Eur. Phys. J. C (2019) 79:576
https://doi.org/10.1140/epjc/s10052-019-7087-7
Letter
Dark sector interaction: a remedy of the tensions between CMB
and LSS data
Suresh Kumar
1,a
, Rafael C. Nunes
2,b
, Santosh Kumar Yadav
1,c
1
Department of Mathematics, BITS Pilani, Pilani Campus, Pilani, Rajasthan 333031, India
2
Divisão de Astrofísica, Instituto Nacional de Pesquisas Espaciais, Avenida dos Astronautas 1758, São José dos Campos, SP 12227-010, Brazil
Received: 24 March 2019 / Accepted: 28 June 2019 / Published online: 9 July 2019
© The Author(s) 2019
Abstract The well-known tensions on the cosmological
parameters H
0
and σ
8
within the CDM cosmology shown
by the Planck-CMB and LSS data are possibly due to the sys-
tematics in the data or our ignorance of some new physics
beyond the CDM model. In this letter, we focus on the
second possibility, and investigate a minimal extension of
the CDM model by allowing a coupling between its dark
sector components (dark energy and dark matter). We ana-
lyze this scenario with Planck-CMB, KiDS and HST data,
and find that the H
0
and σ
8
tensions disappear. In the joint
analyses with Planck, HST and KiDS data, we find non-zero
coupling in the dark sector up to 99% CL. Thus, we find a
strong statistical support from the observational data for an
interaction in the dark sector of the Universe while solving
the H
0
and σ
8
tensions simultaneously.
1 Introduction
The cosmic microwave background (CMB) observations
from Planck [1] together with the observations of cosmic
expansion history from independent measurements, includ-
ing baryonic acoustic oscillations (BAO) [2] and Supernovae
type Ia [3], find a very good statistical fit to the standard model
of cosmology, viz., the CDM (cosmological constant +
cold dark matter) model. However, with the gradual increase
in the data accumulation with precision, the latest Planck-
CMB data show inconsistency with the direct measurements
of Hubble expansion rate from the Hubble Space Telescope
(HST) [4], and some large scale structure (LSS) observa-
tions such as galaxy cluster counts [5,6] and weak lensing
[7,8], in the framework of the CDM model. Specifically,
the value of present Hubble constant H
0
and the value of
a
e-mail: suresh.kumar@pilani.bits-pilani.ac.in
b
e-mail: rafadcnunes@gmail.com
c
e-mail: sky91bbaulko@gmail.com
r.m.s. fluctuation of density perturbation at 8h
−1
Mpc scale
(characterized by σ
8
), inferred from the CMB experiments
are in a serious disagreement with the ones measured from
the LSS experiments [9,10].
At present, it is not clear whether these inconsistencies are
due to systematics in the data or need some physics beyond
the standard CDM model [11,12]. Several studies have
been carried out in the literature to reconcile these tensions
between the CMB and LSS observations [13–17]. But both
the tensions are not resolved simultaneously at a significant
statistical level. Rather, by assuming neutrinos properties, the
parameters are correlated in such a way that lower values of
σ
8
require higher values of total matter density and smaller
values of H
0
, which aggravates the tensions (e.g. [18]). In
[19], it is argued that the presence of sterile neutrinos do not
bring a new concordance, but possibly indicating systematic
biases in the measurements. However, recently in [20], it has
been argued that incorporation of the dissipative effects in
the energy momentum tensor can ameliorate both the ten-
sions simultaneously. Likewise in [21], it is claimed that the
presence of viscosity, shear or bulk or combination of both,
can alleviate both the tensions simultaneously.
At present, the precise nature of constituents of the dark
sector in the CDM model, namely CDM and dark energy
(the vacuum energy mimicked by ), is unknown. More-
over, these two are major energy ingradients accounting for
around 95% energy budget of the Universe. So, a possibil-
ity of exchange of energy/momentum or interaction between
the dark sector components can not be ignored, especially
considering the current issues with the CDM model. Con-
sequently, in recent years, a large number of studies have
been carried out with regard to the interaction between the
dark sector components of the Universe with different moti-
vations and perspectives [22–39] (see [40]forareview).In
particular, a possible interaction in the dark sector has been
investigated in [23–26], where it has been argued that a dark
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