Using 'kMDItemContentModificationDate' in Shell Script

I want to find files modified on a specific date. It is not important what time of day they were modified. I tried the following and got an empty list (no error):

set theFolder to (choose folder)
set folderPOSIX to quoted form of POSIX path of theFolder
set modList to paragraphs of (do shell script "mdfind -onlyin " & folderPOSIX & " 'kMDItemContentModificationDate = 2015-01-15 00:00:00 -0400'")

If I understand this correctly, I am asking for files in a specific folder (directory) which were modified on Jan 15, 2015. If I did this right (apparently not), it should find at least one file that was modified on that date, because I can see in the window of the folder I chose that there is a file modified on Jan 15.

Also, not sure what the '-0400' part is for. Is there some way that I can get the files for Jan 15, regardless of the time of day they were modified.