Asymptotics with a positive cosmological constant. II. Linear fields on de Sitter spacetime

Abstract

Linearized gravitational waves in de Sitter space-time are analyzed in detail to obtain guidance for constructing the theory of gravitational radiation in presence of a positive cosmological constant in full, nonlinear general relativity. Specifically: i) In the exact theory, the intrinsic geometry of I is often assumed to be conformally flat in order to reduce the asymptotic symmetry group from Diff(I) to the de Sitter group. Our results show explicitly that this condition is physically unreasonable; ii) We obtain expressions of energy-momentum and angular momentum fluxes carried by gravitational waves in terms of fields defined at I + ; iii) We argue that, although energy of linearized gravitational waves can be arbitrarily negative in general, gravitational waves emitted by physically reasonable sources carry positive energy; and, finally iv) We demonstrate that the flux formulas reduce to the familiar ones in Minkowski space-time in spite of the fact that the limit Λ → 0 is discontinuous (since, in particular, I changes its space-like character to null in the limit). 1 As a result, in the quantum theory, we cannot decompose fields into positive and negative frequency parts even at I. Therefore, in contrast with the Λ = 0 case, there are no candidate Hilbert spaces of asymptotic arXiv:1506.06152v2 [gr-qc] 19 Jul 2015

Asymptotics with a positive cosmological constant. III. The quadrupole formula

“…But because the value of Λ is so small, at a practical level it seems natural to just ignore it and use the well-developed Λ = 0 framework. However, our study of isolated gravitating systems in asymptotically de Sitter space-times in [15] and of linear fields on a de Sitter background in [16] showed that there are some qualitative differences between the Λ = 0 and Λ > 0 cases, making the limit Λ → 0 quite subtle. 1 In particular, the limit of observable quantities associated with gravitational waves can be discontinuous, whence smallness of Λ does not always translate to smallness of corrections to the Λ = 0 results.…”

“…Consequently, unfamiliar features can arise as we move from Λ = 0 to a tiny positive 1 The origin of these subtleties lies in the fact that the observed accelerated expansion makes the asymptotic space-time geometry in the distant future drastically different from that of asymptotically Minkowski space-times. Therefore, although for concreteness and simplicity we will refer to a cosmological constant, as in [15,16], our main results will not change if instead one has an unknown form of 'dark energy '. value both in full general relativity and in the linearized limit. In particular, for every Λ > 0, all asymptotic symmetry vector fields -including those corresponding to 'time translations'-are also space-like in a neighborhood of I + .…”

“…In particular, for every Λ > 0, all asymptotic symmetry vector fields -including those corresponding to 'time translations'-are also space-like in a neighborhood of I + . As a result, while the energy carried by electromagnetic and linearized gravitational waves is necessarily positive in the Λ = 0 case, it can be negative and of arbitrarily large magnitude if Λ > 0 [16]. Since this holds for every Λ > 0, however tiny, the lower bound on energy carried by these waves has an infinite discontinuity at Λ = 0.…”

Induced gravity II: grand unification

“…. " [40]. It seems as if the infrared problems in such spacetimes are more serious than generally believed and not simple generalizations from QED.…”

“…In fact, it has been known for more than 30 years [17,18] that, to one-loop order, there are no unstable modes in de Sitter background provided the parameters of the model obey certain inequalities, which our present model satisfies. 31 To our knowledge, this has been most thoroughly investigated to by date by Ashtekar, Bonga, and Kesevan [38][39][40][41] who emphasize several distinct features of de Sitter space. No matter how small the cosmological constant, there are "no asymptotic Hilbert spaces in dynamical situations of semi-classical gravity" [39].…”