# Why does inflationary expansion of the very early universe require time duration?

If the grand unified force symmetry breaking separation into the strong force and electroweak force leads to a change in scale of the metric that defines distance within space is the cause of the inflationary (exponential) expansion of the universe, then why does this expansion require a time duration, ~10^-32 seconds? Why would it not be instantaneous?

I am looking for a layperson answer, but I would also appreciate the real answer, even though I probably do not yet have the knowledge to comprehend. The motivation for this question is that since the inflationary expansion is superluminal, what other restriction exists that would prevent this expansion from being instantaneous?

• Please tell us something about your background in math, general relativity, and quantum field theory. Do you want an explanation at the level of a layperson? What makes you think it should be instantaneous?
– user4552
Dec 11, 2019 at 0:25
• I am layperson who has impression that change in Standard Model parameter would have instantaneous effect. Dec 11, 2019 at 0:30
• Cool, I think that clarifies more for me what you're really asking and what would be an acceptable answer. You might want to edit your question to give this clarification. (That's usually preferred on SE rather than clarifying in comments. The idea is that people just want to read the question and not have to read the comment thread to understand what is being asked.)
– user4552
Dec 11, 2019 at 6:28
• This seems like a challenging question to answer. It requires an answerer who understands the topic of inflation very deeply -- deeply enough to be able to explain it without a lot of math. The optimal answerer also needs to avoid the danger of providing an answer that sounds good but doesn't just provide an illusion of understanding on this difficult topic. I don't think I'm the optimal answerer, but I would look forward to learning more from someone who has more expertise.
– user4552
Dec 11, 2019 at 6:50

If the grand unified force symmetry breaking ... is the cause of the inflationary (exponential) expansion of the universe... Why would it not be instantaneous?

That is a big "If" out there bro/sis. Nevertheless, let's just suppose "grand unified force symmetry breaking" is "the cause of the inflationary expansion".

In layman's terms, the explanation is simple: can you boil a kettle of water from the liquid phase to the vapor phase instantaneously? If so, pls let me know pal, 'cause my coffee machine could use an upgrade.

In non-layman terms, we are talking about the transitioning between two phases:

• The GUT phase, where the all forces are grand unified under a single group, being it $$SU(5)$$, $$SO(10)$$, or the surely-right GUT theory engineered by my grandma.
• Symmetry breaking phase, where we have "separation into the strong force and electroweak force".

The key word here is "transitioning": you have to evolve between the above two equilibrium phases. The transitioning is an inequilibrium process, which takes time.

• I appreciate the thermodynamic analogy, but I consider this to be more of a "state transition" rather than "phase transition", as it does not seem to be reversible. I understand state transition involves time and energy in thermodynamics, but I am not certain as to how this extrapolates to case of "Cosmic Thermodynamics". Please find fault with my naive layman interpretation: The physical mechanism for the state transition between "GUT" phase and the separated strong force and electroweak force phase is the symmetry breaking, and inflation is an ancillary artifact. Dec 11, 2019 at 17:39

I found this paper on inflation

Inflation models try to correct the original Big Bang model problems:

Despite its successes, the standard big bang (SBB) model had some longstanding shortcomings. One of them is the horizon problem. The CMBR received now has been emitted from regions which never communicated before sending light to us. The question then arises how come the temperature of the black body radiation from these regions is so finely tuned as the results of the cosmic background explorer (COBE) show. Another issue is the flatness problem. The present universe appears almost flat. This requires that, in its early stages, the universe was flat with a great accuracy. Also, combined with GUTs which predict the existence of superheavy monopoles , the SBB model leads to a catastrophe due to the overproduction of these monopoles. Finally, the model has no explanation for the small density perturbations required for the structure formation in the universe and the generation of the observed temperature fluctuations in the CMBR. Inflation offers an elegant solution to all these problems of the SBB model.

The paper is mathematical , I will copy the conclusions:

We summarized the shortcomings of SBB and their resolution by inflation, which suggests that the universe underwent a period of exponential expansion. This may have happened during the GUT phase transition at which the relevant Higgs field was displaced from the vacuum. This field (inflaton) could then, for some time, roll slowly towards the vacuum providing an almost constant ‘vacuum’ energy density. Inflation generates the density perturbations needed for the large scale structure of the universe and the temperature fluctuations of the CMBR. After the end of inflation, the inflaton performs damped oscillations about the vacuum, decays and ‘reheats’ the universe.

The early inflationary models required tiny parameters. This problem was solved by hybrid inflation which uses two real scalar fields. One of them provides the ‘vacuum’ energy density for inflation while the other one is the slowly rolling field. Hybrid inflation arises ‘naturally’ in many SUSY GUTs, but leads to a disastrous overproduction of monopoles. We constructed two extensions of SUSY hybrid inflation which do not suffer from this problem.

Scanning through the formulae, it is evident that the theory in all its different forms, depends on time $$t_{initial}$$ to $$t_{final}$$ which is entered in the solutions of the differential equations for the models.

then why does this expansion require a time duration, ~10^-32 seconds? Why would it not be instantaneous?

There will always be a time interval for the inflation models, by construction. This interval , depending on the form of the theory, depends on the problems of the Big Bang theory the inflation models try to solve, as described in the first quote. i.e.

1) The horizon problem

2) the flattness problem

3) the monopoles problem

4) the small density pertubation

These four are made consistent with a Big Bang model when inflation is included.

The interval $$t_{initial}$$ to $$t_{final}$$ has to be large enough to solve the above four problems with the original Big Bang model. It cannot be zero, i.e. instantaneous that you ask, because it would not solve the four problems.

Let me give you the example of the small density pertubation problem, the fact that the Cosmic Microwave Background radiation is uniform to the level of $$10^{-5}$$ but has inhomogeneities below that, which can be identified with the location of clusters of galaxies and galaxies. Without inflation models, it cannot be explained. With inflation models it is the inflaton field that homogenizes everything but because of quantum mechanics there are quantum fluctuations that are the small inhomogeneities observed. These need a time interval to appear, by definitions of the term "fluctuation". (this is modeled with solutions of quantum mechanical differential equations at $$t_{initial}$$ to $$t_{final}$$ )

• WHY is it true that "There will always be a time interval for the inflation models, by construction"? Why can't a model be constructed that has no time interval during inflation? Dec 11, 2019 at 14:36
• Note I just added a second paragraph to the original question that provides the rationale for the question. Unfortunately, my lack of understanding at formulating inflation models prevents me from seeing how anna v answer addresses the question. Dec 11, 2019 at 16:20
• I think I have made clear that a time interval is inevitable in the way the inflation models exist. The length of the interval depends on the conditions to the solutions, which are imposed in order to answer the 4 problems that made the invention of an inflation model necessary. Dec 11, 2019 at 16:29
• @S.McGrew if you look at the equations in the link, it is evident why not. The four problems that inspired the inflation model in order to solve them, will not be solved. There has to be a time interval for the solutions $t_{initial}$ to $t_{final}$ .Just an instantaneous function cannot do it because of the form of the differential equations of the model. Dec 11, 2019 at 16:40
• @anna v, If I understand your answer and comments, the reason for the time duration is inherent in the inflation model, rather than due to physical cause? Dec 11, 2019 at 16:46