# Is the Big Bang defined as before or after Inflation?

Is the Big Bang defined as before or after Inflation? Seems like a simple enough question to answer right? And if just yesterday I were to encounter this, I'd have given a definite answer. But I've been doing some reading while writing up my thesis and I'm finding conflicting definitions of the Big Bang.

Everyone agrees that in standard Big Bang cosmology, the Big Bang is defined as the singularity; the moment in time when the scale factor goes to zero. Okay, but when you include the theory of inflation, it gets a bit murky.

So here's what I mean by conflicting definitions. As an example, in The Primordial Density Perturbation by Lythe and Liddle, they define the Big Bang as the beginning of the era of attractive gravity after inflation. However, Modern Cosmology by Dodelson defines the Big Bang as coming before inflation; it effectively uses the old definition that the Big Bang is the moment when the scale factor approaches zero.

This contradiction is evident in multiple places. When doing a google search for it, one can find many persuasive explanations for both definitions. All definitions agree that we cannot any longer define it as the singularity where $a=0$. But every one makes sense in its own way and so, I become more and more confused about which is right the more of them I read.

The argument for the Big Bang coming after is that inflationary theory diverges from the standard Big Bang cosmology around $10^{-30}s$ before we'd expect to run into the singularity, when inflation ended, and that we have no evidence to anything coming before that, thus the big bang is now defined as the initial conditions for the hot, expanding universe that are set up by and at the end of inflation.

The argument for the Big Bang coming before seems to be that inflation is still a period where the scale factor grows and as such, the Big Bang can be defined as the closest value to zero (which is before inflation), or rather, the earliest time as the scale factor approaches zero. This essentially seems to be based on saying "well, we defined it as the moment when the scale factor was smallest before inflation was added. Why would we not continue to have that as the definition after inflation is added?"

The former argument has merit because it defines the start of the epoch where the universe is describable (practically) by the standard Big Bang cosmology. But the latter argument has merit because of its simplicity and that it uses the spirit of the original definition; the smallest scale factor and the moment when the expansion of the universe seems to begin.

Thus, my root question: Which definition is correct? Do we say the Big Bang came before or after inflation?

P.S. I realize that asking this here only serves to add one or more additional persuasive arguments to an already crowded debate. However, this is Physics.SE, so I figure whatever we decide here can be definitive. Even if we can't find a truly correct answer, this can set the record straight, or at least, firmly crooked.

• If you're a Dodelson person, read this. It's pretty convincing until you read others from the opposite side (or at least reread my question) – Jim Aug 27 '14 at 19:31
• Don't take me wrong, I understand your arguments, but I also understand it as a matter of a convention or personal taste. It's just a label given to a state defined by a physical criterion. Even the "Big bang" is originally a derogatory term which could be better described as "Everywhere stretch" as suggested I thiiink in a video by MinutePhysics. In the original sense we could e.g. define it as the whole era during which any normal material would be ripped apart just by the expansion. Etc. etc. – Void Aug 27 '14 at 19:44
• I see this question has a VTC as primarily opinion-based. This, I believe, is unwarranted. My question is not about what people's opinion of the definition is, it asks what the accepted definition is (something not based on opinion). If there is not one but two accepted definitions for the term, whose usage then depends on the opinion of the user, then that in itself would constitute an answer to the question and would still not be an opinion-based answer – Jim Aug 27 '14 at 21:26
• The statement of the questions seems to boil down to "The experts are divided about Proposition X. What is the expert consensus on Proposition X?" – dmckee --- ex-moderator kitten Aug 27 '14 at 23:56
• @dmckee, The correct question should be "The experts are divided about Proposition X. What are the reasons and thought processes which leads to the non-consensus?" – Pacerier May 27 '15 at 5:21

So I've done some further research into this question and the result I found is quite surprising. There truly is no set definition. Some cosmologists will tell you (as John Rennie mentioned) to avoid using the term "Big Bang" unless you absolutely have to. However, that is a luxury not afforded to all cosmologists.

