The recent measurement of the Higgs boson mass implies a relatively slow rise of the Standard Model Higgs potential at large scales, and a possible second minimum at even larger scales. Consequently, the Higgs field may develop a large vacuum expectation value during inflation. The relaxation of the Higgs field from its large postinflationary value to the minimum of the effective potential represents an important stage in the evolution of the Universe. During this epoch, the time-dependent Higgs condensate can create an effective chemical potential for the lepton number, leading to a generation of the lepton asymmetry in the presence of some large right-handed Majorana neutrino masses. The electroweak sphalerons redistribute this asymmetry between leptons and baryons. This Higgs relaxation leptogenesis can explain the observed matter-antimatter asymmetry of the Universe even if the Standard Model is valid up to the scale of inflation, and any new physics is suppressed by that high scale. The baryonic isocurvature perturbations generated by the relaxation leptogenesis can also explain the excess found in the cosmic infrared background (CIB) anisotropy.

We begin this dissertation by reviewing the development of the large vacuum expectation value (VEV) of the Higgs and other scalar fields during inflation. We then discuss the postinflationary relaxation of the Higgs field in full detail, and present the relaxation leptogenesis framework using the Standard Model Higgs field as an example.

Next, we extend the relaxation leptogenesis to the elementary Goldstone Higgs (EGH) framework and the pseudoscalar scenario. In the EGH paradigm, the electroweak (EW) scale is not fundamental but radiatively generated. This allows one to disentangle the EW scale from the vacuum expectation of the elementary Higgs field, and construct a very flat scalar potential directions along which the relaxation leptogenesis mechanism can be implemented with larger parameter space.

In December 2015, the ATLAS and CMS Collaborations have reported evidence of a diphoton excess which may be interpreted as a pseudoscalar boson S with a mass around 750 GeV. To explain the diphoton excess, such a boson is coupled to the Standard Model gauge fields via SFF-dual operators, which provide the chemical potential to the lepton asymmetry. Although the diphoton excess turns out to be a statistical fluctuation in 2016, a similar pseudoscalar with greater mass remains a viable model for relaxation leptogenesis mechanism.

Finally, we discuss the imprint of relaxation leptogenesis on the CIB anisotropy. Observations of CIB exhibit significant fluctuations on small angular scales, whose origin remains a question. We consider the possibility that small-scale fluctuations in matter-antimatter asymmetry could lead to variations in star formation rates which are responsible for the CIB fluctuations. We show that the Higgs relaxation leptogenesis mechanism can produce such small-scale baryonic isocurvature perturbations which can explain the observed excess in the CIB fluctuations.

Scalar fields, though simple conceptually and mathematically, can be responsible for a wide array of emergent phenomena, such as spontaneous symmetry breaking, superconductivity, and the production of solitons. These fields may be responsible for the creation of, or even the identity of, dark matter. This manuscript details the production of dark matter from scalar fields in the form of Q-balls, boson stars, and primordial black holes, and explores the consequences of the existence of such objects and their interactions.

Nearly all of the particles discovered to date have Compton wavelengths that are much too small to mediate long-range forces between atoms. In the early Universe, prior to the formation of atoms, the size of the observable Universe was significantly smaller than today. This difference in scales allows particles with small Compton wavelengths to mediate forces in the earliest stages of the Universe. The forces that mediate attractive interactions between particles, such as Yukawa forces, are of particular interest in that era. Yukawa forces, unlike other particle interactions, are always attractive, and generally such forces are much stronger than gravity. The strength of these forces allows for the swift collection and clustering of heavy particles into structures, even during radiation domination. The same Yukawa forces facilitate the removal of energy and angular momentum from these newly formed halos through radiation of scalar particles. This process initiates rapid collapse of the over-dense regions formed by long-range forces. This early structure formation and collapse has a rich phenomenology and can potentially address many open questions in physics and cosmology.

While the Standard Model of particle physics has undoubtedly been an experimental success, several questions remain unresolved. In particular, the Standard Model cannot account for the observed cosmological preference for matter over dark matter, nor does it provide a viable candidate for dark matter. This motivates us to consider extensions to the Standard Model; in this thesis, we will focus on several extensions of the Standard Model in which the formation of bound states is a significant factor. We will argue that the formation of bound states produces new phenomena that can address these unsettled questions.

First, we consider a strongly-coupled version of the Minimal Supersymmetric Standard Model. We demonstrate that in this model, electroweak symmetry breaking may be triggered by the presence of squark bound states which mix with the fundamental Higgs boson. Next, we show that this model has a viable phenomenology (e.g., it does not have large flavor-changing-neutral-currents or break SUC(3) symmetry). Additionally, this strongly-coupled version of the MSSM can relatively easily accommodate electroweak scale baryogenesis.

Following this, we turn our attention to the possibility of dark matter bound states in asymmetric dark matter models. We first consider a simplistic scalar model and demonstrate that bound state formation can produce a detectable gamma ray excess in certain regions of parameter space. This signal is produced through the decay of the dark force mediator whose emission necessarily accompanies bound state formation. Next, we consider models in which the dark matter self-interactions are described by a broken UD (1) gauge group. We argue that in such models dark matter is generically multi-component, consisting of two species of ions along with dark atoms. We then investigate the possibility of using these self-interactions between the different species to alleviate tension between the cold dark matter paradigm and observations of dwarf galaxies, while retaining the ellipticity of larger halos.

Finally, we consider the formation and growth of Q-balls (non-topological solitons) in a simplified model inspired by the MSSM. In particular models, Q-balls can trigger a phase transition once they reach a critical size. In certain regions of parameter space, small charge Q-balls can be approximated using the Bethe-Salpeter equation. This allows us to study the growth of small Q-balls; by joining this to the semi-classical regime at large charges, we can analyze their growth from individual squarks to critical size. In our simplistic model, we show that Q-balls can indeed reach critical size on cosmological time scales.