Massless scalar field in a de Sitter universe and its thermal flux

Absorption Probability of De Sitter Horizon for Massless Fields With Spin

“…Lohiya and Panchapakesan [4] derived Γ and showed that the result agreed with ours in Eqs. (19) and (20).…”

“…The fact that the the corresponding field equations around black holes can not be expressed by the special functions prevent us from getting analytic expression for high-frequency mode. On the other hand, the Hawking radiation caused by the cosmological event horizon [3] seems to be much easier to handle because it is known that the scalar field equation in static coordinates of De Sitter space can be solved by Legendre functions [4]. We can therefore convert the solution at the event horizon to our observing world by analytic continuation for all the frequency.…”

“…In the case of the scalar fields s = p = 0, by choosing variable as y = z 2 , the singular point of the equation reduces to 0, 1 and ∞ with definite singularity. The equation can then be solved in hypergeometric functions [4]. This choice of the variable is a natural choice because the metric depends only on z 2 .…”

New Spherical Scalar Modes on the De Sitter Expanding Universe

“…[1] Our scalar modes, in their hypergeometric form remind of the ones found long ago on the static chart. [9] An explicit alternate form of the plane-wave energy basis quantum modes, in terms of two hypergeometric functions was also given, that presents similarities with…”

“…Nevertheless, the free scalar field can be a good model for elucidating the inner workings of a field theory. [6,7,8] A number of solutions for the Klein-Gordon equation in different charts on the de Sitter spacetime have been found, such as the static chart [9], the hyperspherical one [10], or the spatially-flat FLRW one. [11] These three solutions are the best known, being treated even in classical texbooks.…”