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We construct semiglobal singular spacetimes for the Einstein equationscoupled to a massless scalar field. Consistent with the heuristic analysis ofBelinskii, Khalatnikov, Lifshitz or BKL for this system, there are nooscillations due to the scalar field. (This is much simpler than theoscillatory BKL heuristics for the Einstein vacuum equations.) Prior resultsare due to Andersson and Rendall in the real analytic case, and Rodnianski andSpeck in the smooth near-spatially-flat-FLRW case. Similar to Andersson andRendall we give asymptotic data at the singularity, which we refer to as finaldata, but our construction is not limited to real analytic solutions. Thispaper is a test application of tools (a graded Lie algebra formulation of theEinstein equations and a filtration) intended for the more subtle vacuum case.We use homological algebra tools to construct a formal series solution, thensymmetric hyperbolic energy estimates to construct a true solutionwell-approximated by truncations of the formal one. We conjecture that theimage of the map from final data to initial data is an open set of anisotropicinitial data.

Semiglobal non-oscillatory big bang singular spacetimes for the Einstein-scalar field system