On the measure problem in slow roll inflation and loop quantum cosmology

Alejandro Corichi; Asieh Karami

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On the measure problem in slow roll inflation and loop quantum cosmology

Alejandro Corichi, Asieh Karami

General Relativity and Quantum Cosmology · Submitted 18 Nov 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The singularity free scenario of loop quantum cosmology offers a natural choice of initial conditions, and suggests that enough inflation is generic.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.62 · compares with prior results 0.97 · mentions code or data availability 0.02.

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We consider the measure problem in standard slow-roll inflationary models from the perspective of loop quantum cosmology (LQC). Following recent results by Ashtekar and Sloan, we study the probability of having enough e-foldings and focus on its dependence on the quantum gravity scale, including the transition of the theory to the limit where general relativity (GR) is recovered. Contrary to the standard expectation, the probability of having enough inflation, that is close to one in LQC, grows and tends to 1 as one approaches the GR limit. We study the origin of the tension between these results with those by Gibbons and Turok, and offer an explanation that brings these apparent contradictory results into a coherent picture. As we show, the conflicting results stem from different choices of initial conditions for the computation of probability. The singularity free scenario of loop quantum cosmology offers a natural choice of initial conditions, and suggests that enough inflation is generic.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider the measure problem in standard slow-roll inflationary models from the perspective of loop quantum cosmology (LQC).	contribution 0.79	0.77	0.04	asserted 0.60
s1	Following recent results by Ashtekar and Sloan, we study the probability of having enough e-foldings and focus on its dependence on the quantum gravity scale, including the transition of the theory to the limit where general relativity (GR) is recovered.	contribution 0.79	0.79	0.06	asserted 0.88
s2	Contrary to the standard expectation, the probability of having enough inflation, that is close to one in LQC, grows and tends to 1 as one approaches the GR limit.	result 1.00	0.80	0.70	asserted 1.00
s3	We study the origin of the tension between these results with those by Gibbons and Turok, and offer an explanation that brings these apparent contradictory results into a coherent picture.	contribution 0.98	0.88	0.10	asserted 0.92
s4	As we show, the conflicting results stem from different choices of initial conditions for the computation of probability.	interpretation 0.62	0.83	0.26	asserted 1.00
s5	The singularity free scenario of loop quantum cosmology offers a natural choice of initial conditions, and suggests that enough inflation is generic.	interpretation 0.94	0.56	0.54	hedged possibility 0.90

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 0.66.

What was examined, and what was not

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arXiv listing abstract v2

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full text
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We consider the measure problem in standard slow-roll inflationary models from the perspective of loop quantum cosmology (LQC). Following recent results by Ashtekar and Sloan, we study the probability of having enough e-foldings and focus on its dependence on the quantum gravity scale, including the transition of the theory to the limit where general relativity (GR) is recovered. Contrary to the standard expectation, the probability of having enough inflation, that is close to one in LQC, grows and tends to 1 as one approaches the GR limit. We study the origin of the tension between these results with those by Gibbons and Turok, and offer an explanation that brings these apparent contradictory results into a coherent picture. As we show, the conflicting results stem from different choices of initial conditions for the computation of probability. The singularity free scenario of loop quantum cosmology offers a natural choice of initial conditions, and suggests that enough inflation is generic.

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References

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Warm bounce in loop quantum cosmology and the prediction for the duration of inflation
gr-qc 2020-09 conditional novelty 6.0 of 10

In loop quantum cosmology, the likely duration of inflation after the bounce is computed for several potentials, with and without pre-bounce radiation, giving median e-fold numbers from about 59 to 144 and showing rad...
Robustness of Inflation to Inhomogeneous Initial Conditions
hep-th 2016-08 accept novelty 6.0 of 10

Small-field inflation fails once initial gradient energy reaches roughly 10^-4 of the potential energy, whereas large-field inflation survives gradients exceeding the potential energy by orders of magnitude.
Probability of Inflation in Loop Quantum Cosmology
gr-qc 2011-03 conditional novelty 6.0 of 10

