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John Wheeler proposed that the fundamental laws of physics actually were emergent from a primordial random/chaotic underlying state. According to this view, every physical law is actually emergent.

Is there some kind of cosmological inflationary model (among all the varieties of inflationary models such as e.g. stochastic inflation, multi-field inflation, quintessence inflation, new inflation...etc) that would be compatible with Wheeler's ideas? Is there some version of cosmological inflation models that assume literally no fundamental laws and propose that all laws of physics are rather emergent (basically from "chaos")?

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I would say that order and chaos are two diametrically opposite poles of the same axiom. So they are equally fundamental. The existence of one intrinsically implies the existence of the other, like two sides of a coin. There is more to my theory, such as the centre point not being fixed, and order/chaos fundamentally emerging from finiteness/infinities. However I do not know of any inflation specific theories along this line of thinking, but rather mentioned it as a theory of lawful/lawlessness in general

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I am not familiar with such a cosmological inflation model, and doubt one can be formulated. There are models wherein some laws of physics emerge from an underlying quantum fluctuation, but there are always more-fundamental laws within which all of this is going on.

However, you might want to look up Max Tegmark's "Mathematical Multiverse" model. In this cosmology, all mathematically consistent structures exist equally (with some nuances). This seems to fit your idea, if you identify the "primordial random/chaotic underlying state" with the plethora of mathematical possibilities. This is the only model I know of where all of the laws of physics are emergent.

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