Tracing New Physics Across scales: From Collider Signatures to Cosmological Probes

The Standard Model (SM) of particle physics is a remarkably successful and well-tested theory, with predictions that align closely with a wide range of experimental results. Nevertheless, certain observations and theoretical puzzles remain unexplained within this framework, strongly indicating the presence of new degrees of freedom beyond the SM. Uncovering the energy scale and nature of this new physics (NP) is today a central goal in particle physics. To this end, complementary approaches are pursued: precision measurements at colliders, studies of early-universe phenomena, explorations of weakly coupled or hidden sectors, advances in formal quantum field theory, and more. This thesis contributes to this broader effort by focusing on the study of heavy new physics potentially residing at energy scales above the electroweak scale, combining diverse theoretical and phenomenological inputs. We start with an overview of the Standard Model, focusing on electroweak symmetry breaking, the Higgs mechanism, and the flavor puzzle. In addition, we review the thermal history of Standard Model particles in the context of cosmology. Then, we explore how current experimental data can serve as indirect probes of high-energy scales, using the bottom-up approach provided by effective field theories. Within this framework, we discuss scenarios in which new physics is predominantly coupled to the third generation of the Standard Model fermions. Next, we discuss the theoretical challenges and opportunities at future colliders seeking to push the boundaries of energy reach, with a focus on the modelling of initial-state radiation phenomena at lepton colliders. In particular, we discuss the origin and the phenomenological impact of the mixed Z/γ Parton Distribution Function. With an interest in the various signatures that may be hiding at the high-energy frontier, in the last part we consider the cosmological implications of Beyond the Standard Model scenarios that involve supercooled first-order phase transitions, with a particular focus on dark matter and the potential phenomenological signatures. The aim of this Thesis is to contribute to our understanding of the current experimental landscape in particle physics, emphasizing the interplay between existing experimental hints, future collider prospects, and early universe signals of new physics.