How has LQG resolved the Big Bang Singularity

In summary, the Loop Quantum Gravity (LQG) models have resolved the big bang singularity into a finite big crunch by using techniques from quantum gravity to extend the standard cosmological perturbation theory. This is a promising avenue as it has been shown in various LQC models that the big bang singularity has been resolved. However, the model still needs to be tested against observations and accepted by the scientific community. The key difference from standard inflation is that in LQG, quantum fields propagate on a quantum geometry that is free of singularities, allowing for a bounce rather than a singularity. This has been checked and rechecked in various cases, making the conclusion fairly robust. The discreteness of spectra of geometric operators in LQC may
  • #1
Naty1
5,606
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I get the impression from the following material that LQG models have 'resolved'
the divergent big bang singularity into a finite big crunch...
If so, what changed and is this a generally accepted 'new start' at the front end of the FLRW model which follows??

I may have missed some discussions in November/December as I was away,
but I did skim this discussion from that time frame:

Penrose's argument that q.g. can't remove the Big Bang singularity
https://www.physicsforums.com/showthread.php?t=649836From that discussion, papers linked to by Marcus were discussed, so I read them and was surprised to find this in the Introduction:

An Extension of the Quantum Theory of Cosmological
Perturbations to the Planck Era
Ivan Agullo, Abhay Ashtekar, William Nelson

http://arxiv.org/pdf/1211.1354v1.pdf
...the FLRW space-times of interest are invariably incomplete in the past
due to the big bang singularity where matter fields and space-time curvature diverge...
... to encompass the Planck regime, one needs a quantum gravity extension of
the standard cosmological perturbation theory. ...Loop quantum gravity (LQG) provides a promising avenue to meet this goal because by now the big bang singularity has been resolved in a variety of models in LQC. It is therefore natural to use LQC as the point of departure for extending the cosmological perturbation theory.

Can someone explain what has been 'resolved'?

From the other paper by the same authors,

A Quantum Gravity Extension of the Inflationary Scenario
Ivan Agullo, Abhay Ashtekar, William Nelson
(Submitted on 7 Sep 2012)
http://arxiv.org/abs/1209.1609

the early text says this:
...Since the standard inflationary paradigm is based on quantum field theory on classical space-times, it excludes the Planck era... Using techniques from loop quantum gravity, the paradigm is extended to a self-consistent theory from the Planck scale to the onset of slow roll inflation, ...Loop quantum gravity (LQG) offers a natural framework to address these issues because effects of its underlying quantum geometry dominate at the Planck scale…The key difference from standard inflation is that quantum fields … now propagate on a quantum geometry represented by Ψo (a, φ) rather than on a classical Friedmann solution (a(t), φ(t)). These quantum geometries are all regular, free of singularities. Thus, by construction, the framework encompasses the Planck regime…., we use the conceptual framework of quantum field theory on cosmological quantum geometries
In layman's terms, did truncating [the author's term] continuous spacetime somehow eliminate the associated divergences??
 
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  • #2
Naty1 said:
...Can someone explain what has been 'resolved'? ...

==Naty's question more in context, quote==
...
...
An Extension of the Quantum Theory of Cosmological
Perturbations to the Planck Era
Ivan Agullo, Abhay Ashtekar, William Nelson

http://arxiv.org/pdf/1211.1354v1.pdfAn Extension of the Quantum Theory of Cosmological
Perturbations to the Planck Era
Ivan Agullo, Abhay Ashtekar, William Nelson

http://arxiv.org/pdf/1211.1354v1.pdf "...Loop quantum gravity (LQG) provides a promising avenue to meet this goal because by now the big bang singularity has been resolved in a variety of models in LQC. It is therefore natural to use LQC as the point of departure for extending the cosmological perturbation theory."

Can someone explain what has been 'resolved'?

From the other paper by the same authors,

A Quantum Gravity Extension of the Inflationary Scenario
Ivan Agullo, Abhay Ashtekar, William Nelson
(Submitted on 7 Sep 2012)
http://arxiv.org/abs/1209.1609

the early text says this:

"...Loop quantum gravity (LQG) offers a natural framework to address these issues because effects of its underlying quantum geometry dominate at the Planck scale…The key difference from standard inflation is that quantum fields … now propagate on a quantum geometry represented by Ψo (a, φ) rather than on a classical Friedmann solution (a(t), φ(t)). These quantum geometries are all regular, free of singularities. Thus, by construction, the framework encompasses the Planck regime…., we use the conceptual framework of quantum field theory on cosmological quantum geometries"
...
...
===endquote===

It will be interesting to see what other people have to say! One simple thing to mention is that "resolve" singularities just means that in your model you get rid of singularities because in your model the singularities in question do not occur.

