Well, in the 'big mom is luffy's mom fanfic', they might have crafted a story where Big Mom is Luffy's mom. But it goes against what we know from the official 'One Piece' story. Fanfictions like this can be really interesting as they can rewrite the story in unexpected ways. They might have some interesting plot twists and explanations within the fanfic to justify this relationship, but it's not part of the main 'One Piece' universe.
One possible plot implication could be a change in Luffy's power source. Since Big Mom has such unique and powerful abilities, Luffy might inherit or be related to some of those powers in the fanfic. Maybe his Devil Fruit ability could be related to Big Mom's in some way.
As of now, in the manga, the identity of Luffy's mom remains unknown. There have been many theories and speculations among fans, but no official confirmation.
She could be a former pirate captain herself. Maybe she was one of the most feared pirates in her time, and her skills and reputation were passed down to Luffy in some way, even if he didn't know it was from his mother.
They could start with a big hug. Then Shanks might tease Luffy about his still - crazy appetite. Luffy, in turn, could show off his new crew members to Shanks.
In a fanfiction where Luffy meets Roger, it could be an amazing encounter. Roger might see in Luffy the same spirit of adventure and freedom that he had. He could pass on some hidden knowledge about the One Piece or give Luffy a cryptic hint about the true nature of the Grand Line. This meeting could also inspire Luffy even more, fueling his determination to become the Pirate King. It would be a moment full of emotion and significance for both characters and for the entire One Piece universe.
It could be a powerful pirate crew that has a vendetta against either Luffy or Sabo. Maybe they have some history with the Straw Hat Pirates or Sabo's group.
Well, in such a fanfiction, Luffy might gain some valuable advice from Roger. Maybe Roger could share his experiences about the One Piece and the Grand Line, which would inspire Luffy further in his journey to become the Pirate King.
A possible plotline could be a battle scenario. Maybe there's a powerful enemy threatening both Luffy's crew and Marco's group. So they meet on the battlefield and have to quickly figure out how to work together. Their different fighting styles, Luffy's Gum - Gum powers and Marco's phoenix - related abilities, make for an exciting combination in combat.