Exploring the self interacting dark matter properties from low redshift observations

Eur. Phys. J. C (2022) 82:1060 https://doi.org/10.1140/epjc/s10052-022-10907-8 Regular Article - Theoretical Physics Exploring the self interacting dark matter properties from low redshift observations Arvind Kumar Mishra1,2,a 1 Theoretical Physics Division, Physical Research Laboratory, Navarangpura, Ahmedabad 380009, India 2 Indian Institute of Technology Gandhinagar, Palaj, Gandhinagar 382355, India Received: 29 June 2020 / Accepted: 11 October 2022 © The Author(s) 2022 Abstract We calculate the shear (η) and bulk viscosity (ζ ) of Self Interacting Dark Matter (SIDM) fluid using the kinetic theory formalism. Using the astrophysical constraints on dark matter self-interaction cross section over mass σ/m, we demonstrate that viscous SIDM fluid violates the lower bound on the ratio of shear viscosity to its entropy density, 1 . Then, considering the η/s bound as universal, η/s = 4π we derive a theoretical upper limit on the ratio of velocity average dark matter self interaction cross-section to its mass and also estimate an upper limit on SIDM mass. We report that mass of the SIDM particle should be sub-GeV scale. Furthermore, with the assumption of a power-law form of η and ζ , we study its evolution in the light of low redshift observations. We show that at the large redshift, the SIDM viscosity is small, but at the small redshift, it becomes sufficiently large and contributes significantly to cosmic dissipation. As a consequence, viscous SIDM can explain the low redshift observations and also consistent with the standard cosmological prediction. 1 Introduction The collision-less cold dark matter (CDM), along with the cosmological constant (ΛCDM model of cosmology) explains the large scale structure (greater than the O (100 Mpc) scale) of the Universe. But on the small scales, it faces major issues such as the core cusp problem, missing satellites problem, too big to fail problem etc. For more detail on the small scale issues, see reviews [1,2]. It has been proposed that instead of the DM to be collision-less, if the DM particles interact with each other via elastic scattering over the scale where the problem is severe, then it can address the above mentioned problems [3–7]. The success of the SIDM a e-mail: (corresponding author) 0123456789().: V,-vol lies in the fact that at the small scale due to large density, the SIDM behaves like a collisional dark matter, but on a large scale due to small density, it behaves like the collision-less DM. Thus the SIDM can explain both the small and large scale observations very well. It is pointed out that the collisional nature of SIDM on the small scales can lead to viscosity. The SIDM fluid having viscosity is defined as viscous self-interacting dark matter (VSIDM) fluid. In Ref. [8], using the kinetic theory formalism, we have calculated the viscous coefficients of the VSIDM fluid. There we show that the viscous dissipation of the VSIDM becomes prominent at present, and consequently, it can explain the present observed accelerated expansion of the Universe. Therefore, the VSIDM fluid model can unify both the dark sectors, i.e., dark matter and dark energy, of the Universe. Furthermore, in Refs. [9,10], using this framework, we study the cosmic evolution at the small redshifts, and report that the decreasing fluid velocity gradients on earlier time can explain the late time cosmological observations. The inclusion of viscosity in the cosmic fluid has richer dynamical consequences in comparison with the ideal cosmic fluid. In literature, the effect of cosmic viscosity, especially bulk viscosity (unlikely shear viscosity, it is consistent with the homogeneity and isotropy on the large scale structure), has been explored in the different epochs of cosmic evolution. For a homogeneous and isotropic expansion (Friedmann– Lamaitre–Robertson–Walker space time metric) of Universe, the presence of the bulk viscosity contribute the negative pressure, so the total cosmic fluid pressure (PT ) becomes, PT = P − 3ζ H , where P is kinetic pressure and H is Hubble expansion rate. In case of sufficiently large cosmic viscosity, the total fluid pressure may be negative and leads to accelerated expansion of the Universe. Therefore, the viscous cosmic fluid may explain the early time acceleration (cosmic inflation) [11–14], and also the late-time cosmic acceleration [15–26]. In recent work, Floerchinger et al. [27], argued that 123 1060 Page 2 of 13 at late time of the cosmic evolution when the structure formation takes place then due to large velocity gradients, the shear viscosity may also become important and play significant role in cosmic dissipation. If the shear viscosity is large enough, it can also leads to accelerated expansion. However, it remains unclear which kind of particles in the Universe can produce such a large viscosity. Later, in Ref. [8], we proposed that the VSIDM could provide a possible source to create such a large viscosity. Further, in Ref. [28], authors have found that the viscous dark matter can reduce the tension between the Planck and local measurements of the Hubble expansion rate. In other works [29,30], we show that the dark matter viscous energy dissipation can increase its temperature, and also lead to visible photon production [30,31]. These generated photons may increase the number density of photons in the Rayleigh–Jeans limit of the Cosmic Microwave Background (CMB) radiation, and can explain the 21-cm anomaly reported by EDGES collaboration [30]. Furthermore, the presence of the cosmic viscosity may cause to alter the standard cosmic evolution history and the large scale structure formation. A large DM viscosity can increase the DM temperature [29], decay of gravitational potential fluctuations [24], reduces the growth of the density perturbation [32,33] and damping of the gravitational waves [34–36]. Therefore, the DM viscosity is severely constrained from the different astrophysical and cosmological observations. For recent work on cosmic viscosity, see Refs. [37–41], and also, to study the effect of cosmic viscosity on early and late time of evolution of the Universe, see review [42]. In this work, we estimate the bulk and shear viscosity of SIDM in the kinetic theory framework and study its evolution at late time of the cosmic evolution. We check the dependency of bulk viscosity onto the sound speed and find that for a large sound speed Cn > 0.0027, ζ becomes large in comparison with the Cn = 0 case. Further, considering the astrophysical limit on σ/m, we show that the VSIDM 1 [43], violates the lower bound on η/s, given by η/s = 4π Then in the assumption that the conjectured KSS bound is universal, we derive a constraint on ratio of velocity average self-interacting scattering cross-section to its mass. Later, we also explore the parameter space for SIDM mass and report that the SIDM particle mass should be sub-GeV scale. Here, we also explore the evolution of SIDM viscosities (both she (...truncated)