Did the universe really have zero extent at the beginning?

[Smattering]

Dear all,

The term "big bang singularity" somehow seems to imply that the universe had zero extent at the beginning. But should this really be taken literally? Because if something has literally zero extent, then not even exponential growth over billions of years could ever result in an extent greater than zero, could it?

So if the universe has an extent greater than zero now, and we assume that it is approx. 14 billion years old, then it must have had an extent greater than zero at $t = 0$, right?Robert

 

[PeterDonis]

The term "big bang singularity" somehow seems to imply that the universe had zero extent at the beginning.

The "initial singularity" that appears in idealized mathematical models is just that, an idealization. Our current model of the actual universe in cosmology does not include it, and whatever properties might be inferred from the idealized mathematical model are not thought to have been properties of the actual universe.

Also, even if we restrict attention to the idealized mathematical model, the initial singularity is not actually part of the model--that is, it's not actually part of the spacetime manifold the model describes. The properties attributed, in sloppy pop science-speak, to the singularity at $t = 0$ are actually properties of limits taken as $t \rightarrow 0$. For example, the limit of the "scale factor" $a$ as $t \rightarrow 0$ is $0$, but that does not mean the universe ever actually has "zero size"; the limit is just a mathematical limit, not a physical description of the universe.

 

[Smattering]

The "initial singularity" that appears in idealized mathematical models is just that, an idealization.

This is a what I thought.

The properties attributed, in sloppy pop science-speak, to the singularity at $t = 0$ are actually properties of limits taken as $t \rightarrow 0$. For example, the limit of the "scale factor" $a$ as $t \rightarrow 0$ is $0$, but that does not mean the universe ever actually has "zero size"; the limit is just a mathematical limit, not a physical description of the universe.

I get what you mean, but in this context, $t = 0$ refers to the beginning of the universe. So if we believe that time is continuous (and not discrete), it seems a bit awkward to exclude $t = 0$, because our model had not beginning then.

 

[Bandersnatch]

because our model had not beginning then.

The model doesn't need to 'have' a beginning. It only needs to have a domain of applicability.

 

[marcus]

Dear all,

The term "big bang singularity" somehow seems to imply that the universe had zero extent ...

Classical (i.e. not quantum) physics is a useful approximation to more fundamental quantum physics. But the approximation cannot be taken to extremes---at extremely high density, extremely small scale etc. it often breaks down and stops giving useful results. As Bandersnatch indicated, it has a limited domain of applicability.

Since you are interested in what cosmologists have to say in a regime where the classical (un quantized) model fails, I suggest you look at current research in quantum cosmology (QC). QC models are approaching testability. So far there is no consensus but it is an active line of research and testable predictions are being made (see especially recent work by Ashtekar, Agullo, Barrau, Wilson-Ewing)

Here's an Inspire data-base search for quantum cosmology research papers from 2009 onwards---ordered by number of citations---most cited papers are listed first:
http://inspirehep.net/search?ln=en&ln=en&p="quantum cosmology" and NOT d 1900->2008&of=hb&action_search=Search&sf=&so=d&rm=citation&rg=25&sc=0

If you want to restrict to more recent just change the year number, for example here it is 2011 onwards:
http://inspirehep.net/search?ln=en&ln=en&p="quantum cosmology" and NOT d 1900->2010&of=hb&action_search=Search&sf=&so=d&rm=citation&rg=25&sc=0

To me this is even more interesting, change the year number to get from 2013 onwards:
http://inspirehep.net/search?ln=en&ln=en&p="quantum+cosmology"+and+NOT+d+1900->2012&of=hb&action_search=Search&sf=&so=d&rm=citation&rg=25&sc=0

This gives an idea of what the very recent research in Quantum Cosmology has been about, looking down the list of titles. It's also sorted by number of citations so you see the papers that aroused the most interest among the other researchers and whose results proved most useful--so they got cited.

