Renormalization and decoupling for the Yukawa model in curved spacetime

Hadamard and boundary conditions for the Big Bang quantum vacuum

“…where β k is one of the Bogoliubov coefficients. The number of created particles is minimized when (for more details see [13])…”

“…Selecting initial data to define the vacuum in a rapidly changing region of the spacetime, as is the case for the Big Bang, does not usually render a physically admissible quantum state in the ultraviolet. However, this non-trivial issue can be satisfactorily sorted out by using the states of low energy prescription [12,13]. In this approach, the vacuum is defined as the state that minimizes the energy density smeared over a temporal window.…”

Instantaneous vacuum and States of Low Energy for a scalar field in cosmological backgrounds

“…where ⟨ρ k ⟩ is given in ( 7), f 2 is a positive definite window function, and √ −g = a 4 is the 4volume factor as introduced in [13]. The main idea of this proposal is to find for which solution h k the smeared energy density (17) is minimal.…”

“…In this framework, the vacuum is defined as the state that minimizes the vacuum expectation value of the energy density averaged over a temporal window function supported around a wellmotivated initial time t = t 0 . This method has been successfully employed to obtain physically motivated vacua in bouncing inflationary scenarios in loop quantum cosmology [12], in a CPTsymmetric universe [13], and for the Schwinger effect [14]. Furthermore, the prescription to construct those states was recently extended in Ref.…”

“…Furthermore, the prescription to construct those states was recently extended in Ref. [13] for spin- 1 2 fields. We note here that these low energy states are constructed starting from an analytic solution of the equation of motion of the scalar field modes.…”