Despite its apparent weakness, gravity is a vital force driving particle production in the early Universe. To explore this production process, two different but well-established frameworks are commonly used, which are known as the Boltzmann and Bogoliubov approaches. I will first discuss a crucial aspect of these frameworks—their equivalence in pure gravitational production—to answer the question of whether these approaches yield consistent outcomes. In doing so, we will see the phase space distribution as a key quantity. This distribution will then serve as a useful tool to address yet another important question: Did the Higgs field predominantly exist as condensate or fluctuations in the earliest times? which will be discussed in the second part of the talk.