The more surprising thing is that among the cosmologists who can't avoid using the term, there is still no consensus and nobody ever talks about how there are two almost equally used definitions. I've confronted several faculty cosmologists about this and every single one says the same thing: you sort of just pick a definition you like best and go with that. Nobody mentions their specific definition in papers or that there are mutually exclusive definitions, it is just ignored as a problem. But I'm ranting, so let me formally answer the question.

There are two valid definitions and they are, for the most part, as I defined in the question. For those of us who can't avoid using "the Big Bang" in our work, the choice of definition seems to rely in part on the area of research of the individual. Most of the time, inflationary cosmologists will choose the definition of the Big Bang as the curvature singularity before the onset of inflation (except for those studying eternal inflation, for whom the period before the onset of inflation is ill-defined). Observational cosmologists and those studying the universe after inflation tend to choose the definition of the Big Bang as the end of inflation and the onset of the hot, radiation-dominated expansion era. Sometimes, I have found that this time is referred to as the "Hot Big Bang", which seems to be quite a useful way of distinguishing this definition from that of the curvature singularity (which I suppose would then be called the "Cold Big Bang").

So the answer to my question of what is the correct definition of the Big Bang is that there are two correct definitions with no canonical way of distinguishing them. It is equally valid to claim the Big Bang happened before inflation as it is to claim the Big Bang happened at the end of inflation. While it can be aggravatingly confusing that no one seems to acknowledge this dichotomy, the definition used in a given circumstance can often be inferred from context; researchers tend to use the definition that marks the beginning of the era(s) they are researching.

• The word Cold big bang got me wondering. - Were there radiation before inflation? In other words, did the universe have a temperature before inflation? – parker Jul 19 '18 at 19:11
• @parker I suppose the answer to that would depend on the specifics of the model you use. But, if my memory serves me, I think in the slow-roll model, the decay of the inflaton field is what gives rise to photons, neutrinos, and other forms of energy. So no, at least in that model, I do not believe there was radiation before inflation – Jim Jul 20 '18 at 11:57
• Thanks. And if we consider the traditional big bang model without inflation, did radiation already exist at the beginning of the universe? – parker Jul 20 '18 at 13:25
• @parker not much of what I read about the old model specifically comments on the existence of radiation at the precise moment of the big bang. However, the records of opinions and discussions that I have read from cosmologists around the time that inflation was introduced seem to indicate that, if it wasn't existing exactly at the beginning, it came into existence extremely soon after. Or, at least, that seemed to be their thinking – Jim Jul 20 '18 at 17:57
• @Jim In a cosmology with dual arrows-of-time, like the Aguirre & Gratton one described in my own answer, do you think such dominant components as "radiation" or "matter" might, during some epochs, be present in one half of the cosmos and absent in the other? (To me, a requirement that they always be present in either one or the other seems to be a temporal equivalent to the spatial idea that widely-separated components of observable homogeneity must have been in physical contact at some past time, although that motivation for inflationary cosmology always seems a little weak to me.) – Edouard Jul 13 '19 at 3:41

The Big Bang was originally defined as the zero time limit of the FLRW metric, so it's a mathematical construct and not primarily something physical. We have chosen to apply it to the zero time limit of the universe because we thought the FLRW metric was a good description of the universe, but then inflation gatecrashed the party and spoiled the fun.

So if you're going to use the phrase Big Bang in connection with the universe, as opposed to its purely mathematical meaning, then it's up to you to define what it means. As you've found, there is currently no consensus on its meaning.

Personally I would avoid using the term unless you're specifically referring to the FLRW metric.

