Evolution of Cosmological Perturbations in the Presence of Primordial Magnetic Fields

Kazuhiko Kojima; Kiyotomo Ichiki

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Evolution of Cosmological Perturbations in the Presence of Primordial Magnetic Fields

Kazuhiko Kojima, Kiyotomo Ichiki

Cosmology and Nongalactic Astrophysics · Submitted 9 Feb 2009

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

The authors' main claim We find that the amplitude of the angular power spectrum of CMB anisotropies can alter at most a order of magnitude at $l \lesssim 4000$ compared with the previous results in the literature.

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arXiv ID0902.1367 (version 2)

Pith IDDHCEZSOC, Pith's permanent record of this paper and its review

CitationKazuhiko Kojima, Kiyotomo Ichiki. "Evolution of Cosmological Perturbations in the Presence of Primordial Magnetic Fields." arXiv:0902.1367 (2009). https://pith.science/paper/DHCEZSOC

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What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.60 · human participants 0.01 · controlled comparison 0.24 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.97 · mentions code or data availability 0.02.

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Possible existence of the primordial magnetic fields has affected the structure formation of the universe. In this paper it is shown that the initial conditions for density perturbations with magnetic fields derived in previous works are inconsistent with Einstein equations. We find that this inconsistency arises due to the unwanted cancellation of contributions from the magnetic fields and primordial radiations. A complete set of equations and consistent initial conditions in the long wavelength limit are given with an explicit derivation in the covariant approach with CDM frame, by newly taking into account a non-relativistic matter contribution in the radiation dominated era. By solving these equations numerically, we derive the angular spectrum of cosmic microwave background anisotropies and the matter power spectrum with magnetic fields. We find that the amplitude of the angular power spectrum of CMB anisotropies can alter at most a order of magnitude at $l \lesssim 4000$ compared with the previous results in the literature.

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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	Possible existence of the primordial magnetic fields has affected the structure formation of the universe.	background 1.00	0.05	0.03	hedged possibility 0.95
s1	In this paper it is shown that the initial conditions for density perturbations with magnetic fields derived in previous works are inconsistent with Einstein equations.	result 0.70	0.62	0.49	asserted 1.00
s2	We find that this inconsistency arises due to the unwanted cancellation of contributions from the magnetic fields and primordial radiations.	interpretation 0.49	0.90	0.14	asserted 1.00
s3	A complete set of equations and consistent initial conditions in the long wavelength limit are given with an explicit derivation in the covariant approach with CDM frame, by newly taking into account a non-relativistic matter contribution in the radiation dominated era.	contribution 0.53	0.96	0.20	asserted 1.00
s4	By solving these equations numerically, we derive the angular spectrum of cosmic microwave background anisotropies and the matter power spectrum with magnetic fields.	method 0.79	0.97	0.10	asserted 1.00
s5	We find that the amplitude of the angular power spectrum of CMB anisotropies can alter at most a order of magnitude at $l \lesssim 4000$ compared with the previous results in the literature.	result 1.00	0.94	0.37	asserted 0.87

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.83.

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arXiv listing abstract v2

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full text
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references and citing sentences
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S sections
T body sentences
C citations
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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

Possible existence of the primordial magnetic fields has affected the structure formation of the universe. In this paper it is shown that the initial conditions for density perturbations with magnetic fields derived in previous works are inconsistent with Einstein equations. We find that this inconsistency arises due to the unwanted cancellation of contributions from the magnetic fields and primordial radiations. A complete set of equations and consistent initial conditions in the long wavelength limit are given with an explicit derivation in the covariant approach with CDM frame, by newly taking into account a non-relativistic matter contribution in the radiation dominated era. By solving these equations numerically, we derive the angular spectrum of cosmic microwave background anisotropies and the matter power spectrum with magnetic fields. We find that the amplitude of the angular power spectrum of CMB anisotropies can alter at most a order of magnitude at $l \lesssim 4000$ compared with the previous results in the literature.

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8 arXiv papers cite this in 20 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 citing it · 6 sentences without a confident label

Contests it 1 paper

We computed the initial conditions for magnetic scalar mode in presence of matter corrections showing how these corrections do not affect the results contrary to what claimed in [ref] .

