On particle creation in the flat FRW chart of de Sitter spacetime

Abstract

The conditions of the Gibbons–Hawking effect, i.e., particle production in the Friedmann–Robertson–Walker chart of the de Sitter spacetime, are revisited. For a theory with a massive scalar and a fermionic field it is shown that, if one considers the Bunch–Davies vacuum state at early times, then only in the case that the condition mc2/ℏH ≫ 1 is fulfilled can one assure that a thermal spectrum of radiation at temperature T = ℏH/2πkB, where kB is the Boltzmann constant, will be obtained at late times. It is pointed out that this important proviso (which is nothing else than the adiabatic condition, as we shall see), is missing in several derivations of this effect in the literature, where the thermal spectrum was obtained without imposing any restriction on the relation between the mass of the field, m and the Hubble constant, H.

Scalar pair production in a magnetic field in de Sitter universe

“…This paper proves for the first time how to solve the Dirac equation when a magnetic field is present, and these results represent the basis for the more recent studies that imply particle production in the presence of external fields [2][3][4][5][6][7][8][9] in curved backgrounds. An important result was obtained recently in [9], where the minimally coupled Klein-Gordon equation was solved in four dimensions in a de Sitter geometry.…”

“…The perturbative approach to the problem of fermions production in magnetic field on de Sitter geometry was used in [13], and the main results prove that the probability of pair production is nonvanishing only in strong gravitational fields. However for a complete picture of the problem of pair production in gravitational fields one needs to combine the nonperturbative results [2][3][4][5][6][7][8], with the perturbative treatment of this problem. This will imply as we mentioned above that the nonperturbative computations to be extended in four dimensions, since only in these cases we will have a complete picture on how the field equations with external field will look like and how these equations can be solved.…”

Different Interpretations of the Particle Production in Quantum Fields Theory

“…Using at this point [20] | (1 + z)| 2 = πz/ sin(πz), we conclude that, when η → 0 − , the number of produced particles, using the diagonalization method, is given by [14] …”

Quantum Dynamics for De Sitter Radiation

“…It has been known that an expanding spacetime produces particles 10 and that the dS space has the Gibbons-Hawking radiation 3,4 (for a recent discussion, see ref. [11]). …”