Your engine appears to require the "VW 507 00" oil specification and No 5w-40 oils are on the Audi usa list of approved oils meeting that spec, so I would not recommend using a different oil.
For your 2.0L Turbo diesel engine, you are better off sticking with the manufacturer's recommended oil weight and oil rating. In fact, according to Audi, using the wrong oil could damage your engine. (See link below).
Check your owner's manual to see the specific VW oil rating that your engine requires.
Update: I found a site (link below) that explains quite a bit about VW TDI oil specs. Most notably, it ends with this observation about oils for TDI engines:
Simple enough. If your car:
Has a rotary injection pump, use oil that meets VW’s 505.00 standard
Is a PD, use oil that meets VW’s 505.01 standard
Is a Common Rail, use oil that meets VW’s 507.00 standard
Your car is one of the "Common Rail" engines which require VW 507.00 oil, and while some different (and earlier) VW oil specs allow 5w40 or other weights, your car's oil specification requires a high quality synthetic oil, and only in 5w30 weight.
As the link above states, TDI engines are very hard on oil and drive components, requiring an oil suspends soot well, lubricates the cams and other parts well under high pressure and strain, and also does not leave deposits on the cylinder walls, on the pistons or on the piston rings, so using the right oil can be critical to longevity in your engine.
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More information and background...
Audi/VW are very specific about which brands and weights of oils meet specific VW/Audi standards. For example, according to this Technical Service Bulletin from Audi USA:
While that list shows that the "VW 502 00" oil standard can be met by multiple different weights of Castrol oil including :
- VW 502 00 Castrol SLX Professional Longtec SAE 0W-40
- VW 502 00 Castrol SLX Professional OE SAE 5W-30
- VW 502 00 Castrol Syntec European Formula SAE 0W-30
- VW 502 00 Castrol TXT 505 01 SAE 5W-40
- VW 502 00 Castrol Syntec SAE 5W-40
Note that for the "VW 504 00 / 507 00" oil specification, while 17 different oils are listed, ALL of the 17 oils listed are SAE 5W-30 ONLY.
Audio was very specific in testing and specifying oils, so you would be well advised to consult your owner's manual to look up the correct VW oil spec for your particular engine, and only use an approved oil brand, type and weight.
It must have taken a fair amount of engineering and probably testing for VW/Audi to determine these oil specifications and compile a list, and given the level of specificity and detail in the different oil specifications, I would not recommend deviating from their specification.
It's safe to assume that the manufacturer made these recommendations for a good reason. We can only hypothesize why, but it could be related to known weaknesses or known failure modes with the engine, and the recommendations may very well be there to try to minimize issues from known failure modes (more info and a link are below, which is what leads me to take an educated guess that the oil specifications could be critically important to the longevity of your VW TDI engine.) -- although I will also concede that, especially for VW/Audi TDI engines, it also could be related to regulatory issues such as fuel economy requirements and emissions and pollution control... again, without more specifics one can only speculate... but if it were my car and my engine, I would tend to be cautious and stick to the specification and only the specification.
Also be aware that your particular engine sometimes suffers from a problem related to the failure of a "hexagon gear" that drives the oil pump.
You should ask your mechanic about this issue, and determine the cost and whether it makes sense to replace the oil pump and related parts as preventative maintenance, since a failure can ruin the engine.
As a reference see this site: https://www.torquecars.com/volkswagen/2-0-tdi-140-170-tuning.php - (c) TorqueCars
Which states in part:
The ... problem is in the module itself, how it drives the oil pump, this is done by a small hexagon that also breaks because of the wear.
... the hexagon [issue] is still present in newer CR engines [Note: your engine is a 'newer CR engine', as opposed to the older 'PD' engines], but this time not just in the Passat, A4/A6 and SuperB. The only engine we are aware of that doesn’t use the balance shaft module is the 110HP 2.0 TDI(CBDC) [Not your engine]. Luckily enough there is a solution, for the PD and CR engines. It is replacing the balance shaft module for a chain driven oil pump as seen in other TDI engines. The 140hp 2.0 8v PD TDI (BMM) for example has that oil pump and it has been flawless.-- Read more at: https://www.torquecars.com/volkswagen/2-0-tdi-140-170-tuning.php - (c) TorqueCars
Your engine is considered one of the "newer CR" engines... so at least be aware that while VW/Audio changed the design from earlier engines, and although VW made the hexagon shaped drive gear stronger, it appears that this part still has a tendency to fail, it just lasts longer before failing, and their is a preventative fix that at least some people recommend.