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.
Highlights
Gaussian statistics [9,10]
In the usual anisotropic inflation model [19,20,21,22,23,24,25,26,27,28,29], a primordial vector field aligned in a preferred direction is involved and the rotational symmetry is broken
The term 3bk · nz in the primordial power spectrum Pδφ represents the effect of rotational symmetry breaking
Summary
Gaussian statistics [9,10]. These facts support the idea that the inflation model is a preferred model that generates the primordial quantum fluctuations. In the usual anisotropic inflation model [19,20,21,22,23,24,25,26,27,28,29], a primordial vector field aligned in a preferred direction is involved and the rotational symmetry is broken. Following the standard quantization process in the inflation model [60], we can obtain the primordial power spectrum from the solution of Eq (8) The term 3bk · nz in the primordial power spectrum Pδφ represents the effect of rotational symmetry breaking
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