$, $m_H$) = (600, 300) GeV, corresponding to a local significance of 2.14$\sigma$. Upper limits on the signal cross-section and the relevant exclusion in the $m_A$--$m_H$ plane are obtained for the $CP$- and flavour-conserving 2HDM interpretation, extending the results of previous analyses to higher $m_A$ values. The results are also provided as model-independent upper limits on the production cross-section of a $b\bar{b}$ resonance in association with \met. The nature of DM is explored with a study within the 2HDM+$a$ with a Type-I Yukawa sector. This study lifts the assumption of a degenerate Higgs spectrum, which has been adopted by all collider searches for DM, leading to novel collider signatures. Furthermore, considering a Type-I Yukawa sector relaxes the constraints from flavour physics, expanding the mass range of the additional Higgs bosons to the region below the mass of 125 GeV. The study proposes new benchmark scenarios and signal signatures for future ATLAS and CMS searches.