Tegmark's Computable Universe Hypothesis & Apart from the (well founded) critics to Tegmark's Mathematical Universe Hypothesis (https://arxiv.org/abs/0704.0646 ) I´d like to know how he justifies the assumption of the Computable Universe Hypothesis. 
It seems that it uses it to avoid Godel incompleteness but I can´t find in the cited paper,  where he  explains why he assumes it.
In fact, in his book "Our Mathematical Universe" he says (bold is mine):

A first concern about the CUH is that it my sound like a surrender to
  philosophical high ground, effectively conceding that athough all
  possible mathematical structures are "out there", some have privileged
  status. However my guess is CUH turns out to be correct, it will be instead be because the rest of the mathematical landscape was mere illusion, fundamentally undefined and simply not existing in any meaningful sense

So does anybody know the reason for Tegmark´s CUH assumption?
 A: The CUH can be justified by invoking the Church–Turing–Deutsch principle:

The principle states that a universal computing device can simulate every physical process.

No counterexamples are known, one can then turn this around; if one assumes the validity of the CUH then the Church–Turing–Deutsch principle follows from that. Tegmark's ideas are  very radical, but they are interesting as by assuming that only algorithms really exists, you get rid of most of the intractable philosophical issues about the nature of reality, existence, consciousness etc. etc. It implies that I should consider myself as the computational state of an algorithm that my brain is running, and that is actually quite a mainstream idea in cognitive science, see e.g. here. But by assuming that the physical brain actually does not exist separate from its mathematical formulation, you get rid of the problem of how the physical object leads to consciousness.
A: 
Apart from the (well founded) critics to Tegmark's Mathematical Universe Hypothesis (https://arxiv.org/abs/0704.0646 ) I´d like to know how he justifies the assumption of the Computable Universe Hypothesis. 

He doesn't justify it. It's like a rabbit from the hat. It's an assumption with no justification whatsoever.  

It seems that it uses it to avoid Godel incompleteness but I can´t find in the cited paper, where he explains why he assumes it.

That's because he doesn't. 

In fact, in his book "Our Mathematical Universe" he says (bold is mine): "
  A first concern about the CUH is that it my sound like a surrender to philosophical high ground, effectively conceding that although all possible mathematical structures are "out there", some have privileged status. However my guess is CUH turns out to be correct, it will be instead be because the rest of the mathematical landscape was mere illusion, fundamentally undefined and simply not existing in any meaningful sense"

I think the first concern about the CUH and the rest of Tegmark's mathematical universe is that it's headline-grabbing self-promotional nonsense that brings science into disrepute. 

So does anybody know the reason for Tegmark´s CUH assumption?

It gets Tegmark in the papers and on TV. It advances his career. See what Woit said:
"Tegmark’s career is a rather unusual story, mixing reputable science with an increasingly strong taste for grandiose nonsense. In this book he indulges his inner crank, describing in detail an utterly empty vision of the “ultimate nature of reality”. What’s perhaps most remarkable about the book is the respectful reception it seems to be getting, see reviews here, here, here and here. The Financial Times review credits Tegmark as the “academic celebrity” behind the turn of physics to the multiverse..." 
Personally I think it's all rather Emperor's New Clothes. And I rather fear that this is the sort of thing that makes the public and politicians think scientific funding should be cut.   
