The interrelation between the generation of large-scale electric fields and that of large-scale magnetic fields during inflation

Bamba, Kazuharu

doi:10.1088/1475-7516/2007/10/015

Cited by 36 publications

(10 citation statements)

References 79 publications

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“…We are not able to obtain the exact solution of equation (2.17) for the case in which I is given by a general function of η. In fact, however, we can obtain an approximate solution with sufficient accuracy by using the Wentzel-Kramers-Brillouin (WKB) approximation on subhorizon scales and the long-wavelength approximation on superhorizon scales, and matching these solutions at the horizon crossing [29,30].…”

Section: Jcap04(2008)024mentioning

confidence: 99%

Inflation and late-time cosmic acceleration in non-minimal Maxwell-F(R) gravity and the generation of large-scale magnetic fields

Bamba

Odintsov

2008

J. Cosmol. Astropart. Phys.

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196

172

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We study inflation and late-time acceleration in the expansion of the universe in non-minimal electromagnetism, in which the electromagnetic field couples to the scalar curvature function. It is shown that power-law inflation can be realized due to the non-minimal gravitational coupling of the electromagnetic field, and that large-scale magnetic fields can be generated due to the breaking of the conformal invariance of the electromagnetic field through its non-minimal gravitational coupling. Furthermore, it is demonstrated that both inflation and the late-time acceleration of the universe can be realized in a modified Maxwell-F (R) gravity which is consistent with solar system tests and cosmological bounds and free of instabilities. At small curvature typical for current universe the standard Maxwell theory is recovered. We also consider classically equivalent form of non-minimal Maxwell-F (R) gravity, and propose the origin of the non-minimal gravitational coupling function based on renormalization-group considerations.

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Section: Jcap04(2008)024mentioning

confidence: 99%

Inflation and late-time cosmic acceleration in non-minimal Maxwell-F(R) gravity and the generation of large-scale magnetic fields

Bamba

Odintsov

2008

J. Cosmol. Astropart. Phys.

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196

172

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“…where (23) the turning point is predominantly fixed by the largeness of σ τ i rather than by the smallness of kτ i : while kτ i is (at most) of order 1 (and it is much smaller than 1 for the galactic scale) we have instead that σ τ i 1, as already stressed in explicit numerical integrations of the of the power spectra 11 (see, in particular, the last paper of [19][20][21]). The hypermagnetic power spectra for generalized quantum mechanical Cauchy data can therefore be expressed as (24) where N B depends on the suddenness of the transition (parametrized, in the above example, by the value of β); when β 1, we will have N B = (4π 2 ) −1 + O(β −1 ).…”

mentioning

confidence: 89%

“…F → −F) the two equations appearing in Eq. (2) are interchanged provided E → − B and B → E. Equations (1) and (2) contain, as a particular case, a class of magnetogenesis models based on the evolution of the inflaton or of some other spectator field (see, e.g., [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] for an incomplete list of references 3 ). Various scenarios aim at producing magnetic fields with approximate intensities of a few hundredths of a nG (1 nG = 10 −9 G) and over typical comoving scales between few Mpc and 100 Mpc.…”

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confidence: 99%

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Effective horizons, junction conditions and large-scale magnetism

Giovannini

2017

Eur. Phys. J. C

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The quantum mechanical generation of hypermagnetic and hyperlectric fields in four-dimensional conformally flat background geometries rests on the simultaneous continuity of the effective horizon and of the extrinsic curvature across the inflationary boundary. The junction conditions for the gauge fields are derived in general terms and corroborated by explicit examples with particular attention to the limit of a sudden (but nonetheless continuous) transition of the effective horizon. After reducing the dynamics to a pair of integral equations related by duality transformations, we compute the power spectra and deduce a novel class of logarithmic corrections which turn out to be, however, numerically insignificant and overwhelmed by the conductivity effects once the gauge modes reenter the effective horizon. In this perspective the magnetogenesis requirements and the role of the postinflationary conductivity are clarified and reappraised. As long as the total duration of the inflationary phase is nearly minimal, quasi-flat hypermagnetic power spectra are comparatively more common than in the case of vacuum initial data.The qualitative description of large-scale cosmological perturbations [1][2][3] stipulates that a given wavelength exits the Hubble radius at some typical conformal time τ ex during an inflationary stage of expansion and approximately reenters at τ re , when the Universe still expands but in a decelerated manner. By a mode being beyond the horizon we only mean that the physical wavenumber is much less than the expansion rate: this does not necessarily have anything to do with causality [2]. Indeed, the initial conditions of the Einstein-Boltzmann hierarchy (mandatory for the calculation of the temperature and polarization anisotropies) are set when the relevant modes are larger than the Hubble radius prior to matter-radiation equality [3]. Similarly the physical wavenumbers of the hyperelectric and hypermagnetic fields a e-mail: massimo.giovannini@cern.ch can be much smaller than the rate of variation of the susceptibility (χ in what follows) which now plays the role of the effective horizon. The junction conditions of the gauge power spectra will be derived in general terms and then corroborated by specific examples with particular attention to the case of sudden (but continuous) postinflationary transitions. Using the obtained results the gauge power spectra will be computed in the case of generalized quantum mechanical initial conditions of the hypercharge field.The four-dimensional action discussed in [4-9] concisely summarizes a large class of magnetogenesis scenarios and it can be written, for the present ends, as 1where g denotes the determinant of the four-dimensional metric; 2 Y αβ and Y αβ are, respectively, the gauge field strength and its dual. While the two symmetric tensors M ρ σ and N ρ σ parametrize, in full generality, the dependence upon the electric and magnetic susceptibilities, Eq. (1) includes, as a special case, the derivative couplings typical of the relativistic th...

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“…We note that finding the exact solution of Eq. ( 414) for any arbitrary coupling function I(η) is not possible while with the use of the Wentzel-Kramers-Brillouin (WKB) approximation on subhorizon scales and the long-wavelength approximation on superhorizon scales, and finally matching these solutions at the horizon crossing [664,665], an approximate solution can be found as…”

Section: J Non-minimal Maxwell-einstein Gravitymentioning

confidence: 99%

Finite-time cosmological singularities and the possible fate of the Universe

de Haro,

Nojiri,

Odintsov

et al. 2023

Physics Reports

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The interrelation between the generation of large-scale electric fields and that of large-scale magnetic fields during inflation

Cited by 36 publications

References 79 publications

Inflation and late-time cosmic acceleration in non-minimal Maxwell-F(R) gravity and the generation of large-scale magnetic fields

Inflation and late-time cosmic acceleration in non-minimal Maxwell-F(R) gravity and the generation of large-scale magnetic fields

Effective horizons, junction conditions and large-scale magnetism

Finite-time cosmological singularities and the possible fate of the Universe

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