The Perils of Analytic Continuation
Abstract
A nice paper by Morrison 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 2-point 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 , 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.
Keywords
Cite
@article{arxiv.1306.5410,
title = {The Perils of Analytic Continuation},
author = {S. P. Miao and P. J. Mora and N. C. Tsamis and R. P. Woodard},
journal= {arXiv preprint arXiv:1306.5410},
year = {2014}
}
Comments
40 pages, 2 figures (6 figure files), uses LaTeX2e, Version 2 expanded to 43 pages, principally in section 3 to show that even the closed coordinate mode sums break de Sitter invariance and that claims to the contrary are based upon the (admitted) use of negative normed states