There's a lot riding on the US CPI report later today, especially with Treasury yields having threatened multi-decade highs over the past week. Going into the report, the consensus is that headline inflation is going to look rather ugly. The question now though is whether markets will actually care all that much.Headline inflation is expected to rise by 0.6% on the month, taking the annual estimate to 3.6%. It is anticipated that much of the rise will be driven by higher gasoline prices amid the ongoing tensions in the Middle East. Looking to core inflation, that is expected to rise by a more modest 0.2% on the month and 2.5% annually.Now, the Fed can arguably afford to look past a temporary spike in energy prices. And that is something I would expect policymakers to do in reacting to this report. But if those price pressures start filtering through to other parts of the economy, that is where the story starts becoming something different altogether.As such, the main focus should really be on core prices today - alongside the details such as shelter costs and services inflation. A surprise there would suggest that underlying price pressures are proving stickier than the Fed might like.As for the bond market, the reaction there could be telling for how broader markets might react to the inflation numbers.A hotter headline figure accompanied by a relatively benign core reading might actually give Treasury yields some room to retreat. After all, the market has already been preparing for an ugly headline print as mentioned above.At this stage, I would argue that it would take a significant upside surprise in core inflation to really send yields surging again. The short-end of the curve is not likely to see much action unless traders become convinced that any inflation surprise warrants a reassessment of the Fed outlook.Now, could that put an October rate hike back on the table? Possibly, but I reckon that's a really tall order. Fed funds futures are showing just roughly 22% odds of traders expecting the Fed to hike again this month. That's a rather slim chance, especially with higher borrowing costs already doing some of the Fed's tightening work.As such, it would probably take a genuine shock in core inflation to change that thinking. Otherwise, December remains the more plausible timeline for the next rate hike with traders pricing in roughly 88% odds already of a move.Taking that into consideration, I would say that we shouldn't be all too surprised if the headline number looks bad but bonds decide to rally anyway in the aftermath of the report. But even then, such a move is likely just traders sensing some short-term relief after all the pressure over the past few weeks.What matters today isn't necessarily how hot inflation looks at first glance, but whether the underlying details give the Fed another reason to act sooner rather than later. So, that could be what markets choose to focus on in terms of reacting to the inflation numbers this week.But in the bigger picture, the narrative hasn't exactly changed for the bond market and for broader markets in general. The US-Iran war is still ongoing and keeping energy prices elevated. Fiscal concerns are still very much present and will not be going away any time soon. And inflation pressures are slowly making their way into the broader economy, so that is not allowing for the Fed and other major central banks to rest on their laurels. This article was written by Justin Low at investinglive.com.