• TBH it's entirely reasonable to use the term in astrophysical contexts such as "One billion years after the Big Bang ...". The term is only troublesome if you need to distinguish the phases of the early universe. – MSalters Aug 28 '14 at 10:48
• I like this answer's message. So I +1'd it. But something about it doesn't feel complete enough yet for an acceptance. You can try to improve or expand on it if you like. If not, then what I might do in the future (and with your permission) is add whatever answers and info I get from other sources to this answer and try to establish when to use each definition more rigidly while maintaining the message of this post. After all, there's no real point in me writing up my own answer for acceptance when I could add to yours and thus give somebody a +15, right? – Jim Aug 28 '14 at 13:29
• @jim: if you want to use my post as a basis for an extended answer let me know and I'll turn it into a community wiki. However my personal belief remains that Big Bang strictly means the FLRW Big Bang, and using the term in an inflationary universe is a potential source of confusion. I wouldn't use the term in any context where its precise meaning matters. – John Rennie Aug 28 '14 at 17:01
• I'll keep that in mind, but I would never consider changing your answer away from the intended message you posted. If I do add any information, it would only be used to elaborate on and potentially reinforce your point – Jim Aug 28 '14 at 17:43

In my opinion it all hinges on whether one includes quantization of gravity or not.

The classical Big Bang just uses General Relativity and solutions of its equations. A singularity has a well defined meaning in the classical approach.

As physicists are convinced that the underlying framework of nature is quantum mechanical it is expected that gravity will also be quantized . The Inflationary epoch appears in the model where effective quantization of gravity is assumed. Quantization carries the Heisenberg Uncertainty principle which in effect eliminates singularities that appear in the classical theories, for example the 1/r electric potential does not create a singularity in the quantum mechanical formulation.

The classical theories generally are emergent from the underlying quantum mechanical framework. This does not invalidate the theoretical models that describe so successfully the classical data. It just limits their region of validity. The Big Bang model is successful in its region of validity and it is modeled as if there is a singularity at the very beginning because that is what the data say.

When the limits of the validity in energy density, space and time of classical GR are reached, then QM has to be invoked and the data modeled with it, which is what the inflationary model does. That does not invalidate the classical BB. It will still emerge and apply at its region of validity . The various definitions you state are due to this confusion of trying to keep both the classical and QM frame at once .

When a solid model of quantized gravity in a Theory Of Everything appears these confusions will be resolved. My view is that the classical Big Bang is no longer validated for the small dimensions, and thus its singularity, as the inflationary period is validated by the cosmic microwave background. Nevertheless, the emergent behavior at large dimensions is as if there exists a singularity at the beginning, so in large dimensions the Big Bang is valid. It is similar to the difference between the hydrogen atom quantum mechanically, and two charged balls attracting each other macroscopically. There is no singularity in the hydrogen atom, the two charged balls modeled as points in their center of mass have singularities there, and their macroscopic behavior fits the model with singularities.

• But none of the new definitions make use of a singularity. Or are you saying we should do away with the "Big Bang" term altogether? – Jim Aug 27 '14 at 19:34
• The ambiguity in what we call the BB has nothing to do with mysteries of quantum gravity. – innisfree Aug 27 '14 at 19:49
• @innisfree I am not talking about mysteries of quantum gravity. I am talking of mixing two frameworks that have different postulates and axioms and expect consistency. Generally in quantum mechanics singularities disappear. The classical frame is an emergent frame. When one is actually "handwaving" , mixing two frames, confusions will arise. – anna v Aug 28 '14 at 3:13
• We actually live our everyday lives in a classical physics framework. That it is emergent and the underlying framework is quantum mechanical does not invalidate the theoretical models that describe so successfully our classical experience. It just limits their region of validity. The Big Bang model is successful in its region of validity and it is modeled as if there is a singularity at the very beginning. When the limits of the validity of classical GR are reached then QM has to be invoked and the data modeled with it, which is what the inflationary model does. That does not invalidate the – anna v Aug 28 '14 at 3:16
• classical BB. It will still emerge and apply at its region of validity . The various definitions you state are due to this confusion of trying to keep both the classical and QM frame at once . – anna v Aug 28 '14 at 3:20

To my mind, the Big Bang doesn’t refer to a distinct event but to a cosmogonic theory as a whole, that “predicts” ( should we say “retrodicts”?) many different events of the deep past. For example, there is such established term as “Big Bang nucleosynthesis” that describes an epoch several seconds past the Beginning of Time. The Beginning of Time in the narrow sense must be rigorously referred to as “cosmological singularity”. But even professional physicists do not always distinguish the terms consistently.

