... you probably have a time zone issue.

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When you get

Timecop.travel(Date.parse("2011-11-11 00:00") do
  Time.current   => Thu, 10 Nov 2011 23:00:01 UTC +00:00
  Time.now       => Fri Nov 11 00:00:02 +0100 2011
  Date.today     => Fri, 11 Nov 2011
  Date.tomorrow  => Fri, 11 Nov 2011
end

you probably haven't defined a zime zone yet.

So might fix this by adding the following lines to your application.rb:

class Application < Rails::Application
  config.time_zone = 'Berlin' # or whatever your time zone
end

It seems Date.yesterday uses the time zone Time.current uses and Date.today uses the same time zone like Time.now.