Perils of analytic continuation

Abstract

A nice paper by Morrison [1] demonstrates the recent convergence of opinion that has taken place concerning the graviton propagator on de Sitter background. We here discuss the few points which remain under dispute. First, the inevitable decay of tachyonic scalars really does result in their 2point functions breaking de Sitter invariance. This is obscured by analytic continuation techniques which produce formal solutions to the propagator equation that are not propagators. Second, Morrison's de Sitter invariant solution for the spin two sector of the graviton propagator involves derivatives of the scalar propagator at M 2 = 0, where it is not meromorphic unless de Sitter breaking is permitted. Third, de Sitter breaking does not require zero modes. Fourth, the ambiguity Morrison claims in the equation for the spin two structure function is fixed by requiring it to derive from a mode sum. Fifth, Morrison's spin two sector is not "physically equivalent" to ours because their coincidence limits differ. Finally, it is only the noninvariant propagator that gets the time independence and scale invariance of the tensor power spectrum correctly.1 The same de Sitter breaking occurs using the different field variables favored by Kitamoto and Kitazawa [15].2 Ignoring this problem in scalar quantum electrodynamics leads to on-shell singularities in the scalar self-mass-squared [23].3 The mathematical physics computation [29] had a number of significant errors that were discovered by comparison with the cosmological result [19] and then corrected [30].

Graviton loop corrections to vacuum polarization in de Sitter in a general covariant gauge

“…Morrison [93] has shown that constructions which purport to give a de Sitter invariant propagator differ from ours in two ways: (1) the propagator for a scalar with general mass-squared M 2 S must be considered as both de Sitter invariant and well defined for all M (2) it must be accepted that, for constructing the graviton propagator, an arbitrary constant can be added to equation (50). Both of these deviations are illegitimate, resulting in formal solutions to the propagator equation which are not true propagators in the sense of being the expectation values, in the presence of positive-normed states, of the time-ordered product of two graviton field operators [94]. In Appendix B we show that acting the derivatives gives,…”

Perturbative quantum gravity comes of age

“…204 However, the net result was simply to clarify the illegitimate analytic continuations which must be employed to derive formal de Sitter invariant solutions that are not true propagators. 183 There are still some who believe that the de Sitter breaking evident in the all correct solutions (159)(160)(161)(162) and (171)(172)(173)(174)(175)(176) will drop out when gauge invariant operators are studied, as it does from the linearized Weyl-Weyl correlator. 205,206 I doubt this, and I will point out in section 5.4 that it amounts to re-fighting the same controversy over fields versus potentials which was decided for electromagnetism by the Aharomov-Bohm effect.…”

Vacuum states for gravitons field in de Sitter space

“…Motivated by all of these reasons, in this work, we deal with one of the most striking aspects of de Sitter QFT which is still a source of contention in the literature, that is, the question of the existence of a state for free gravitons in dS spacetime that shares the background symmetries (In this regard, see for instance [11][12][13][14]). Let us be more precise.…”