Could the basic fundamental laws of physics change between universes in cosmological inflationary models? According to cosmological inflationary models, different universes governed by different effective/low-energy laws of physics could exist, but the most fundamental laws of nature would remain the same. In other words, while the effective laws of physics would change, fundamental laws would stay the same.
But is this always true? Could Inflation give birth to universes with extremely different laws of physics? Even different fundamental laws of physics?
I am asking this because some of the most famous proponents of cosmological inflation models seem to suggest this possibility:
For example, Andrei Linde is one of the most prominent physicists that propose that inflation theory is true. In one of his articles 1 he says:

Inflationary theory allows our universe to be divided into different parts with different laws of low-energy physics that are allowed by the unique fundamental theory. Most importantly, it makes each of such domains exponentially large, which is a necessary part of justification of the anthropic principle. The diversity of possible laws of physics can be very high, especially in the models of eternal chaotic inflation where quantum fluctuations can have an extremely large amplitude, which makes the transition between all possible states particularly easy.

So far, he has explained that cosmological inflation models would predict universes where the effective laws of a more fundamental theory would change, while the fundamental laws of that theory would remain the same. Nothing new.
But then, he says:

In addition to that, one can consider different universes with different laws of physics in each of them. This does not necessarily require introduction of quantum cosmology, many-world interpretation of quantum mechanics, and baby universe theory. It is sufficient to consider an extended action represented by a sum of all possible actions of all possible theories in all possible universes. One may call this structure a ‘multiverse.’

And then he proposes the universes with different fundamental laws of physics could exist.
This seems to indicate that in inflation theory we could also consider or include universes where not only low-energy laws of physics would be different, but also the more fundamental ones. The problem is that the author does not clarify and does not indicate whether is it there any specific version of inflation theory that allows this.
Also, Andreas Albrecht, one of the discoverers of inflation, has proposed in multiple occasions that fundamental laws of physics are not so fundamental because when a universe is born, its fundamental laws are selected among a random set of laws, as it is indicated here 2:

I have argued that a standard approach to defining time in quantum gravity leads to absolute ambiguity in the fundamental laws of physics

Since he is one of the creators of inflation, I assume he thinks that the fundamental laws of physics could change between universes in the context of inflationary cosmology.
So, my question is: Could the basic fundamental laws of physics change between universes in cosmological inflationary models? Is it there any model of inflation where there could be different universes governed by different laws of high-energy physics? Could there be universes governed by different theories at high energy physics?
 A: Although it's not mentioned in your question, you're thinking of the string theory landscape. The idea here is that there are tons of ways to "compactify" the extra dimensions of the theory, and presumably each of those ways will give rise to different laws of physics. These correspond to the different universes the question alludes to, and is also why string theory is sometimes said to predict $\sim 10^{500}$ universes. So the brief answer to your question is "yes".
In addition to the landscape, the other term you want to look for is eternal inflation.
A: 
"The idea of such a structure called the multiverse has attracted a
lot of attention in the past years and we refer to [79] for a more
exhaustive account of this debate. While many versions of what such a
multiverse could be, one of them finds its root in string theory. In
2000, it was realized [66] that vast numbers of discrete choices,
called flux vacua, can be obtained in compactifying superstring
theory. The number of possibilities is estimated to range between
10100 and 10500, or maybe more. No principle is yet known to fix which
of these vacua is chosen. Eternal inflation offers a possibility to
populate these vacua and to generate an infinite number of regions in
which the parameters, initial conditions but also the laws of nature
or the number of spacetime dimensions can vary from one universe to
another, hence being completely contingent."

https://link.springer.com/article/10.12942/lrr-2011-2