Anyway, as a rule in the quantum cosmology models quantum effects take over at extreme density and distances do NOT go to zero. and there is no "singularity". Singularity just means unphysical failure of a model. So these researchers are exploring what might have happened instead and what happened before the start of expansion, before classical (non-quantum) models start to make sense.

 

[PeterDonis]

in this context, $t = 0$ refers to the beginning of the universe.

No, it doesn't. It refers to a mathematical limit that can be taken, but there is no actual physical point or region in spacetime that corresponds to $t = 0$.

 

[Smattering]

No, it doesn't. It refers to a mathematical limit that can be taken, but there is no actual physical point or region in spacetime that corresponds to $t = 0$.

O.k., then one of following statements must be true:

1. The universe has no beginning.
2. The model simply does not cover this case.

 

[haushofer]

Indeed, point 2 is the case. An axiom of general relativity is that spacetime is a manifold, and hence has a smooth structure. In a physical singularity this axiom is invalid, and your theory breaks down.

 

[PeterDonis]

one of following statements must be true:

1. The universe has no beginning.
2. The model simply does not cover this case.

Both 1. and 2. could be true. We don't know whether 1. is true or not; but 2. is true because we expect classical GR to break down when spacetime curvature gets large enough (or, equivalently, when the density gets large enough) for quantum gravity effects to become significant. That is expected to happen at some finite value of curvature (or density); our best guess at this point is the Planck density--one Planck mass per Planck volume, or about $10^{94}$ times the density of water.

However, in saying that, as far as the idealized model is concerned, 1. must be true, is mistaken if by 1. you mean that the universe must have existed, according to the model, for an infinite time in the past. That is not the case. In the idealized model, every observer has only a finite amount of time in his past. The fact that the singularity at $t = 0$ is not actually part of spacetime does not change that. You can still take limits as $t \rightarrow 0$, as I said before, and one of those limits gives you the amount of time in the past of a "comoving" observer. That limit is finite.

 

[Smattering]

However, in saying that, as far as the idealized model is concerned, 1. must be true, is mistaken if by 1. you mean that the universe must have existed, according to the model, for an infinite time in the past.

No, I mean that for any point in time that you specify, I can specify an earlier point in time such that the universe also existed. Of course, this is only valid if time is continuous. If time is discrete, we can exclude $t = 0$ and just specify $t = 1$ as the earliest point in time after the universe came into existence.

 

[PeterDonis]

I mean that for any point in time that you specify, I can specify an earlier point in time such that the universe also existed.

Ah, ok. Yes, this is true in the idealized model; but it's also true in any spacetime model, because any spacetime model must be an open set, and the property you describe is one of the properties of an open set.

Of course, this is only valid if time is continuous.

Yes, but that's also a property of any classical spacetime model; the model is built using a continuous 4-dimensional set of points.

 

[marcus]

Smattering, with all respect I think it is a waste of time to quibble about the well-known limitations of the Classical Cosmology model.
It is based on 1915 Einstein GR and it fails to give interesting/meaningful results about the Natural world if you push it to extremes beyond where it is known to be applicable. Peter has made that point for you several times, as I recall.
So no conclusions, philosophical or otherwise, can be drawn from what the standard cosmic model does if you get too close to its limits of applicability.

If you are interested in current cosmology research as it applies to conditions around and before the start of expansion then I would suggest learning something about recent quantum cosmology models. A hot issue at present is the testability or in other words falsifiability of these models. To be meaningful a theory's predictions have to able to be confronted with observation and it has to be possible to show the theory wrong if it doesn't fit the data.

