Do I need to bring a printout or digital copy of my travel authorization to the airport?

No. DHS will be able to report the traveler’s ESTA status to the carriers. However, DHS recommends that travelers print the response to the travel authorization application to keep the travel authorization application number and have proof of their ESTA status.

U.S. regulations do NOT require travelers participating in the Visa Waiver Program (VWP) to show a printed copy of the ESTA authorization page for travel. However, it is recommended that you print a copy for your records. If you have not or cannot find your application number, you can obtain it through the ESTA website by entering your passport number, country of nationality, date of passport issue, passport expiration date and date of birth.