Using the bounce surface of loop quantum cosmology as a canonical time slice, the authors compute that the probability of a WMAP-compatible slow-roll inflation is greater than 0.999997.
Robustness of Inflation to Large Tensor Perturbations
hep-th 2017-12 conditional novelty 5.0 of 10

Adding a transverse-traceless metric perturbation to inhomogeneous small-field inflation first reduces the number of e-folds, but the reduction saturates and reverses above a perturbation energy density comparable to ...
Initial Conditions for Inflation - A Short Review
hep-th 2016-01 accept novelty 2.0 of 10

Large-field inflation's slow-roll trajectory is a local attractor in initial-condition space, whereas small-field inflation requires a tuned initial field velocity.

How the literature uses it

29 arXiv papers cite this in 39 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 2 papers

It is also shown that these loop quantum gravity corrections can overcome the classical suppression of the probability only for extremely unnatural choices of ambiguity parameters, implying that single field, slow-roll inflation is exponentially unlikely.

The probability of inflation in Loop Quantum Cosmology · 0.93
We conclude that, for such a class of inflationary models and for natural values of the loop quantum cosmology parameters, a successful inflationary scenario is highly improbable.

On the Onset of Inflation in Loop Quantum Cosmology · 0.92

Papers citing it · 24 sentences without a confident label

Compares with it 1 paper

This is reminiscent of the divergences manifest in the non-gauge fixed approach assuming a flat probability distribution [ref] .

Polymer inflation · Probability of inflation · 0.90

Cites it as support 3 papers

However, because the inflationary trajectory is an attractor, this solution can be reached starting from `almost any' initial data (within the high accuracy of numerical codes) [ref] .

Quantum Gravity in the Sky: Interplay between fundamental theory and observations · Selection of the dressed effective background solution · 0.99
In fact, it has been shown [ref] (see also [ref] ) that the measure gets squeezed by time evolution into regions of phase space which yield inflation.

Initial Conditions for Inflation - A Short Review · Initial Conditions in Mini-Superspace · 0.99
That is indeed true if you note that the Higgs field has the peak in its effective potential below the Planck scale field value, and that all potential inflaton fields with their plataue or their peak below the Planck scale have a “slow roll” problem [ref] .

PREdicted the Higgs Mass · The Inflaton Could be a Higgs ? · 0.99

Cites it as background 10 papers

In literature, many interesting physical implications of this phase have been studied (see Ref. [ref] for a review), including the qualitative dynamics of different potentials [ref] and computation of probability for inflation in $ϕ^2$ potential to occur [ref] .[Dynamics of bounce and inflation has also been studied in models not incorporating LQC.

Non-singular Power-law and Assisted inflation in Loop Quantum Cosmology · Effective dynamics in LQC · 0.90
The issue of initial conditions for inflation and the stability of de Sitter and inflationary spacetimes have been under investigation for as long as inflation itself [ref] , and there are many analytic and semi-analytic [ref] as well as numerical studies [ref] (see [ref] for a short review).

Robustness of Inflation to Inhomogeneous Initial Conditions · Introduction · 1.00
The problem of initial conditions for inflation has been extensively studied using analytic and semi-analytic methods [ref] .

Robustness of inflation to kinetic inhomogeneities · Introduction · 0.97

What it cites · 50 sentences without a confident label

Compares with 2 papers

Next, we give an argument based on global properties of the dynamics and the Liouville measure to understand the results of both [ref] and [ref] .

The Measure Problem in Cosmology · Introduction · 0.82
Next, we give an argument based on global properties of the dynamics and the Liouville measure to understand the results of both [ref] and [ref] .

Loop quantum cosmology and slow roll inflation · Introduction · 0.82

Cites as background 5 papers

This has been answered with different levels of sophistication [ref] .

Quantum Nature of the Big Bang · Introduction · 0.84
This has been answered with different levels of sophistication [ref] .

Robustness of key features of loop quantum cosmology · Introduction · 0.84
This has been answered with different levels of sophistication [ref] .

Polymer Quantum Mechanics and its Continuum Limit · Introduction · 0.84

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