CMB Constraints on a Stochastic Background of Primordial Magnetic Fields · Conclusions · contest 0.87

Builds on it 1 paper

In this article, we expand on our previous work [ref] by also considering the influence on the matter contributions [ref] .

Constraints on the neutrino mass and the primordial magnetic field from the matter density fluctuation parameter $\sigma_8$ · Introduction · 1.00

Uses its method or tool 3 papers

We adopt the model of Ref. [ref] for estimating the effects of finite-mass neutrinos and the PMF on fluctuations of the matter density fields in the early Universe.

Constraints on the neutrino mass and the primordial magnetic field from the matter density fluctuation parameter $\sigma_8$ · The Model · 0.99
In order to solve this problem, we have adopted the numerical approach and initial conditions for the matter contributions from Ref. [ref] .

Primordial Magnetic Field Effects on the CMB and Large Scale Structure · Comparison with other determinations · 0.95
For the scalar mode, we use adiabatic initial conditions for the matter contribution as in Ref. [ref] .

New Constraints on the Primordial Magnetic Field · Model · 0.93

Compares with it 1 paper

We have now confirmed that our results are consistent not only with results of Ref. [ref] , but also those of other groups which employ semi-numerical methods [e.g. Ref. [ref] ].

Primordial Magnetic Field Effects on the CMB and Large Scale Structure · Comparison with other determinations · 1.00

Cites it as support 1 paper

However, as demonstrated in [ref] , one cannot neglect the matter contributions in the case of existence of PMFs due to the compensation mechanism between the radiation density perturbations and those of PMFs.

Acoustic signatures in the Cosmic Microwave Background bispectrum from primordial magnetic fields · Compensated magnetic initial conditions · 0.98

Cites it as background 4 papers

Recently, several different groups [ref] have been developing the complex analysis of PMF effects on the CMB and matter power spectrum.

New Constraints on the Primordial Magnetic Field · Model · 0.87
[ref] , and the formation of LSS [ref] .

Constraints on the neutrino mass and the primordial magnetic field from the matter density fluctuation parameter $\sigma_8$ · Introduction · 0.85
The contributions to the CMB angular power spectrum from the scalar perturbations induced by PMFs are investigated in [ref] , from the vector perturbations in [ref] and from tensor mode in [ref] , respectively.

Acoustic signatures in the Cosmic Microwave Background bispectrum from primordial magnetic fields · Introduction · 0.94

What it cites · 17 sentences without a confident label

Uses the method or tool of 5 papers

Here we assume that the magnetic field has power-law spectrum in $k<k_D$ in the same manner as in previous works [ref] , [equation] with $P_ij≡δ_ij-k̂_ik̂_j$, which is the divergence free condition of the magnetic field.

Microwave Background Signatures of a Primordial Stochastic Magnetic Field · Spectrum of the magnetic field · 0.84
Here we assume that the magnetic field has power-law spectrum in $k<k_D$ in the same manner as in previous works [ref] , [equation] with $P_ij≡δ_ij-k̂_ik̂_j$, which is the divergence free condition of the magnetic field.

CMB anisotropies from primordial inhomogeneous magnetic fields · Spectrum of the magnetic field · 0.84
Here we assume that the magnetic field has power-law spectrum in $k<k_D$ in the same manner as in previous works [ref] , [equation] with $P_ij≡δ_ij-k̂_ik̂_j$, which is the divergence free condition of the magnetic field.

CMB anisotropies due to cosmological magnetosonic waves · Spectrum of the magnetic field · 0.84

Cites as background 16 papers

The vector type perturbations, which would give the most dominant contribution to CMB anisotropies at small angular scales, have been studied by [ref] , and also the tensor type perturbations [ref] .

Microwave Background Signals from Tangled Magnetic Fields · Introduction · 0.97
The vector type perturbations, which would give the most dominant contribution to CMB anisotropies at small angular scales, have been studied by [ref] , and also the tensor type perturbations [ref] .

Microwave Background Signatures of a Primordial Stochastic Magnetic Field · Introduction · 0.97
The vector type perturbations, which would give the most dominant contribution to CMB anisotropies at small angular scales, have been studied by [ref] , and also the tensor type perturbations [ref] .

Small-scale microwave background anisotropies due to tangled primordial magnetic fields · Introduction · 0.97

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