Anisotropic inflation in the Finsler spacetime

Abstract

We suggest the universe is Finslerian in the stage of inflation. The Finslerian background spacetime breaks rotational symmetry and induces parity violation. The primordial power spectrum is given for the quantum fluctuation of the inflation field. It depends not only on the magnitude of the wavenumber but also on the preferred direction. We derive the gravitational field equations in the perturbed Finslerian background spacetime, and we obtain a conserved quantity outside the Hubble horizon. The angular correlation coefficients are presented in our anisotropic inflation model. The parity violation feature of Finslerian background spacetime requires that the anisotropic effect only appears in the angular correlation coefficients if l = l + 1. The numerical results of the angular correlation coefficients are given describing the anisotropic effect.

Finslerian dipolar modulation of the CMB power spectra at scales $$2<l<600$$ 2 < l < 600

“…The dipolar modulation of the primordial power spectrum is given in Ref. [36]. At large scales (l < 100), this model could approximately explain the released data of Planck satellite for the power asymmetry [11,12].…”

“…The Randers spacetime is a special kind of Finsler spacetime, which has been widely discussed elsewhere [36,[40][41][42][43]. The Finsler structure of Randers spacetime takes the form…”

“…In Finslerian gravity, the direction of y will appear in the field equation and affect the gravitational field. During the stage of inflation, following our former treatment [36,46], we take the direction of y to be parallel to the wave vector k in the momentum space. Therefore, in the momentum space, Eq.…”

“…In Ref. [36], we have studied anisotropic inflation in which the background spacetime is taken to be Finslerian. This Finslerian background spacetime breaks rotational symmetry and induces parity violation.…”

Spatial and temporal variations of the fine-structure constant in the Finslerian universe

“…Furthermore, in high-redshift region (z > 1.6), it has been shown that the variation of α e is well represented by an angular dipole model pointing to the direction (l, b) = (330 • , −15 • ) in the galactic coordinates with ∼ 4.2σ statistical significance, and the dipole amplitude is about (0.97 +0. 22 −0.20 ) × 10 −5 [7]. Recently, Pinho & Martins [9] carried out a joint analysis of a larger number of old α e data [8] and ten more recent measurements of α e [10][11][12][13][14][15][16][17], and found that the dipolar variation of α e with amplitude (0.81±0.17)×10 −5 is still a good fit to the combined data set, while the statistical uncertainty is significantly reduced compared with previous results.…”