RECORD
Fluctuations of the Gravitational Constant in the Inflationary Brans-Dicke Cosmology
Astrophysics · Submitted 16 Dec 1993
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We have found that in some inflationary models the probability distribution P_p rapidly approaches a stationary regime.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
According to the Brans--Dicke theory, the value of the gravitational constant G which we measure at present is determined by the value of the Brans--Dicke scalar field \phi at the end of inflation. However, due to quantum fluctuations of the scalar fields produced during inflation, the gravitational constant G(\phi) may take different values in different exponentially large parts of the Universe. We investigate the probability distribution P_p to find a domain of a given volume with a given value of the gravitational constant G at a given time. The investigation is performed for a wide class of effective potentials of the scalar field \sigma which drives inflation, and with two different time parametrizations. Our work is based on the analytical study of the diffusion equations for P_p, as well as on the computer simulation of stochastic processes in the inflationary Universe. We have found that in some inflationary models the probability distribution P_p rapidly approaches a stationary regime. The shape of the distribution depends, however, on the choice of the time parametrization. In some other models the distribution P_p is not stationary. An interpretation of our results and of all ambiguities involved is outlined, and a possible role of anthropic considerations in determination of the gravitational constant is discussed.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | According to the Brans--Dicke theory, the value of the gravitational constant G which we measure at present is determined by the value of the Brans--Dicke scalar field \phi at the end of inflation. | background 1.00 | 0.06 | 0.05 | asserted 1.00 |
| s1 | However, due to quantum fluctuations of the scalar fields produced during inflation, the gravitational constant G(\phi) may take different values in different exponentially large parts of the Universe. | background 0.96 | 0.09 | 0.08 | hedged possibility 1.00 |
| s2 | We investigate the probability distribution P_p to find a domain of a given volume with a given value of the gravitational constant G at a given time. | contribution 0.96 | 0.85 | 0.04 | asserted 0.92 |
| s3 | The investigation is performed for a wide class of effective potentials of the scalar field \sigma which drives inflation, and with two different time parametrizations. | method 0.95 | 0.84 | 0.03 | asserted 0.99 |
| s4 | Our work is based on the analytical study of the diffusion equations for P_p, as well as on the computer simulation of stochastic processes in the inflationary Universe. | method 1.00 | 0.92 | 0.03 | asserted 1.00 |
| s5 | We have found that in some inflationary models the probability distribution P_p rapidly approaches a stationary regime. | result 1.00 | 0.97 | 0.31 | asserted 0.99 |
| s6 | The shape of the distribution depends, however, on the choice of the time parametrization. | result 0.99 | 0.86 | 0.12 | asserted 0.99 |
| s7 | In some other models the distribution P_p is not stationary. | result 1.00 | 0.88 | 0.11 | asserted 1.00 |
| s8 | An interpretation of our results and of all ambiguities involved is outlined, and a possible role of anthropic considerations in determination of the gravitational constant is discussed. | interpretation 1.00 | 0.62 | 0.15 | hedged possibility 0.51 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
According to the Brans--Dicke theory, the value of the gravitational constant G which we measure at present is determined by the value of the Brans--Dicke scalar field \phi at the end of inflation. However, due to quantum fluctuations of the scalar fields produced during inflation, the gravitational constant G(\phi) may take different values in different exponentially large parts of the Universe. We investigate the probability distribution P_p to find a domain of a given volume with a given value of the gravitational constant G at a given time. The investigation is performed for a wide class of effective potentials of the scalar field \sigma which drives inflation, and with two different time parametrizations. Our work is based on the analytical study of the diffusion equations for P_p, as well as on the computer simulation of stochastic processes in the inflationary Universe. We have found that in some inflationary models the probability distribution P_p rapidly approaches a stationary regime. The shape of the distribution depends, however, on the choice of the time parametrization. In some other models the distribution P_p is not stationary. An interpretation of our results and of all ambiguities involved is outlined, and a possible role of anthropic considerations in determination of the gravitational constant is discussed.
Human review
References
How the literature uses it
35 arXiv papers cite this in 81 sentences
Papers citing it · 48 sentences without a confident label
Contests it 2 papers
-
Indeed, the probability distribution proposed in [ref] was very far from stationary at the beginning of the process, when $t < max{t_21, t_45}$, see Fig. [ref].
Towards a gauge invariant volume-weighted probability measure for eternal inflation · Volume-weighted measure for slow-roll inflation · contest 0.79
-
This fact was not taken into account in our earlier papers [ref] ; the calculations of the probabilities started everywhere at the same time, even if the corresponding parts of the universe did not yet approach the stationary regime.
Inflationary Cosmology · Inflationary multiverse, string theory landscape and the anthropic principle · contest 0.76
Builds on it 1 paper
-
[ref] and dynamical analysis in ref.
Slow-Roll Inflation in the Jordan Frame · Introduction · 0.89
Uses its method or tool 1 paper
-
Meanwhile the volume-weighted anthropic probability measure, which was first proposed in [ref] , uses the methods developed in [ref] , but calculates the probability currents through the hypersurface of a given temperature/density/scalar field.
Towards a gauge invariant volume-weighted probability measure for eternal inflation · Volume-weighted measure for slow-roll inflation · 0.81
Compares with it 1 paper
-
It is instructive to compare this result to the result which we would obtain using the old measure of [ref] prior to its improvement: P(T_1, τ)P(T_2, τ) = V(T_1)V(T_2) e^H_3^βΔt , where $Δt = t(T_2) - t(T_1)$, and $t(T)$ is the time when the universe cools down to the temperature $T$.
Towards a gauge invariant volume-weighted probability measure for eternal inflation · Volume-weighted measure for slow-roll inflation · 1.00
Cites it as support 1 paper
-
In Ref. [ref] , this measure is called the “pseudo-comoving volume-weighted measure.”] [ref] has been shown to be free of all of the above issues [ref] , we consider it to be a promising candidate for the measure of the multiverse.
Boltzmann brains and the scale-factor cutoff measure of the multiverse · Introduction · 0.96
Cites it as background 19 papers
-
The problem is to define precisely what it means to be “typical” among infinitely many possible observers and to compute the resulting distribution of observed parameters [ref] .
Stationary Measure in the Multiverse · Introduction · 0.82
-
The first global-local duality was described in Ref. [ref] : The (global) scale factor time cut-off [ref] is dual to the (local) “fat geodesic” cut-off, in which the neighborhood of the geodesic is chosen to have fixed physical volume, and one averages over geodesics starting in a particular vacuum: that which occupies the greatest proper volume fraction at late scale factor time.
Global-Local Duality in Eternal Inflation · Introduction · 0.80
-
Finally, we comment on the use of measure probabilities [ref] in this work.
Inflating to the Weak Scale · Model Discussion · 0.92
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.