Conversion of relic gravitational waves into photons in cosmological magnetic fields

Gravitational waves propagating through a stationary gauge field transform into gauge field waves and back again. When multiple families of flavor-space locked gauge fields are present, the gravitational and gauge field waves exhibit novel dynamics. At high frequencies, the system behaves like coupled oscillators in which the gravitational wave is the central pacemaker. Due to energy conservation and exchange among the oscillators, the wave amplitudes lie on a multidimensional sphere, reminiscent of neutrino flavor oscillations. This phenomenon has implications for cosmological scenarios based on flavor-space locked gauge fields.In a remarkable series of papers starting with the work of Gertsenshteyn [1], the authors showed that a gravitational wave propagating through a stationary magnetic field converts into an electromagnetic wave and back again [2][3][4]. Now that gravitational waves have been directly detected [5], no doubt there will be searches for this effect [6].Here we consider the more general phenomenon of the conversion of a gravitational wave into a stationary gauge field, as may be present in the early stages of the Universe [7][8][9]. In particular, we show that gravitational waves transform into tensor waves of a gauge field, disappearing and reappearing much like neutrino flavor oscillations. More complicated oscillation patterns are possible for multiple families of gauge fields. Quantization of these gravitational and gauge field tensor modes reveals a novel relationship between the energy and flavor eigenstates that may leave an imprint on a spectrum of primordial gravitational waves, or even suggest a new mechanism for the origin of a primordial spectrum.We consider a gauge field under general relativity,with metric signature − + ++, M P is the reduced Planck mass, and L m represents any other fields that may be present. We take an SU(2) fieldwhere g Y is the Yang-Mills coupling and the vector notation indicates direction in the three-dimensional flavor space. It is essential for this effect that the gauge field have a vacuum expectation value (vev), the analog of a stationary electric or magnetic field. To match the symmetries of our cosmological spacetime, we build a homogeneous and isotropic configuration as recently considered in the context of cosmic acceleration for inflation [7][8][9] or dark energy [10][11][12]. We work in the timelike gauge, so that A t = 0, and require that the remaining components, one per each group generator, be spatially independent in order to ensure homogeneity. Isotropy is then achieved by identifying the global symmetry of SU(2) with the rotational O(3) symmetry of Euclidean space. Hence, we write A µ = φ(τ ) e µ where e µ is a set of three mutually orthogonal, spacelike basis vectors. That is, the vector fields for flavors 1, 2, 3 point along the x, y, z directions, and we call this configuration flavorspace locked. The equation of motion in an expanding spacetime with line element ds, which may be solved exactly in terms of elliptic Jacobi functions. The...

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“…Now that gravitational waves have been directly detected [5], no doubt there will be searches for this effect [6].…”

mentioning

confidence: 99%

Gravitational wave–Gauge field oscillations

2016

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“…Such a GW detector applies the electromagnetic perturbation effects produced by high frequency GWs to detect GWs. This graviton-to-photon transition was first suggested by Gertsenshtein [70][71][72]. A different gravitational origin that could generate high frequency GWs has been discussed [73][74][75][76].…”

Section: Introductionmentioning

confidence: 90%

Test the mergers of the primordial black holes by high frequency gravitational-wave detector

Wang

Jin

2017

Eur. Phys. J. C

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The black hole could have a primordial origin if its mass is less than 1M . The mergers of these black hole binaries generate stochastic gravitational-wave background (SGWB). We investigate the SGWB in high frequency band 10 8 -10 10 Hz. It can be detected by high frequency gravitational-wave detector. Energy density spectrum and amplitude of the SGWB are derived. The upper limit of the energy density spectrum is around 10 −7 . Also, the upper limit of the amplitude ranges from 10 −31.5 to 10 −29.5 . The fluctuation of spacetime origin from gravitational wave could give a fluctuation of the background electromagnetic field in a high frequency gravitational-wave detector. The signal photon flux generated by the SGWB in the high frequency band 10 8 -10 10 Hz is derived, which ranges from 1 to 10 2 s −1 . The comparison between the signal photon flux generated by relic gravitational waves (RGWs) and the SGWB is also discussed in this paper. It is shown that the signal photon flux generated by the RGW, which is predicted by the canonical single-field slow-roll inflation models, is sufficiently lower than the one generated by the SGWB in the high frequency band 10 8 -10 10 Hz. Our results indicate that the SGWB in the high frequency band 10 8 -10 10 Hz is more likely to be detected by the high frequency gravitational-wave detector.

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“…Let us start by briefly summarizing the description of graviton-photon mixing in GR. Raffelt and Stodolsky argued that the quantum corrections to the electrodynamic system could be relevant for graviton-photon oscillation in regions of strong magnetic fields [4] (see also reference [6]). Those corrections, which can be taken into account adding an Euler-Heisenberg term into the Lagrangian, lead to an effective refractive index that the photon experience even in vacuum.…”

Section: Graviton-photon Mixingmentioning

confidence: 99%

“…where A j is the vector potential of the electromagnetic wave and m γ is the effective photon mass implied by the effective refractive index [6]. We fix the z axis along the direction of propagation of the waves without loss of generality.…”

Section: Graviton-photon Mixingmentioning

confidence: 99%

“…where the polarization tensors have non-vanishing componentes ǫ + xx = −ǫ + yy = 1 and ǫ × xy = ǫ × yx = 1, and we have introduced a phase in the vector for convenience, as it was explicitly done in reference [6]. Taking into account the form of the expansion (6) in the interaction term h ij B i e B j , one can conclude that only the external magnetic field transverse to the direction of the wave propagation contribute to the phenomenon, that is B T = B e sin φ with cos φ =B e ·k.…”

Section: Graviton-photon Mixingmentioning

confidence: 99%

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Graviton-photon oscillation in alternative theories of gravity

Cembranos

Díaz

Martín–Moruno

2018

Class. Quantum Grav.

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In this paper we investigate graviton-photon oscillation in the presence of an external magnetic field in alternative theories of gravity. Whereas the effect of an effective refractive index for the electromagnetic radiation was already considered in the literature, we develop the first approach to take into account the effect of the modification of the predictions for gravitational waves in alternative theories of gravity in the phenomenon of graviton-photon mixing.

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Conversion of relic gravitational waves into photons in cosmological magnetic fields

Cited by 51 publications

References 64 publications

Gravitational wave–Gauge field oscillations

Gravitational wave–Gauge field oscillations

Test the mergers of the primordial black holes by high frequency gravitational-wave detector

Graviton-photon oscillation in alternative theories of gravity

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