list of xfinity approved modem routers

... could you please send me a list of approved modem routers

Follow the "See all modems" link near the bottom of https://www.xfinity.com/support/internet/customerowned and view the devices under the "All compatible modems by brand" heading. For modem/router combination devices. look for the tag "Built-in WiFi: Yes" and rated for the speed you subscribe to. Consider a device perhaps a notch or two faster than your current plan to allow for Comcast/Xfinity's periodic speed increases.