Sorry if this is redundant. I did a quick search and saw nothing on using Chrome cast directly with the goggles.
I bought a cable adapter for HDMI to HDMI micro to fit the goggle input. The Chrome cast can then be plugged in to that cable and powered with any small USB battery charger. The cable to the charger is about 12" long and I haven't optimized a way to secure both the chrome cast and battery to avoid any imbalance of the goggles so I have just draped them over my head for now . The input is recognized in the HDMI source on the goggles and plays nicely.
I bought a cable adapter for HDMI to HDMI micro to fit the goggle input. The Chrome cast can then be plugged in to that cable and powered with any small USB battery charger. The cable to the charger is about 12" long and I haven't optimized a way to secure both the chrome cast and battery to avoid any imbalance of the goggles so I have just draped them over my head for now . The input is recognized in the HDMI source on the goggles and plays nicely.