I No symmetries in the Universe at the Big Bang...?

[Suekdccia]

TL;DR Summary

No symmetries in the universe at the Big Bang...?

I apologize in advance if this is a stupid question but...

According to some scenarios about the beginning of the universe (namely cosmological inflation), in layman's terms, everything was born out of a quantum fluctuation which caused a violent expansion. In this case, since an expanding universe breaks the time translation symmetry, energy conservation does not necessarily hold and therefore energy and matter could have appeared from """nowhere""" ()

However, if these conditions were "repeated" in a spacetime with no (global) symmetries, could all conservation laws and the rest fundamental laws of physics have been also violated or approximate? Would this be theoretically possible?

 

[PeterDonis]

According to some scenarios about the beginning of the universe (namely cosmological inflation), in layman's terms, everything was born out of a quantum fluctuation which caused a violent expansion.

Actually not all inflation models say that. The common feature that all inflation models have is that the "Big Bang" state--the hot, dense, rapidly expanding state that is the earliest state of the universe for which we have good evidence--happened because inflationary expansion ended when the inflaton field (the scalar field driving inflationary expansion) went through a phase transition from a "false vacuum" state to a "true vacuum" state and transferred all of its energy density to the Standard Model fields.

Where inflation models differ is on how the inflationary expansion came about. The original inflation models assumed that inflationary expansion was triggered by some event (possibly a previous phase transition, for example from some kind of Planck scale physics). However, the main front runner inflation models today appear to be "eternal inflation" models, in which inflationary expansion extends infinitely far back into the past--it never starts and there is no state previous to it. Universes like ours get "born" when a fluctuation causes inflation to stop via the phase transition from "false vacuum" to "true vacuum" described above.

since an expanding universe breaks the time translation symmetry, energy conservation does not necessarily hold and therefore energy and matter could have appeared from """nowhere"""

This is a fairly common statement in pop science videos, even by experts like Guth, but you have to be careful about what it means. The inflaton field in its "false vacuum" state, i.e., while inflation is going on, works like dark energy: its energy density is constant everywhere in the inflating region of spacetime. If we look at successive spacelike slices in FRW coordinates with increasing scale factor, this looks like inflaton field energy is continuously being "created from nothing". But, as you will see if you read, for example, Carroll's classic blog post "Energy Is Not Conserved", that's not the only possible interpretation. What is true on any interpretation is that, as you say, there is no time translation symmetry in an expanding universe, and therefore there is no globally conserved energy.

if these conditions were "repeated" in a spacetime with no (global) symmetries, could all conservation laws and the rest fundamental laws of physics have been also violated or approximate? Would this be theoretically possible?

We have no idea since nobody has proposed any model along these lines. It's pointless to ask what is "possible" if you throw out all constraints.

 

[Suekdccia]

We have no idea since nobody has proposed any model along these lines. It's pointless to ask what is "possible" if you throw out all constraints.

Even if it has not been proposed, would inflation occurring in a spacetime that lacks all (global) symmetries mean that all laws associated with these symmetries would be violated in the formation of the universe?

 

[Drakkith]

Even if it has not been proposed, would inflation occurring in a spacetime that lacks all (global) symmetries mean that all laws associated with these symmetries would be violated in the formation of the universe?

If the laws require symmetry, then without that symmetry existing the laws wouldn't appear to apply. So there's not really any violation that could even occur since the laws wouldn't apply in the first place.

 

[Suekdccia]

If the laws require symmetry, then without that symmetry existing the laws wouldn't appear to apply. So there's not really any violation that could even occur since the laws wouldn't apply in the first place.

Well, that makes sense

 

[PeterDonis]

Even if it has not been proposed

The question is pointless if it is about a model that nobody has proposed and does not exist. How can anyone possibly say anything about a model that does not exist?

 

[Jaime Rudas]

However, the main front runner inflation models today appear to be "eternal inflation" models, in which inflationary expansion extends infinitely far back into the past--it never starts and there is no state previous to it.

