# Is inflation deterministic?

In some theories inflation is supposed to be able to turn quantum fluctuations into macroscopic inhomogeneities.

I don't understand how an isolated system such as the universe can undergo such a random transformation : if at the beginning the universe is in a state $A$, quantum mechanics says that $A$ will evolve to $B=UA$ with $U$ being a unitary operator, and general relativity is also a deterministic theory.

So does inflation suppose that the universe is not isolated or does it use some modified theories which include randomness?

• I wanted to clarify what you meant when you say the universe can undergo a "random transformation". As I understand it, the "fluctuations" are just uncertainties in the values of certain observables, i.e. the universe, early on, is in a state in which these observables don't have definite values. So is your question "how does inflation cause these variables, which were uncertain, to become frozen?", i.e. for them to "collapse" to definite values, when Copenhagen is clearly inapplicable to the universe. Sep 28 '13 at 10:52
• "I wanted to clarify what you meant when you say the universe can undergo a "random transformation" " : In inflation the universe is supposed to be totally homogeneous at the beginning, after inflation we obtain a random distribution of matter (and energy) : how cant it be with fully deterministic theory ? Sep 28 '13 at 11:02
• Quantum mechanically, the properties of whatever fields/particles are present just don't have definite values and that's where the randomness ultimately originates, so for this reason "totally homogeneous" isn't an appropriate picture. You're right that even quantum mechanically, the evolution (via the Hamiltonian) is deterministic, and the question is how the (apparent) collapse to fixed values happens. I think this would need a consistent histories approach to explain. Sep 28 '13 at 11:21
• "just don't have definite values and that's where the randomness ultimately originates" : I do not agree : $\frac{1}{\sqrt 2} (|0> + |1>)$ is a perfectly defined state and there is no randomness, the only one comes from collapsing, which can't happen if the system is isolated Sep 28 '13 at 11:47
• Yes, I'm saying the same thing: the randomness originates in not being in an eigenstate of <whatever> and the randomness manifests itself with measurements. This is impossible with the universe hence my suggestion that consistent histories might provide the right way to look at it. Sep 28 '13 at 12:20

In quantum mechanics, the state indeed evolves. But when you do an observation, it needs to choose one of the observable states - that's why we talk about superposition of states as long as you don't observe a quantum variable.

For inflation, as long as we were at high energies and short distances, the states could evolves, but once the inflation started, stretch distances and modes crossed the horizon, they had to pick up a state and then were fixed. What happen next is given by deterministic theories.

• "In quantum mechanics, the state indeed evolves. But when you do an observation, it needs to choose one of the observable states" : but if the universe is isolated, nothing can observe it. Sep 28 '13 at 10:16
• "they had to pick up a state" : why ? Wave function collapse comes from the interaction of a system with another one with much more degrees of freedom (the measurement device or just the environment) , but an isolated system will undergo a unitary evolution Sep 28 '13 at 10:17

Ok I ask the question to some specialists and it just seems that indeed the evolution of the whole universe is not unitary in inflation theory.

• As long as we do not have a total theory of everything, i.e. a mathematical model that quantizes all four forces, gravity, weak, strong and electromagnetic, the theories proposed are a hand waving mix of deterministic/classical theories and suppositions taken from quantum mechanics. Plausible statements but not rigorously derived. Jan 22 '14 at 8:38
• Yeah exactly, but what seems strange is that by mixing deterministic theory they succeed to make a non deterministic one. In fact I think there are some thermodynamical steps in the theory wich somewhat introduce a random evolution of the universe Jan 22 '14 at 8:42
• To be more precise one step in inflation I think is to consider each part of the universe as a small thermodynamical system in interaction with the rest of the universe Jan 22 '14 at 8:48
• Well, the randomness enters by the assumption that one can mix quantum mechanics and deterministic theories a la cart. Thermodynamics is classical, and breaks spectacularly down at quantum levels ( black body radiation for example). Jan 22 '14 at 9:46