Background mode selection during asymptotic-de Sitter inflation

Abstract

For the first time, we choose non-flat vacuum mode for background spacetime based on the minimum number of created particles during early non-de Sitter inflation. In conventional methods for calculating the number of created particles, the flat background is selected automatically and causes a negative number problem for created particles during asymptotic-de Sitter inflation. In a covariant approach to curved spacetime, both real and background spacetimes should be selected, curved and consequently the relation for particle creation should be modify. As an interesting finding from this research, flat space does not include minimum number of particles and there are some asymptotic de Sitter spacetimes with fewer number. Therefore, in the generalized formula for particle creation, we choose a non-flat background containing the minimum number of created particles.

Quasi-de sitter solution, negative norm state and Krein space in cosmology

“…• By adopting method (3), and using ( 12) and ( 33), the spectrum of particles created by purely geometric perturbations in Krein space can be expressed [18,19].…”

“…On the other hand, given that the theory of quantum fields in curved space plays a significant role in the discussion of inflation, so it can be expected that the result of considering the period of quasi-de Sitter inflation can affect the initial value of the quantum fluctuations of the scalar field in the early universe [11]. In fact, these effects can be reflected in the power spectrum of temperature fluctuations in cosmic background radiation [8,[12][13][14][15][16][17][18], which today, with the help of observational information sent to us by satellites, it has provided an important tool for judging the theories and models of cosmologists [9]. Reviewing of the published paper by using our proposal, it will be shown that the choice of non-flat background geometry will have an impact on the final results.…”

“…Reviewing of the published paper by using our proposal, it will be shown that the choice of non-flat background geometry will have an impact on the final results. It will also be more appropriate to use a non-flat background in cosmology because the general convergence principle in the Krein method for cosmology can become establish [18,19]. For this purpose, in the section II, by considering the background field method, we introduce the quasi-de Sitter space-time and it's relation with Krein space.…”