Figure 3 presents the plot of [[??].sub.tot] at apparent horizon by taking logarithmic entropy at apparent horizon.
Hence, validity of GSLT is verified for t [greater than or equal to] 1.5 at apparent horizon with logarithmic entropy.
For flat FRW universe, Hubble parameter relates to the apparent horizon as [R.sub.A] = 1/H.
The relation between thermodynamics and Einstein field equations was found by Jacobson with the help of Clausius relation at apparent horizon described as
For isotropic and homogeneous universe model, the above relation gives the radius of apparent horizon
Then the entanglement energy of quantum particles across the apparent horizon
is missed in the cosmological equations written for the Hubble volume.
However, for this energy branch, the effective volume ([??]) and the area ([??]) of the apparent horizon
are negative, which are not physical.
. Physically, apparent horizons
constitute the observable boundary which is the largest boundary of Universe in an instant.
Consequently, applying the thermodynamics laws to the apparent horizon
and attributing the Cai-Kim temperature to it, we could find out some simple modified Friedmann equations.
The temperature of the apparent horizon
is given by the Hawking temperature [T.sub.h] = [absolute value of ([[kappa].sub.s])]/2[pi], where [mathematical expression not reproducible] is the surface gravity at the apparent horizon
At the apparent horizon
r = [r.sub.A], it is clear that the function f(r) vanishes; that is, f([r.sub.A]) = 0.
Here, we focus on the general case of [[phi].sub.[nu]] = ([beta](t), 0, 0, 0) and find the entropy of apparent horizon