Desingularization of the Milne Universe

Abstract

Resolution of cosmological singularities is an important problem in any full theory of quantum gravity. The Milne orbifold is a cosmology with a big-bang/big-crunch singularity, but being a quotient of flat space it holds potential for resolution in string theory. It is known however, that some perturbative string amplitudes diverge in the Milne geometry. Here we show that flat space higher spin theories can effect a simple resolution of the Milne singularity when one embeds the latter in 2+1 dimensions. We explain how to reconcile this with the expectation that non-perturbative string effects are required for resolving Milne. Along the way, we introduce a Grassmann realization of the \.{I}n\"on\"u-Wigner contraction to export much of the AdS technology to our flat space computation.Comment: 4 pages, revtex, v2: minor clarifications/corrections, refs added, v3: minor error corrected, v4: published PLB version (essentially

Low tension strings on a cosmological singularity

“…The purpose of our analysis is to show that the problematic tree-level divergences identified in [1] disappear in the large α limit, which resolves the apparent tension between the pathological behavior of tree-level string scattering amplitudes on the Milne orbifold [1] and the recent results suggesting that higher spin theory is well-behaved on the same space [11]. The possible connection between string theory and higher spin theory suggests that string loop corrections should also be well-behaved in the large α limit, but this would be much harder to verify directly, and we will not attempt to do so here.…”

“…That s as a function of v 2 does not have a maximum/minimum at v 2 (v 4+ ) is readily checked. 11 The conclusion of all this is that the potential divergences that could have arisen from (4.5) and (4.6) when they correspond to gamma function poles are actually spurious, and in fact there are no divergences from them (unless the Mandelstam invariants have a maximum/minimum at v 4+ as discussed in the footnote). The conclusion of all this is that the potential divergences that could have arisen from (4.5) and (4.6) when they correspond to gamma function poles are actually spurious, and in fact there are no divergences from them.…”

“…This suggests that this divergence can be understood in terms of intermediate tower of string states going on-shell and is therefore a "good" divergence unrelated to the singu- 11 An exception to this is when we have a maximum/minimum of s or t at v4+. This corresponds to the condition (m3 + m4) = (m1 + m2) which coincides with v4+ = 1 and gives rise to divergences.…”

“…Recently, it was observed in [10,11] that certain cosmological singularities arising as quotients of dS 3 or flat space can in fact be resolved, if we embed these singularities into higher spin theories. 1 In particular, [11] (see also [14]) shows that the Milne singularity can be resolved in the context of flat space higher spin theories [15,16].…”

“…1 In particular, [11] (see also [14]) shows that the Milne singularity can be resolved in the context of flat space higher spin theories [15,16]. The idea is that one can get rid of the metric singularity via higher spin gauge transformations, while preserving the holonomy in the Chern-Simons language.…”