The model still has to be tested against observation. Nothing has been "resolved" in a general sense until the model has passed whatever tests people can devise and has become accepted.

What they mean is they have constructed a number of LQC models (both equation models and computer models) and they all show a bounce from a prior contraction, rather than stopping at a singularity as you go back in time.
By now they have constructed LQC models with a lot of non-uniformities, unevenness, not-homogeneous, not-isotropic, more degrees of freedom than just one or two. So far the conclusion that in LQC there is a bounce is fairly "robust". This does not mean that it happened in Nature. That is still controversial and has to be checked.

that is what it means to say the singularities have been resolved in LQC.

We already knew that in 2005 or 2006 but then it had only been checked in a few of the simpler cases, with a comparatively few computer simulations etc. Since then it has been checked and rechecked in more different cases with varying the parameters, changing details, putting in the little non-uniformities and so forth.
 
  • #3
Naty, if you have a question about the word "truncating" which you say the authors used, could you find a passage and quote it and tell us the page so we can find the context?

I think what you are referring to could have to do with the discreteness of the spectra of geometric operators in LQC. There is a GAP between zero volume and the lowest positive volume that can be measured. Space might be continuous but when it comes to making measurements and defining operationally meaningful quantities there are limits, in the theory.

In the theory (which may or may not agree with Nature) there are limits to how small you can measure and how dense something can be. This might be what they were talking about. I'm not thoroughly versed in this but if you can find the passage, and give a page reference, I'll take a look.
 
  • #4
oh, Boo...big disappointment...if this all there is:

Marcus:
One simple thing to mention is that "resolve" singularities just means that in your model you get rid of singularities because in your model the singularities in question do not occur.
TRUNCATE COMES from the page two, second paragraph of this paper, Introduction,

An Extension of the Quantum Theory of Cosmological
Perturbations to the Planck Era
Ivan Agullo, Abhay Ashtekar, William Nelson

http://arxiv.org/pdf/1211.1354v1.pdf

...However, to do so, we cannot just mimic
the standard procedure used in general relativity because LQG does yet offer the quantum version of full Einstein’s equations which one can linearize around a quantum FLRW spacetime. Therefore we will use the general strategy that has been repeatedly followed in LQG: First truncate the classical theory in a manner appropriate to the physical problem under consideration, then carry out quantization using LQG techniques, i.e., paying due attention to the underlying quantum geometry, and finally work out the physical implications of the framework. This strategy has led to advances in the cosmological models referred to above, as well as in the investigation of quantum black holes [32–34] and the spin foam derivation of the graviton propagator [35–37]...
TRUNCATING caught caught my attention because earlier space-time discussions in these forums suggested maybe, based on information theory for example, 'quantized' and 'continuous' space-time might be indistinguishable. So imagine my surprise when "TRUNCATING the classical theory" eliminates Big bang divergence...if that's what happens.

edit: I see TRUNCATING is explained in Part III of the same paper...
TRUNCATED HAMILTONIAN FRAMEWORK...oh boy, is THAT above my pay grade...except if it IS a popular approach now, maybe a non mathematical explanation of the motivation could be helpful.

edit:

Marcus: "Space might be continuous but when it comes to making measurements and defining operationally meaningful quantities there are limits, in the theory."

How would you interpret this from the same paper Introduction

"This paper …. provides a detailed extension of the cosmological perturbation theory to the Planck regime...Specifically, we will consider gravity coupled to a scalar field and study the dynamics of quantum fields representing scalar and tensor perturbations on quantum cosmological space-times. "

I took this to mean they quantized Einstein continuous spacetime at Planck scale...I think they said as much somewhere...Maybe I am reading too much into the explanations...
 
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  • #5
The big bang singularity is not resolved in LQG.

It does seem to be resolved in several versions of LQC. The difference between LQC and LQG is that LQC only allows solutions with a high degree of symmetry - this is essentially what is meant by "truncate" - the solutions with low or no symmetry are not allowed. For this reason, LQC is not considered a full theory of quantum gravity as LQG aims to be. In these papers, there is some degree of inhomogeneity allowed in LQC, but these are assumed not to backreact on the quantum geometry, so LQC is still symmetry restricted.
 
