Particle production in the Early Universe is one of the cornerstones of modern cosmology and plays an important role in dark matter phenomenology. In this talk, I will first discuss the gravitational production of scalars during inflation. I will compare Bogolyubov coefficient and Starobinsky stochastic approaches, showing that they only agree in the limit of infinitely long inflation. High-scale inflation is very efficient in particle production, leading to constraints on the existence of free, light, and stable scalars: such particles are viable only if their masses are below the eV scale or if the reheating temperature is in the GeV range. These constraints motivate scenarios in which dark matter is produced via low-temperature freeze-in. In this framework, I will consider warm Higgs portal dark matter. In scenarios where the Standard Model thermal bath never reaches high temperatures, dark matter production can be suppressed. This allows for a significant dark matter-Higgs coupling, enabling warm dark matter detection via Higgs decay at colliders. I will further discuss the strong Lyman-α bound on the dark matter mass, excluding masses below 50-100 keV, and show how the shape of the warm dark matter momentum distribution is highly non-thermal and not captured by the commonly used αβγ-parametrization.
Seminar organizers