Back to the original question. Inflation certainly occurs after the cosmological singularity, but before several important events of the Big Bang. In other words, the inflation is an optional epoch that can occur within the Big Bang era and theory.

• It seems you side on the "first moment of time" definition. Note that, as explained in the question, not all definitions of the Big Bang state that it is the first moment of time. BBN is also not considered a Big Bang per se, it is a separate event(s) happening moments after the Big Bang and is distinguished by the word "Nucleosynthesis". The two competing definitions are both valid since they both attempt to preserve part of the spirit of the original meaning of the term. They simply preserve different parts of the original meaning and, in doing so, become mutually exclusive. – Jim Oct 21 '14 at 13:53
• Ī side with mentioned “original meaning” and with neither of two “conflicting definitions”. Big Bang is a theory, also an era in the universe (a coordinate time started from presumed/extrapolated singularity) and, by synecdoche, early universe in general, certainly up to the end of nucleosynthesys and possibly beyond. Ī am unsure whether should the recombination be counted as one of Big Bang events: it is directly observable as CMBR. But all events not directly observed but predicted (or, more precisely, retrodicted) by the theory, should be counted as Big Bang events. But Ī am not an expert. – Incnis Mrsi Oct 21 '14 at 14:16
• The sum of events you refer too is now called the "Big Bang Era" and the description you provide is that of the old Big Bang Cosmology. The Big Bang itself as an event was and is defined as a moment of time. Whereas the Big Bang Events up to recombination are part of the Big Bang Epoch. Regardless, however, there are two competing definitions now because the introduction of inflation has made the old definition impossible. From your points, I gather you would much prefer the definition of the Big Bang as being after inflation. This allows you to group BBN etc under the umbrella of the Big Bang – Jim Oct 21 '14 at 14:25
• Nice update, I like the form of this answer, +1 – Jim Oct 21 '14 at 14:32

The physicist Vilenkin (much involved in the development of the theory of field-based eternal inflation), in his popular science book "Many Worlds in One", describes the energy of the inflaton field as releasing itself in a hot bath of particles upon each of its potentially infinite number of endings in local (i.e., "bubble" or "pocket") universes, including the one we inhabit, where that release equates to "the" Big Bang. He also deals with the timing issue mentioned by John Rennie, by sketching a difference between "cosmological" time and time within each of the LU's, which are generally expected to remain causally separated from each other, with no evidence to the contrary yet encountered. All this is similar, if not identical, to the treatment given to the relation between the BB and inflation by Guth, in his well-indexed book titled "The Inflationary Universe".

However, regarding any beginning (in cosmological time) of phenomena as basic as radiation, the conclusion drawn by an earlier answerer is very far from certain. Vilenkin, Guth, and Borde collaborated on the BGV Theorem: It's often construed as requiring a beginning for any inflation (asymptotically-exponential expansion) that might be eternal into the future. However,in the last (2003) revision of their theorem, those 3 authors included a footnote, in their list of references at the end of that revision, which specifies that Aguirre and Gratton's "steady-state eternal inflation", described at https://arxiv.org/abs/astro-ph/0111191, is compatible with it, even though steady-state eternal inflation definitely does NOT require a beginning for the inflationary multiverse: In that version of inflation, dual arrows of time extend in opposite directions from a Cauchy surface, and formally-identical versions of the BGV theorem apply separately in each of those temporal directions.

• This answer adds an important perspective to the topic at hand that we've thus far been lacking. Thank you. – Jim Jul 15 '19 at 11:55

Is the Big Bang defined as before or after Inflation?

The word "defined" makes this a question about opinion rather than fact. I always try to stick to the facts determined from empirical evidence. But hey ho, I'll do my best.