Typically these QC models concern what was happening before inflation (or they make it unnecessary--a prior contracting phase prepares suitable conditions). So in the case where inflation is assumed the question comes up of how do you test---here's a recent 5 page paper grappling with that:

http://arxiv.org/abs/1510.08766
Observational Exclusion of a Consistent Quantum Cosmological Scenario
Boris Bolliet, Aurelien Barrau, Julien Grain, Susanne Schander
(Submitted on 29 Oct 2015)
It is often argued that inflation erases all the information about what took place before it started. Quantum gravity, relevant in the Planck era, seems therefore mostly impossible to probe with cosmological observations. ...
...We emphasize that neither loop quantum cosmology in general nor loop quantum gravity are disfavored by this study but their falsifiability is established.
5 pages, 1 figure

Here are some sample excerpts from the Introduction at the beginning and the Conclusions paragraph at the end.
==quote==
Introduction.—This Letter aims at giving a concrete example of a fully consistent quantum cosmology scenario with general relativity (GR) as its low-energy limit and leading to a standard phase of inflationary expansion of the Universe that is excluded by current experimental data. Although the considered model belongs to the loop quantum cosmology (LQC) framework, we emphasize from the beginning that the claim is not that loop quantum gravity (LQG) or LQC is excluded. The other way round: the fact that some specific settings within LQC are excluded demonstrates that the theory can fill the bridge between calculations and observations, which makes it an especially appealing quantum gravity proposal.
...
...
...
Our main conclusion is that although the quantum cosmology model that is considered in this work is well-defined, well-motivated, has the standard Friedmann equation as its low-density limit and, even more importantly, leads to the required amount of inflation, it is excluded by current data. This illustrates with a concrete example that the usual statement claiming that “whatever happens before inflation cannot be probed” is incorrect. Cosmological tests of quantum gravity are now possible, even with mainstream models without any tuning of the parameters. However it is important to underline that only a very specific version of LQC is excluded: a universe filled with a massive scalar field, treated in the deformed algebra approach, with initial conditions set in the remote past before the bounce, no backreation, no anisotropies and no cutoff scale. This is, in itself, a substantial result to establish loop quantum cosmology as a predictive theory.
==endquote==

 

[Smattering]

Smattering, with all respect I think it is a waste of time to quibble about the well-known limitations of the Classical Cosmology model.
It is based on 1915 Einstein GR and it fails to give interesting/meaningful results about the Natural world if you push it to extremes beyond where it is known to be applicable. Peter has made that point for you several times, as I recall.
So no conclusions, philosophical or otherwise, can be drawn from what the standard cosmic model does if you get too close to its limits of applicability.

If you are interested in current cosmology research as it applies to conditions around and before the start of expansion then I would suggest learning something about recent quantum cosmology models.

I fear that LQG is far beyond what I can learn in a reasonable amount of time. So just to get an idea: How does the LQG approach deal with $t = 0$?

 

[marcus]

The main classical (pre quantum) equation is the 1915 GR equation. There are various ways to make that into a quantum equation, LQG is one of the main ways people use and it leads to a quantized Friedmann (cosmology) equation.
Then one finds that quantum corrections to the equation begin to dominate at very high energy density. At a critical density gravity becomes repellent instead of attractive. So a universe like ours, but collapsing, must reach the critical maximum density and REBOUND.

This gives expansion its initial kick. It explains why our universe is expanding. Even if the cosmo constant were zero it would still be expanding.
It avoids the failure called "singularity". And some versions of LQC also have an inflaton field---the bounce gives energy to start inflation.
But some versions don't need to resort to inflation.

Attention is now focusing on how do you test these various versions of bounce cosmology. What kind of observations can be used to exclude some but not others.

 

[Smattering]

Then one finds that quantum corrections to the equation begin to dominate at very high energy density. At a critical density gravity becomes repellent instead of attractive. So a universe like ours, but collapsing, must reach the critical maximum density and REBOUND.

This is very interesting. I have heard about that bounce hypothesis before, but I did not know that it is due to gravity becoming repellent at a certain energy density.

However, if the speculation is that the big bang might have resulted from the collapse of a preceding universe, why does our universe seem to be expanding at an increasing rate? As far as I understood, the big crunch scenario is currently considered less likely than a big chill or big rip.

