Edit: After half day, my wife’s Mac started having the same problem. I have then applied the solution that I found in the Apple
iOS 7 Developers Beta Now Available From Developers Centre
Apple announced that the developers beta of iOS 7 will be available to developers from today but shortly after the WWDC keynote had finished Apple’s developers centre went down.
It seem the Developers Centre is back up and waiting for the thousands of developers who cannot wait to get their hands on the betas for Mac OS X Maverick and iOS 7.
We have a full run down of everything you need to know about iOS 7 here