Polypolar spherical harmonic decomposition of galaxy correlators in redshift space: Toward testing cosmic rotational symmetry
Abstract
We propose an efficient way to test rotational invariance in the cosmological perturbations by use of galaxy correlation functions. In symmetry-breaking cases, the galaxy power spectrum can have extra angular dependence in addition to the usual one due to the redshift-space distortion, k ^ .n ^ . We confirm that, via the decomposition into not the usual Legendre basis Lℓ(k ^.n ^) but the bipolar spherical harmonic one {Yℓ(k ^)⊗Yℓ'(n ^)}LM, the symmetry-breaking signal can be completely distinguished from the usual isotropic one since the former yields nonvanishing L ≥1 modes but the latter is confined to the L =0 one. As a demonstration, we analyze the signatures due to primordial-origin symmetry breakings such as the well-known quadrupolar-type and dipolar-type power asymmetries and find nonzero L =2 and 1 modes, respectively. Fisher matrix forecasts of their constraints indicate that the Planck-level sensitivity could be achieved by the SDSS or BOSS-CMASS data, and an order-of-magnitude improvement is expected in a near future survey as PFS or Euclid by virtue of an increase in accessible Fourier mode. Our methodology is model-independent and hence applicable to the searches for various types of statistically anisotropic fluctuations.
- Publication:
-
Physical Review D
- Pub Date:
- March 2017
- DOI:
- 10.1103/PhysRevD.95.063508
- arXiv:
- arXiv:1612.02645
- Bibcode:
- 2017PhRvD..95f3508S
- Keywords:
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- Astrophysics - Cosmology and Nongalactic Astrophysics;
- General Relativity and Quantum Cosmology
- E-Print:
- 13 pages, 2 figures, 3 tables