Graviton-photon mixing

Abstract

In the era of gravitational wave (GW) detection from astrophysical sources by LIGO/VIRGO, it is of great importance to take the quantum gravity effect of graviton-photon (GRAPH) mixing in the cosmic magnetic field to the next level. In this work, we study such an effect and derive for the first time perturbative solutions of the linearized equations of motions of the GRAPH mixing in an expanding universe. In our formalism we take into account all known standard dispersive and coherence breaking effects of photons such as the Faraday effect, the Cotton-Mouton effect, and the plasma effects in the cosmic magnetic field. Our formalism applies to a cosmic magnetic field either a uniform or a slowly varying nonhomogeneous field of spacetime coordinates with an arbitrary field direction. For binary systems of astrophysical sources of GWs at extragalactic distances with chirp masses M CH of a few solar masses, GW present-day frequencies ν 0 ≃ 50-700 Hz, and present-day cosmic magnetic field amplitudes B 0 ≃ 10 −10 − 10 −6 G, the power of electromagnetic radiation generated in the GRAPH mixing at present is substantial and in the range P γ ≃ 10 6-10 15 ðerg=sÞ. On the other hand, the associated power flux F γ is quite faint depending on the source distance with respect to the Earth. Since in the GRAPH mixing the velocities of photons and gravitons are preserved and are equal, this effect is the only one known to us, whose certainty of the contemporary arrival of GWs and electromagnetic radiation at the detector is guaranteed.

Upper limits on the amplitude of ultra-high-frequency gravitational waves from graviton to photon conversion

“…In this section we closely follow Ref. [20]. To start with it is necessary first to write the total Lagrangian density L of the graviton-photon system.…”

“…where R is the Ricci scalar, g is the metric determinant, F µν is the total electromagnetic field tensor, κ 2 ≡ 16πG N with G N being the Newtonian constant and Π µν is the photon polarisation tensor in a magnetised medium. The equations of motion from (A1) and (A2) for the propagating electromagnetic and GW fields components, A µ and h ij , in an external magnetic field are given by [20] ∇ 2 A 0 = 0,…”

“…In other words, gravitons mix with photons in electromagnetic fields. This effect has been studied in the literature by several authors in the context of a static laboratory magnetic field [12][13][14][15] and in astrophysical and cosmological situations [16][17][18][19][20]. The effect of gravitonphoton (also denoted as GRAPH) mixing is the inverse process of photon-graviton mixing studied in Refs.…”

CMB circular andB-mode polarization from new interactions

“…We can express the G i coefficients defined in (20) in terms of the A i coefficients. The results are…”

“…Before proceeding, it is worth to rewrite the factor of G 2 in Eq. (20) in a new form for the case of forward scattering. Using the following identity regarding the Levi-Civita pseudotensor [50] g λµ ǫ ναβγ − g λν ǫ µαβγ + g λα ǫ µνβγ − g λβ ǫ µναγ + g λγ ǫ µναβ = 0 ,…”