An Air Canada Boeing 787-900, registration C-FNOE performing flight AC-43 from Delhi (India) to Toronto,ON (Canada) with 297 passengers and 14 crew, was enroute at FL310 about 830nm eastnortheast of Moscow Domodedovo (Russia) when the left hand engine (GEnx) flamed out. The crew successfully restarted the engine, declared emergency and diverted to Moscow Domodedovo for a safe landing about 2 hours later. The Canadian TSB reported Russia's Federal Air Transport Agency decided to not open an investigation. Maintenance found a loose connector on the fuel metering unit. The connector was tightened and an engine run successfully performed. The aircraft remained on the ground in Moscow for about 38 hours, then positioned to Toronto as flight AC-7070.