When customer is logged in and then he wants to go to Home Page by url i.e. www.prestashop.com/index.php then after page reload he is still logged. But when url is without index.php, just only www.prestashop.com, then page behaviorus like client logged out. No USERNAME in top, and he must log in again. I can't find reason.
EDIT
There's no problem with index.php or without in url, there's problem with https/http. Default SSL is enabled. When customer types http instead https then problem apear.