Headscratchers / Star Trek Deep Space Nine S 05 E 22 Children Of Time

• Ignoring most of the Timey-Wimey Ball stuff, Yedrin tells the crew all about the time anomaly, giving them the choice of whether or not to avoid it, then lies in an attempt to trick them into not avoiding it. But if he'd simply not told the crew about the anomaly and their future fate, he wouldn't have needed to lie. All he needed to do was avoid contact with the crew as much as possible for two days and let history play out.
• Wouldn't Yedrin know that Jadzia would be able see through his fake science, since he was her?
  • He may simply assume that he's smart enough to have tricked his younger self to give her enough false data that she will believe he's told the truth. Frankly, that part is what always annoyed me about this scenario; Harry Kim spends the better part of a decade trying to find a way to save Voyager ("Timeless"), but the even more brilliant Dax apparently never seriously spent any time trying to find a way to both let the crew go home and maintain the colony even with the better part of two centuries to find a solution?
• The Defiant has access to Starfleet’s records, and they seem to even be locally-stored. So, why didn’t the time-travelling crew try slingshotting around the sun, like that other crew that travelled back in time a couple centuries?
  • Spin-off media, such as Star Trek: Millennium, has established that time travel of any sort leaves the traveller out of sync with the wider universe, so once someone has travelled in time using a particular method, the only way they can go back to their original time is to repeat the circumstances that displaced them from their home time period in the first place. Exactly what would happen to anyone attempting something as suggested above is speculative, but it's generally agreed that at best it wouldn't work and at worse the traveller might be forced out of the universe itself.