This is why whole drive encryption is bad. Even creating a "hidden volume" for plausible deniability is going to look suspicious if anyone bothers to ask who so much of the physical HD space is unused by a dummy OS with a curiously small amount of activity recorded in the system logs.
A safer solution is to randomize new drives with GNU shred (faster PRNG than /dev/*random) and store critical info in smaller encrypted containers that hide amongst the noise. Disable swap or use encrypted swap (with random keys) and disable browser disk caching to eliminate saving sensitive transient data to disk. Use an OS that won't record potentially incriminating info in a registry such as USB device serial numbers.
At that point it's much easier to deny the presence of encrypted data or, if forced to admit its presence, you can use the "I forgot" or "I can't regenerate the password" excuse which can't be done believably with a computer in regular use that has whole disk encryption.