Do you have a reference that supports this? I ask this because, as I understand it, Alan Guth's eternal inflation model doesn't extend infinitely into the past.

 

[Jaime Rudas]

Do you have a reference that supports this? I ask this because, as I understand it, Alan Guth's eternal inflation model doesn't extend infinitely into the past.

In this regard, I found that, under reasonable assumptions, the Borde-Guth-Vilenkin theorem demonstrates that inflationary cosmological models doesn't extend infinitely into the past.

 

[PeterDonis]

under reasonable assumptions, the Borde-Guth-Vilenkin theorem demonstrates that inflationary cosmological models doesn't extend infinitely into the past.

Hm, yes, I'd forgotten about the BGV theorem when I posted before.

As the paper mentions, de Sitter spacetime does extend infinitely into the past. It can do so because it violates the "averaged expansion condition" that is the key premise of the BGV theorem.

The question is whether that condition is really necessary. It's true that in a model where it's violated, like de Sitter spacetime, you can't describe the history into the infinite past as "inflating", because it's not always expanding (more precisely, there is no geodesic congruence which has a positive expansion scalar into the infinite past). But do we need to have a model which is "inflating" into the infinite past? Or do we just need a model that extends infinitely into the past?

Another question might be whether a model with a simple scalar field (there is no such field in de Sitter spacetime, the only "stress-energy" present is the fixed cosmological constant) can look like de Sitter spacetime, or whether such a model has to obey the averaged expansion condition. If the latter is the case, that would make it much more plausible that a realistic inflation model would have to obey that condition and would thus be covered by the BGV theorem.

The BGV paper you cite was published in 2003; I don't know what the current state of the literature is regarding it. Is it generally accepted by now that it covers all physically reasonable inflation models?

 

[Jaime Rudas]

The BGV paper you cite was published in 2003; I don't know what the current state of the literature is regarding it. Is it generally accepted by now that it covers all physically reasonable inflation models?

In this paper, I interpret Adrei Linde as saying yes, but no, referring to the BGV theorem:

Similarly, if one concentrates on any particular geodesic in the past time direction, one can prove that it has finite length […], i.e., inflation at any particular point in the universe should have a beginning at some time $\tau_i$. However, there is no reason to expect that there is an upper bound for all $\tau_i$ on all geodesics. If this upper bound does not exist, then eternal inflation is eternal not only in the future but also in the past.

Is this reasoning correct? Isn't it self-contradictory? It seems to me to imply that if all geodesics have a beginning, but if there is no upper bound for the past time at which that beginning took place, then one can conclude that there are geodesics that had no beginning.

 

[PeterDonis]

It seems to me to imply that if all geodesics have a beginning, but if there is no upper bound for the past time at which that beginning took place, then one can conclude that there are geodesics that had no beginning.

No, one can't conclude that. Every geodesic still has a finite extension into the past--it's just that you can never find a geodesic whose finite extension into the past is maximal, there will always be some other geodesic with a longer finite extension. Similar to the way every natural number is finite, but there is no maximal natural number. The fact that there is no maximal natural number number does not mean that $\infty$ is a natural number. Similarly, the fact that there is no maximal past extension for geodesics does not mean there are geodesics with infinite past extension.

What is true about such a model, as opposed to one where there is some maximal past extension that any geodesic can have (as in a standard FRW cosmology with an initial singularity), is that it is much more plausible to describe it with the term "eternal inflation".

 

[Jaime Rudas]

Regarding whether inflation can or cannot be eternal in the past, I found this paper by Leonard Suskind where he discusses the topic. Unfortunately, my level of knowledge isn't up to the task of understanding it in depth, but what is clear to me is that it's a topic on which there is no consensus.

 

[PeterDonis]

Regarding whether inflation can or cannot be eternal in the past, I found this paper by Leonard Suskind where he discusses the topic.

Note that Susskind's paper is using the framework of the string theory landscape. (As seems to be usual with Susskind, he just assumes implicitly that that's the right framework to use.) What he says in the paper might well not apply to other frameworks for modeling inflation.