Starting today, you can use your own custom domain for the hosted Login UI — offering your users a unified login experience into user directories managed by Amazon Cognito. To add a custom domain, from the service console enter your domain name, and link it with a security certificate obtained from AWS Certificate Manager. With the newly announced feature, users can now stay within your application’s domain, and thus enjoy a consistent branding experience.

Source: Amazon Web Services News Amazon Cognito Now Supports Custom Domains for a Unified Login Experience