Scalar Tachyons in the de Sitter Universe

Abstract

We provide a construction of a class of local and de Sitter covariant tachyonic quantum fields which exist for discrete negative values of the squared mass parameter and which have no Minkowskian counterpart. These quantum fields satisfy an anomalous non-homogeneous Klein-Gordon equation. The anomaly is a covariant field which can be used to select the physical subspace (of finite codimension) where the homogeneous tachyonic field equation holds in the usual form. We show that the model is local and de Sitter invariant on the physical space. Our construction also sheds new light on the massless minimally coupled field, which is a special instance of it.

Scale-invariant power spectra from a Weyl-invariant scalar–tensor theory

“…Here = −d 2 /dη 2 + ∇ 2 with ∇ 2 = ∂ 2 i is the Laplacian operator. Varying (26) and (27) with respect to i and h i j leads to linearized equations of motion for vector and tensor perturbations,…”

“…where the propagators of massless minimally coupled (mmc) scalar [27] and massless conformally coupled (mcc) scalar [28] in dS spacetime are given by…”

Massless scalar field vacuum in de Sitter spacetime

“…Sitter space (four-sphere) [30,9]. Note that the Lorentzian Wightman function of the Euclidean vacuum can be obtained via continuing the Euclidean z(x, x ′ ) on the S 4 to its Lorentzian version, and assuming the same iǫ prescription as in (12).…”

“…However, if we omit the zero-eigenvalue term in the sum, we get a result that is finite even when m = 0 and then is uniquely defined as [30,9] …”

“…A similar viewpoint has been expressed by Kirsten and Garriga [7], who obtained several results overlapping ours. Related constructions for the massless scalar field have also been carried out using Krein spaces by Bertola, Corbetta, and Moschella [8] and by Bros, Epstein, and Moschella [9].…”