Behavior of interacting Ricci dark energy in logarithmic f(T) gravity
Journal of Theoretical and Applied Physics
Behavior of interacting Ricci dark energy in logarithmic f (T ) gravity
Rahul Ghosh 0
Antonio Pasqua 2
Surajit Chattopadhyay 1
0 Department of Mathematics, Bhairab Ganguly College , Kolkata 700 056 , India
1 Pailan College of Management and Technology , Bengal Pailan Park, Kolkata 700 104 , India
2 Department of Physics, University of Trieste , Via Valerio 2, Trieste 34127 , Italy
In the present work, we have considered a modified gravity model dubbed as 'logarithmic f (T ) gravity' as reported by Bamba et al. (J. Cosmol. Astropart. Phys 1101:21, 2011) and investigated the behavior of Ricci dark energy interacting with pressureless Dark Matter. We have chosen the interaction term in the form Q = 3Hδρm and investigated the behavior of the Hubble parameter H as a function of the redshift z. For this reconstructed H, we have investigated the behavior of the fractional density contribution due to the Ricci dark energy and torsion. Subsequently, we investigated the equation of state parameter wRDE which is found to have a phantom-like behavior for all choices of c2 in the Ricci dark energy density.
Logarithmic f (T ) gravity; Ricci dark energy; Dark Matter (DM)
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Background
The accelerated expansion of the universe is well
established by the works of [1,2]. The ‘dark energy’ (DE),
characterized by negative pressure, is responsible for this
cosmic acceleration [3-6]. The importance of modified
gravity for late acceleration of the universe has been
reviewed by [7,8]. Various modified gravity theories have
been proposed so far. These include f (R) [9,10], f (T )
[11-14], f (G) [15,16], Hoˇrava-Lifshitz [17,18], and
GaussBonnet [19,20] theories. One of the newest extended
theories of gravity is the so-called f (T ) gravity, which is
a theory formulated in a spacetime possessing absolute
parallelism [12]. Some fundamental aspects of f (T )
theories have been studied in the works of [21] and [22]. In
this theory of modified gravity, the teleparallel Lagrangian
density described by the torsion scalar T has been
promoted to be a function of T, i.e., f (T ), in order to account
for the late time cosmic acceleration [23,24]. Some
relevant works in f (T ) theory must be mentioned here. Jamil
et al. [25] derived the exact solutions of static
wormholes in f (T ) modified gravity theory. Jamil et al. [26]
investigated the null, weak, strong, and dominant energy
conditions in generalized teleparallel gravities. Jamil et al.
[27] studied the statefinder parameters {r, s} in f (T )
cosmology. Jamil et al. [28] studied the Noether symmetries
of f (T ) cosmology involving matter and DE. Jamil et al.
[29] tried to resolve the Dark Matter (DM) problem in the
light of f (T ) modified gravity theory, successfully
obtaining the flat rotation curves of galaxies containing DM as
component. They also obtained the density profile of Dark
Matter in galaxies. Jamil et al. [30] studied the
interacting DE model in the framework of f (T ) modified gravity
theory for a particular choice of f (T ). Bamba et al. [31]
studied the generalized second law of thermodynamics in
the framework of f (T ) modified gravity.
Models of DE include quintessence [32], quintom [33],
phantom [34], Chaplygin gas [35], tachyon [36], h-essence
[37], etc. Other relevant works on models of DE have been
recently done. Setare [38] studied the interacting
holographic dark energy (HDE) model in non-flat universe.
Setare [39] studied the bulk brane interaction in order to
obtain the equation of state (EoS) parameter for the HDE
model in non-flat universe enclosed by the event horizon.
Setare [40] studied the cosmological application of the
HDE model in the framework of Brans-Dicke cosmology.
Setare et al. [41] considered the HDE model in a
nonflat universe from the viewpoint of statefinder parameters.
All DE models can be classified according to the
behavior of the equation of state parameter wD as follow [33]:
(1) Cosmological constant: its EoS parameter is exactly
equal to −1, that is, wDE = −1; (2) Quintessence: its
EoS parameter remains above the cosmological constant
boundary, that is, wDE ≥ −1; (3) Phantom: its EoS
parameter lies below the cosmological constant boundary, that
is, wDE ≤ −1; and (4) Quintom: its EoS parameter is
able to evolve across the cosmological constant
boundary. Inspired by the holographic principle [42,43], a new
model of DE, dubbed as Holographic DE (HDE), has been
recently proposed and studied.
Recently, Gao et al. [44] proposed the Ricci scalar
curvature as infrared cutoff of the system; this model is
now known as Ricci dark energy (RDE) model. With a
proper choice of parameters involved, the equation of
state parameter of the RDE model can cross the value
−1, so it has a quintom-like behavior [45]. We must
remember here that the Ricci scalar curvature for a
Friedmann-Robertson-Walker (FRW) universe is given by
R = −6 H˙ + 2H2 + ak2 , where H is the Hubble
parameter, a is the scale factor, (...truncated)