  • #6
  • #8
Key insights from the Wiki link:

The distinguishing feature of LQC is the prominent role played by the quantum geometry effects of LQG. In particular, quantum geometry creates a brand new repulsive force which is totally negligible at low space-time curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction and thereby resolving singularities of general relativity. Once singularities are resolved, the conceptual paradigm of cosmology changes and one has to revisit many of the standard issues —e.g., the ‘horizon problem’— from a new perspective... In LQC the big bang is replaced by a quantum bounce...

Sounds like quantum geometry repulsion effects prevent classical space-time divergence?Rereading the Penrose thread, Marcus posted there:

"
[Penrose argues against LQC bounce, but the essence of the bounce is that gravity becomes repellent due to quantum corrections at near-Planck density--that's why there is a bounce./QUOTE]"

Now I am unsure how I got LQG in the title of this thread; Looks like it should have been LQC...
 
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  • #9
atyy:

Wiki has a short bit on Yorkies:

http://en.wikipedia.org/wiki/Yorkshire_Terrier

Lol/////you know I never looked! Thanks...

from Wiki:
Temperament

The ideal Yorkshire Terrier character or "personality" is described with a "carriage very upright" and "conveying an important air."[2] Though small, the Yorkshire Terrier is active, very overprotective, loves attention, and should not show the soft temperament seen in lap dogs. Yorkshire Terriers, also known as Yorkies, are a easy dog breed to train. This results from their own nature to work without human assistance.
Yorkshire Terriers tend to bark a lot. This makes them excellent watch dogs because they will sound the alarm when anyone gets near. This barking problem can be resolved with proper training.


This description is maybe 2/3 correct! Not overprotective: our Schnauzer mix is more so, some Yorkies show LOTS 'SOFT temperament'...when THEY want; NOT always so easy to train...not mentioned: VERY smart, BIG vocabulary, strong willed, got to watch what you say..because THEY KNOW...and are especially sensitive to cues...All I have to do is take my travel bag out of the closet, and my two are READY to travel!

No wonder I can't follow some of Wiki's physics!
 
  • #10
Naty1 said:
Lol/////you know I never looked! Thanks...

from Wiki:
This description is maybe 2/3 correct! Not overprotective: our Schnauzer mix is more so, some Yorkies show LOTS 'SOFT temperament'...when THEY want; NOT always so easy to train...not mentioned: VERY smart, BIG vocabulary, strong willed, got to watch what you say..because THEY KNOW...and are especially sensitive to cues...All I have to do is take my travel bag out of the closet, and my two are READY to travel!

No wonder I can't follow some of Wiki's physics!

Ha, ha - actually I looked it up because I didn't know what "Yorkies" were. Big vocabulary - as in English (or whatever language you speak to them)?
 
  • #11
Naty1 said:
Rereading the Penrose thread, Marcus posted there:

"Penrose argues against LQC bounce, but the essence of the bounce is that gravity becomes repellent due to quantum corrections at near-Planck density--that's why there is a bounce."

Reading one of the earlier Ashtekar papers with Pawlowski and Singh, he comments that this is consistent with Asymptotic Safety (p37):

"The modified field equations (B6) and (B7) can be interpreted as saying that the effective Newton’s constant is given by Geff = G(1 − ρ/ρcrit), where G is the low energy Newton’s constant and ρcrit ≈ 0.82ρPl. Now, the renormalization group analysis based on Euclidean quantum gravity [33] strongly suggests the existence of a non-trivial fixed point at which the theory becomes asymptotically free. The behavior of Geff in LQC is in qualitative agreement with that picture."

I recently came across another piece of evidence supporting this view - unexpected for me, because I don't think these guys generally work on asymptotic safety: Marunovic & Prokopec, On antiscreening in perturbative quantum gravity and resolving the Newtonian singularity.
 
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  • #12
ok, no more 'Yorkie jibber jabber'...back to the papers:

So the behavior of G in LQC is consistent with asymptotic safety according to Ashtekar.
Fine.

Wikipedia has a qualitative explanation about asymptotic freedom in the Standard Model:

The variation in a physical coupling constant under changes of scale can be understood qualitatively as coming from the action of the field on virtual particles carrying the relevant charge. ... In the vicinity of a charge, the vacuum becomes polarized: virtual particles of opposing charge are attracted to the charge, and virtual particles of like charge are repelled. The net effect is to partially cancel out the field at any finite distance. ...In QCD the same thing happens with virtual quark-antiquark pairs; they tend to screen the color charge...

