Eur. Phys. J. C (2017) 77:840
https://doi.org/10.1140/epjc/s10052-017-5417-1
Regular Article - Theoretical Physics
Interacting dark energy model and thermal stability
Pritikana Bhandari
1,a
, Sourav Haldar
1,b
, Subenoy Chakraborty
1,c
1
Department of Mathematics, Jadavpur University, Kolkata, West Bengal 700032, India
Received: 7 August 2017 / Accepted: 24 November 2017 / Published online: 7 December 2017
© The Author(s) 2017. This article is an open access publication
Abstract In the background of the homogeneous and
isotropic FLRW model, the thermodynamics of the interact-
ing DE fluid is investigated in the present work. By studying
the thermodynamical parameters, namely the heat capacities
and the compressibilities, both thermal and mechanical sta-
bility are discussed and the restrictions on the equation of
state parameter of the dark fluid are analyzed.
1 Introduction
The present era of cosmic evolution is a challenging issue to
the cosmologists due to the recent observational predictions
[1–9]. The explanation of the late-time accelerated expan-
sion of the Universe has become one of the biggest and
open problems in modern cosmology today. In the frame-
work of Einstein gravity, the most reasonable description for
this accelerating phase introduces some hypothetical exotic
matter, known as dark energy (DE) (having large negative
pressure), which comprises about 70% of the total energy
density [10] of the Universe. The simplest as well as a large
number of available observational data supported candidate
for the DE is the cosmological constant , associated with the
zero point energy of the quantum fields. In spite of this great
success of -cosmology, it suffers from serious objections
in the interface of cosmology and particle physics, namely
the Cosmological Constant problem [11,12] and the Coinci-
dence problem [13]. As a result of these serious problems in
, several alternative dynamical DE models have been pro-
posed and studied for the last several years [14] but still the
Cosmological Constant is the best DE candidate supporting
the observational results. Furthermore, most of the proposed
DE models try to adjust the data seamlessly, so observational
data are not sufficient to decide between different kinds of
a
e-mail: pritikanab@gmail.com
b
e-mail: sourav.math.ju@gmail.com
c
e-mail: schakraborty.math@gmail.com
DE. Hence, one has tried to invoke the Interacting DE model
for a better understanding of the mechanism behind this cos-
mic acceleration.
In recent years, cosmological theories with interacting
dark fluids are receiving much attention due to their ability
to address the small value of the cosmological constant and
to have a reasonable explanation to the cosmic coincidence
problem [15–17]. Further, from observational point of view,
recent data favor the late time interaction between DM and
DE [18–23]. Also the coupling parameter in the interaction
can be measured by various observations [21–30]. Moreover,
it is speculated that class of interacting dark fluid models may
resolve the current tensions on σ
s
and the local value of the
Hubble constant H
0
[22–31]. Additionally, cosmologists are
of the opinion that the interaction between the dark sectors
may leave an imprint on the perturbation analysis and as a
result there may be significant changes in the lowest multi-
poles of the CMB spectrum [32,33]. The motivation of the
present paper is in this direction.
The thermodynamical study of DE is an important aspect
for a better understanding of the unknown nature of DE.
As the thermodynamical laws are applicable to all types of
macroscopic systems and are based on experimental evi-
dence, in contrast to classical mechanics or electromag-
netism, thermodynamics does not predict specific numeri-
cal values for observables; rather it sets limit on physical
processes. Hence the thermodynamic behavior of the cos-
mic fluid may give some clue to unveil the unknown nature
of the content of the Universe (i.e. the hypothetical DE).
In the recent past Barboza et al. [34] investigated the ther-
modynamic aspects of DE fluids. They analyzed both ther-
mal and mechanical stability demanding the positivity of the
heat capacities and compressibility of the dark fluid. They
showed that due to the stability of the DE fluid, it should
have negative constant equation of state parameter and it
was also shown to be in contradiction with the observational
constraints imposed by type Ia supernova, BAO and H(z)
data on a general DE fluid. Hence they concluded that DE
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