A6 engine ''deep rattling'' noise

Sounds like you damaged the oil pump or the pickup screen.
You won't know until someone removes the oil pan.

I would check exhaust system for loose heat shields or bracket.

Your describing a broken drive belt tensioner, you can probable see it in the engine compartment as the engine is running

READ THIS (happy ending so far...):
audi a4 2L turbo quattro, manual transmission with 98,000 KM. Perfect conditions, no oil leaks whatsoever.

Left the car off for two weeks in very cold weather (-10C down to -25C). When I restarted, it started immediately but with heavy rattling noise due to camshaft adjuster not getting enough oil pressure. After 3 minutes of warming up (outside temp.: -12C) at very low rpm (below 2,000rpm), I start moving the car. Still hearing heavy rattle noise. As soon as I pass 2,000 rpm, I get a scary red warning, low oil pressure. Turn off the engine immediately. In 1 minute, I re-start the car and the engine lights check ok, so I drive in first gear super slow (1,200rpm) hearing the same rattling noise. After another minute, finally the noise all the sudden disappears and the car starts running just fine.

Called Audi dealer and they told me that in extreme weather conditions, I should warm the engine for 10-15 minutes if necessary before start moving.
Take away: luckily, I didn't screw up the engine since I was using it at extremely low rpm (easy to do with clutch and manual transmission) until the oil reached full pressure. I am pretty sure now that the problem was leaving the car off for such a long time in freezing weather. All the oil flows back to the bottom, and when I restarted it, the cold oil with high viscosity took a long time to reach all the parts of the engine, specially the camshaft adjusters that are actuated by using oil pressure. Next day, the car started at -9C perfectly without making any noise (as usual). Basically, the longer you leave your audi in cold weather, the longer you might hear the rattling noise until the oil reach full pressure inside the engine. My car took 6 minutes to fix it after couple of weeks in cold weather. This makes sense to me; in fact, in the past I only heard the rattling noise after leaving the car off for a couple of days in the winter.
So far, this has had an happy ending....

lots of parts, alternator, water pump, a/c compressor lower area . many of them are on the serpentine belt. the pulleys and tensioner can make rattles. you need to confirm which part has the rattle or vibration, use a stick or screw driver. touch one end on the part and the other near your temple...any noise/vibration coming through?

fiind which one it is. lower noise on the crank can also sound like its coming from up front and that's a deep rattle.

Have the code extracted it may have to do with your transmission and weird rattling noise you hear.

if it is under warranty the dealer should have no choice, but you can check this out just in case.
http://www.lemonlawamerica.com/

I had rattling noises as well (over bumps and when I reved the engine) and it turned out to be the heat shields under the car. I took out 2 heat shields covering the two cats on both sides AND two rusted out dangling rings hanging from the exhaust coupler (have NO clue what they were for)..This has TOTALLY gotten rid of the rattling noise. Good luck!

Lou,I belive your right.When an axle goes this is the sound they make.

It may be a wheel bearing going bad. The A4 is known for wheel bearing issues, and the A6 shares many drivetrain parts with the A4.