2017/10/28 by Abril Suárez, Pierre-Henri Chavanis · 1 citation
Physics and Astronomy · #Axion #Boson #Cosmology #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #Dark energy #Dark matter #Hubble's law #Mathematical physics #Particle physics #Physics #Pulsars and Gravitational Waves Research #Quantum electrodynamics #Quantum mechanics #Scalar (mathematics) #Scalar field #gr-qc
paper · pdf · doi:10.1103/physrevd.98.083529
published as Phys. Rev. D 98, 083529 (2018)
arxiv created 2017/10/28 · openalex created_date 2017/11/10 · openalex publication_date 2018/10/17 · arxiv updated 2018/10/24 · openalex updated_date 2026/08/05
We study the gravitational instability of a general relativistic complex scalar field with a quartic self-interaction in an infinite homogeneous static background. This quantum relativistic Jeans problem provides a simplified framework to study the formation of the large-scale structures of the Universe in the case where dark matter is made of a scalar field. The scalar field may represent the wave function of a relativistic self-gravitating Bose-Einstein condensate. Exact analytical expressions for the dispersion relation and Jeans length \ensuremathλJ are obtained from a hydrodynamical representation of the Klein-Gordon-Einstein equations [ and , Phys. Rev. D 92, 023510 (2015)]. We compare our results with those previously obtained with a simplified relativistic model [, , and , Mon. Not. R. Astron. Soc. 215, 575 (1985)]. When relativistic effects are fully accounted for, we find that the perturbations are stabilized at very large scales of the order of the Hubble length \ensuremathλH. Numerical applications are made for ultralight bosons without self-interaction (fuzzy dark matter), for bosons with a repulsive self-interaction, and for bosons with an attractive self-interaction (QCD axions and ultralight axions). We show that the Jeans instability is inhibited in the ultrarelativistic regime of the scalar field (early Universe and radiationlike era) because the Jeans length is of the order of the Hubble length (\ensuremathλJ\ensuremath∼\ensuremathλH), except when the self-interaction of the bosons is attractive. By contrast, structure formation can take place in the nonrelativistic regime of the scalar field (matterlike era) for \ensuremathλJ\ensuremath≤\ensuremathλ\ensuremath≤\ensuremathλH. Since the scalar field has a nonzero Jeans length due to its quantum nature (Heisenberg uncertainty principle or quantum pressure due to the self-interaction of the bosons), it appears that the wave properties of the scalar field can stabilize gravitational collapse at small scales, providing halo cores and suppressing small-scale linear power. This may solve the CDM crisis such as the cusp problem and the missing satellite problem. We also compare our results with those obtained in the case where dark matter is made of fermions instead of bosons.