Extravagant defense spending is another cherished art form of representative democracy. This is primarily due to its stimulating effects on shareholder value - and the contributions shareholders make to political campaigns. External threats do help up the extravagance, it is true. However, the Triglavian conquest of several star systems provides ample external threat, not to mention the existence of Adversary Kim. Starting yet another war is probably not necessary.
That said, the president has extended an invitation to the Empire to participate directly in the investigation of this incident:
President Celes Aguard has pledged a “full investigation of Crux Special Tasks Group” and invited the Amarr Empire to send intelligence officers to the Federation for purposes of “sharing any and all evidence uncovered by the FIO, Federation Naval Intelligence and Gallente Police Directorate.”
source