Seems like a simple enough question to answer right? And if just yesterday I were to encounter this, I'd have given a definite answer. But I've been doing some reading while writing up my thesis and I'm finding conflicting definitions of the Big Bang.

That's because there's confusion in cosmology.

Everyone agrees that in standard Big Bang cosmology, the Big Bang is defined as the singularity; the moment in time when the scale factor goes to zero.

Many cosmologists might agree about that, but IMHO it's going too far to say that everybody agrees about a singularity. A singularity sometimes denotes an issue, indicating that a theory has gone awry. I think it's possible to shed some light on the early universe by thinking about gravity and relativity and black holes, and appreciating that there is no central point-singularity in a black hole.

Okay, but when you include the theory of inflation, it gets a bit murky.

The theory of inflation is definitely "a bit murky". Not the expanding universe, inflation. I like to think that one reaches a position wherein inflation is a solution to a problem that does not exist.

So here's what I mean by conflicting definitions. As an example, in The Primordial Density Perturbation by Lythe and Liddle, they define the Big Bang as the beginning of the era of attractive gravity after inflation.

That's not a definition I'd use. By the way, note that gravity is always attractive, and that it alters the motion of light and matter through space, but it doesn't make space fall down. The big crunch didn't happen when the universe was small and dense, and it isn't ever going to happen.

However, Modern Cosmology by Dodelson defines the Big Bang as coming before inflation; it effectively uses the old definition that the Big Bang is the moment when the scale factor approaches zero.

I think that's better, but not quite right. It's kind of missing the trick.

This contradiction is evident in multiple places. When doing a google search for it, one can find many persuasive explanations for both definitions. All definitions agree that we cannot any longer define it as the singularity where a=0. But every one makes sense in its own way and so, I become more and more confused about which is right the more of them I read.

None of them are exactly right.

The argument for the Big Bang coming after is that inflationary theory diverges from the standard Big Bang cosmology around 10−30s.

Forget that. There was no inflation.

before we'd expect to run into the singularity

Forget that too. There was no singularity.

when inflation ended, and that we have no evidence to anything coming before that, thus the big bang is now defined as the initial conditions for the hot, expanding universe that are set up by and at the end of inflation.

There's no evidence for inflation. But there is confusion in cosmology.

The argument for the Big Bang coming before seems to be that inflation is still a period where the scale factor grows and as such, the Big Bang can be defined as the closest value to zero (which is before inflation), or rather, the earliest time as the scale factor approaches zero. This essentially seems to be based on saying "well, we defined it as the moment when the scale factor was smallest before inflation was added. Why would we not continue to have that as the definition after inflation is added?"

Big bangs are associated with things getting bigger. IMHO it makes no sense to define the big bang as something that occurs after the universe got a whole lot bigger fast.

The former argument has merit because it defines the start of the epoch where the universe is describable (practically) by the standard Big Bang cosmology. But the latter argument has merit because of its simplicity and that it uses the spirit of the original definition; the smallest scale factor and the moment when the expansion of the universe seems to begin.

If there was no inflation, things get a whole lot simpler, don't they?

Thus, my root question: Which definition is correct? Do we say the Big Bang came before or after inflation?

Does not compute. There was no inflation. On that basis the second definition is more correct, but not wholly correct. PS: I noticed your comment about the documentary. If you'd like to consult me, please don't hesitate to email me on myname at btconnect dot com. LOL!

• 1) The question was based in the framework of inflationary cosmology. I also asked for the accepted definition in that regime, which means you can't just deny the theory and claim the question as nonsensical. 2) I signed a non-disclosure agreement concerning the content of the documentary. I will not be consulting with others myself – Jim Feb 1 '17 at 21:58
• Jim, I didn't claim the question was nonsensical. And sorry if I came over as somewhat negative, but the theory of inflation has been around for forty years and there's still no evidence for it. In fact, it seems to be untestable. See articles like this: Physicist Slams Cosmic Theory He Helped Conceive. – John Duffield Feb 2 '17 at 19:30