construction at Stockholm Central station

I hope I'm local enough. It is correct that there is no construction at the central station, the railway bridges south of the central station are being renovated. So all southbound trains leaves from the southern station, just south of the bridges in question. It happens that Arlanda Express stops elsewhere, but not at the moment.

And I agree that a commuter train from Arlanda direct to the Southern station is probably the best idea. You can buy the whole trip from Arlanda to Linköping at www.sj.se and then the only difference is that you'll change at a different station. (Leave the train when the sign says "Stockholm Södra").

We flew into Stockholm on 6 June and took the bus from the airport to the main train station, then a taxi to our hotel. I don't remember seeing any construction there.
Two days later we took the train to Copenhagen.

Thank you all SO much!! This is extremely helpful. Can't thank you enough.

Yes, some trains use other stations as well. Just book a ticket from Arlanda C to Linköping at sj.se and the system will tell you the best way to reach Linköping.

Thank you for making this very straightforward! We have used the trains in Germany extensively but Sweden is our new adventure. We have the SJ app all installed and are ready to book a ticket. Thank you very much.