 

[marcus]

There is no contradiction. The equations are reversible. the same universe, with the same cosmological constant, can contract, bounce, and re-expand---following the same curve in that it is now following out. This is not a "cyclic" picture---no indication of its repeating. (Why should there be?)
AFAIK there is no conjecture as to where the whole thing "came from" or "what made it?" Or "why does existence exist?"
Perhaps those are unproductive questions to be asking at this point---not ripe for humans to tackle yet.

What seems answerable and currently attracting intelligent attention focuses on the immediate problem---what came immediately before our own start of expansion. We have a huge amount of relevant observational data and more will be coming in. Even as early as 2016 Planck mission has some more to release.

There are "cyclic" bounce cosmic models (including some LQC-based ones) and there are one-shot bounce models. An example of the latter was presented in a December 2014 paper co-authored by Edward Wilson-Ewing called "LambdaCDM bounce scenario" LambdaCDM is the technical name for the standard cosmic model people currently use in Cosmology: based on a positive cosmo constant Lambda, and cold dark matter (CDM).
It is a one-shot bounce model that fits currently available data and moreover does away with the need for an inflation episode, which makes it kind of interesting
http://arxiv.org/abs/1412.2914

 

[marcus]

This is very interesting. I have heard about that bounce hypothesis before, but I did not know that it is due to gravity becoming repellent at a certain energy density...

That particular bounce mechanism is only in LQC as far as I know. There are many cosmologists who have studied bounce models and several mechanisms are considered. LQC is only one line of research among a number of approaches that replace the "singularity" with a bounce of one sort or another.

 

[Torbjorn_L]

I get what you mean, but in this context, $t = 0$ refers to the beginning of the universe.

No necessarily. Ever since inflation cosmology replaced the old singularity models of Big Bang, the local universe that has some physics of relevance for life (stars) began at the Hot Big Bang era. The preceeding inflation era was cold and contained only inflatons, was of indefinite duration and could naturally have spawned any number of universes. Admittedly the latest Planck data releases that implies a spatially infinite universe and a finite duration inflation era puts those possibilities in tension. But it shows that there is some difficulty with identifying a useful beginning of the universe elsewhere than with the HBB.

However, in saying that, as far as the idealized model is concerned, 1. must be true, is mistaken if by 1. you mean that the universe must have existed, according to the model, for an infinite time in the past. That is not the case. In the idealized model, every observer has only a finite amount of time in his past. The fact that the singularity at $t = 0$ is not actually part of spacetime does not change that. You can still take limits as $t \rightarrow 0$, as I said before, and one of those limits gives you the amount of time in the past of a "comoving" observer. That limit is finite.

Linde was able to reject that in one of his papers on chaotic inflation. Turns out inflation means you can always choose a longer past timeline among observers, making the global set of indefinite (infinite) duration in the same way as counting finite numbers indefinitely does.

But current Planck data may imply - as far as this layman understands - that didn't happen.

There are "cyclic" bounce cosmic models (including some LQC-based ones) and there are one-shot bounce models. An example of the latter was presented in a December 2014 paper co-authored by Edward Wilson-Ewing called "LambdaCDM bounce scenario" LambdaCDM is the technical name for the standard cosmic model people currently use in Cosmology: based on a positive cosmo constant Lambda, and cold dark matter (CDM).
It is a one-shot bounce model that fits currently available data and moreover does away with the need for an inflation episode, which makes it kind of interesting

Planck polarization data shows that there will always be a need for inflation from now on, the LambdaCDM universe is the only one that naturally predicts the correct polarization curves without adding a single parameter. It behooves us to point out that besides a few diehards inflation is now the consensus. (Unless I have misunderstood the last year's cosmologist sundry web posts.) I guess we should also point out - despite it being superfluous seeing the former point - that LQG are non-viable math theories that have never been able to become a physics theory of dynamics (no lower energy bound, no harmonic oscillators).

EDIT: Typo.