Fine. [Apparently the interaction behavior of the vacuum and virtual particles changes at high energy and short distance.]

Is there a similar qualitative explanation for what's happening in LGC that goes a step or two further than Marcus' explanation and the overview from Wiki:

...quantum geometry creates a brand new repulsive force which is totally negligible at low space-time curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction and thereby resolving singularities of general relativity...In LQC the big bang is replaced by a quantum bounce...
edit:
I skimmed the earlier Ashtekar paper with Pawlowski and Singh,
but did not find much in the way of physical interpretations as to what causes a bounce...but here are some physical interpretations of the math...

Mathematically "..., to obtain the expression of the quantum constraint, one has to first introduce an operator representing curvature of the gravitational connection...An improved Hamiltonian constraint operator is introduced... while with the Hamiltonian constraint used so far in loop quantum cosmology the quantum bounce can occur even at low matter densities,with the new Hamiltonian constraint it occurs only at a Planck-scale density...the scalar field was shown to serve as an internal clock, thereby providing a detailed realization of the ‘emergent time’ idea...Models discussed so far are too simple to be physically realistic.."
 
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  • #13
Naty1 said:
...
Is there a similar qualitative explanation for what's happening in LGC that goes a step or two further than Marcus' explanation and the overview from Wiki...

There is a superb paper about the bounce on the current MIP poll.

I assume you believe the Heisenb. uncer. princ. (nature resists being pinned down) and accept that this has physical effects, so there can be quantum corrections e.g. to the Friedmann equation which are due to these (quantum) physical effects.

So in most of the papers you find a quantum corrected Friedmann equation---Friedmann eqn is derived from Einstein eqn so that is talking about quantum effect on the geometry and that is ENOUGH to cause a bounce because of the term ρ/ρcrit in the corrected Fr. eqn. When it dominates it changes the sign of the Hubble constant H from neg to pos---ie. bounce. contraction changes to expansion.

But this new paper goes further and considers quantum effect on the matter, which also does not like to be pinned down. And a correction to another equation. This contributes extra springiness so that the bounce occurs earlier, at a substantially lower density. It's important work, and really still in progress. This is the first Loop paper of this type, there will be more along these lines. So this will change the relevant physical intuition IMHO.
 
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  • #15
A paper which had an impact on me with regard to the true nature of singularity avoidance in LQG (rather than LQC) was the paper arXiv:gr-qc/0505032 by Thiemann and Brunnemann.

Would like to hear Francesc's opinion as she has experience with understanding inhomogeneous fluctuations in LQC.
 
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FAQ: How has LQG resolved the Big Bang Singularity

How does LQG explain the singularity in the Big Bang theory?

The Loop Quantum Gravity (LQG) theory proposes that the singularity in the Big Bang theory is resolved by the use of a quantum description of gravity. According to LQG, the universe was not infinitely small at the beginning of the Big Bang, but rather had a minimum size determined by the fundamental units of space and time called "loops". These loops prevent the universe from collapsing into a singularity and instead give it a bounce, leading to a cyclical model of the universe.

What evidence supports LQG's resolution of the Big Bang singularity?

LQG is still a developing theory and there is currently no direct evidence to support its resolution of the Big Bang singularity. However, some predictions of LQG, such as the existence of a minimum size to the universe, have been confirmed by observations made by the Planck satellite. In addition, LQG offers a potential solution to the problem of the singularity in general relativity, which is the current theory of gravity.

How does LQG differ from other theories that attempt to resolve the Big Bang singularity?

LQG differs from other theories, such as string theory, in its approach to resolving the singularity. While string theory focuses on the behavior of particles at extremely high energies, LQG focuses on the fundamental units of space and time. LQG also incorporates concepts from both quantum mechanics and general relativity, while other theories may focus on one or the other.

What challenges does LQG face in resolving the Big Bang singularity?

One of the main challenges facing LQG is the lack of direct evidence to support its resolution of the singularity. Additionally, the theory is still being developed and there are many unanswered questions and inconsistencies that need to be addressed. LQG also faces challenges in reconciling its predictions with observations and experiments, as well as integrating it with other theories of physics.

How does LQG's resolution of the Big Bang singularity impact our understanding of the beginning of the universe?

If LQG's resolution of the singularity is confirmed, it would significantly change our understanding of the beginning of the universe. It would suggest that the universe has existed in a cyclical manner, with no true beginning or end. This would also have implications for our understanding of time and the nature of the universe itself. However, more research and evidence is needed to fully understand the implications of LQG's resolution of the singularity.

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