Viscosity in cosmic fluids

Eur. Phys. J. C (2020) 80:767 https://doi.org/10.1140/epjc/s10052-020-8341-8 Regular Article - Theoretical Physics Viscosity in cosmic fluids Pravin Kumar Natwariya1,2,a , Jitesh R. Bhatt1,b , Arun Kumar Pandey3,c 1 Theoretical Physics Division,Physical Research Laboratory, Ahmedabad 380 009 Gujarat, India 2 Department of Physics, Indian Institute of Technology Gandhinagar,, Palaj,Gandhinagar 382 355 Gujartat, India 3 Department of Physics and Astrophysics, University of Delhi, Delhi 110 007, India Received: 19 February 2020 / Accepted: 10 August 2020 © The Author(s) 2020 Abstract The effective theory of large-scale structure formation based on CDM paradigm predicts finite dissipative effects in the resulting fluid equations. In this work, we study how viscous effect that could arise if one includes self-interaction among the dark-matter particles combines with the effective theory. It is shown that these two possible sources of dissipation can operate together in a cosmic fluid and the interplay between them can play an important role in determining dynamics of the cosmic fluid. In particular, we demonstrate that the viscosity coefficient due to self-interaction is added inversely with the viscosity calculated using effective theory of CDM model. Thus the larger viscosity has less significant contribution in the effective viscosity. Using the known bounds on σ/m for self-interacting darkmatter, where σ and m are the cross-section and mass of the dark-matter particles respectively, we discuss role of the effective viscosity in various cosmological scenarios. 1 Introduction In order to study large scales structures in the Universe, there are two important length-scales: one is comoving Hubble −1 . Here, scale H−1 and the another is the non-linear scale kNL −1 kNL describes the scales at which gravitational collapse takes place; it is typically considered to be of the order of the size of a Galactic cluster, i.e., ∼ a few Mpc. The Universe is homogeneous at a scale of ∼ 200 Mpc, and there are roughly 153 homogeneous patches within the Hubble volume. The dynamics of the perturbations can be analyzed in terms of a parameter k = kNL /k, where k is the inverse length scale. The hierarchy between these two scales is quantified by the parameter k  1 which is responsible for the success of a e-mails: ; (corresponding author) b e-mail: c e-mail: 0123456789().: V,-vol linear perturbation theory in describing the observed large scale structures (LSS) (for a recent review see [1] and also [2]). The dark energy (cosmological constant ) plus cold dark-matter (CDM) model, (i.e. CDM) is highly successful in predicting the large scale structure of the Universe. The model is consistent with observations from the length scales typically of the order of ∼ 1 Mpc (i.e., intergalactic scale) to the scale of the horizon (∼ 15,000 Mpc) [1]. In this model, structure formation in the dark-matter (DM) sector occurs more rapidly than the baryonic matter. The structure formation in the dark sector provides a gravitational potential for the baryonic matter and hence gives the information about the distribution of visible matter in the Universe. Although this model provides extensive agreement with the large scale structure and cosmic microwave background (CMB) radiation observations, it faces difficulty at small length scale ( 1Mpc). These problems include ‘missing satellite problem’ [3,4] (prediction of too many dwarf galaxies within the viral radius of the Milky Way from the N-body simulations than observed), the ‘cusp-core problem’ [5] (Observations show nearly constant dark-matter density in the inner parts of galaxies, but simulations show a steeper density behavior) and the ‘too-big-to-fail problem’ [6,7] (from simulations it is not possible to explain the dynamics of the massive satellites in the Milky Way galaxy). Especially, these problems become more evident in studying the galaxy rotation curve [1,8]. There have been attempts to address some of these issues within CDM and also by modifying the CDM model (see the review [1] and references therein). One of the exciting proposals to resolve the issues related to the small scales is by introducing self-interaction between dark-matter particles. Such models are called self-interacting dark-matter (SIDM) models. In these models typical mean free path of dark-matter particle is taken to be in the range of 1 kpc to 1 Mpc, proposed as a remedy for tension between observations and numerical simulations at the scale of a few Mpc (k  1) 123 767 Page 2 of 7 [9–11]. Inclusion of interaction can introduce dissipation in the dark-matter fluid, and one can define coefficients of bulk and shear viscosities [12]. This small scale physics can affect the large scale behavior of the Universe- it has been shown that the viscous effect can lead to an accelerated expansion of the Universe [12–18]. Further, the dissipative dynamics of dark-matter can resolve the tension between Planck CMB and LSS observations [19]. In other scenarios, viscous cosmology can also be used for constraint the neutrino mass [20]. It also explains the cosmic chronometer and type Ia supernova data [21,22]. As well, dissipations can play a role at suppressing the growth of density perturbations and delaying the nonlinearities in the Universe [23]. The dissipative effect may arise due to dark-matter-baryon interaction also. Recently a systematical inclusion of baryon-DM interaction has been incorporated in the Boltzmann-Fokker-Planck formalism [24,25]. It ought to be noted that the baryon-DM interaction has also been considered in the literature to explain 21-cm line [26– 29]. The damping of the gravitational waves in the viscous fluid can be used to constrain the mean free path and the DM mass [30,31]. In this work we critically examine the role of the viscosity that arises due to self-interaction among dark-matter particles. Before we proceed further, it is important to note that the dissipative effects may arise even for the case of coldcollisionless dark-matter (CCDM) in the presence of selfgravity. In Ref. [2] the effective fluid theory of the longwavelength Universe was obtained by integrating out the short-wavelength perturbations. The effective fluid behaves as a viscous medium coupled to gravity. Here the shortwavelength contributes to the viscous stress tensor of the DM fluid, which depends on the gravitational potential. The effective fluid description of CCDM is based on the truncation of the Boltzmann hierarchy [2,32]. This stress tensor can potentially change the bias parameters in the galaxy bispectrum [33]. The perturbations contributing to the background in the effective viscous fluid may affect the baryon acoustic oscillation [2,34]. If the self-interaction among dark-matter particle is turned on it can change the physics described in Ref. [2] . Thus to incorporate effect of the self-interaction, in the present work, we consider the Boltzmann kin (...truncated)