Bianchi type $${\hbox {VI}}_0$$VI0 cosmological model in self-creation theory in general relativity and Lyra geometry

The Friedmann Robertson Walker Space time in Lyra Geometry

“…In three cases the additional term introduced by Lyra has an effect on the behaviores of the pressure and density but has no effect on the entropy of the universe because it is not a part of the energy momentum tensor. This result in agreement with Hegazy and Farook [36] and Hegazy [37]. The curve of the distance modulus of our universe obtained in the case of time dependent deceleration parameter is closer to the distance modulus of Supernova la than the curve obtained in the case of constant deceleration parameter.…”

“…The enthalpy (H), the Helmholtz free energy (F) and the Gibbs free energy (G) are constants and read as [34], [35], [36], [37]: (10) Halford [39] has pointed out that if we put , we can achieve almost a complete equivalence between Lyra cosmological theory and the relativistic theory. For the case of stiff matter solutions with a cosmological constant in general relativity theory, Beesham [40] has shown that the corresponding equations are equivalent in both geometries if we set .…”

Thermodynamic Functions of the Universe in the Presence of Viscosity in the Relativity Theory and Lyra Geometry

“…Hegazy and Rahman [12] proved that the additional component introduced by Lyra has no effect on the entropy because its arises from geometry and is not a part of the momentum tensor.…”

“…Hence, in the presence of the perfect fluid, the gravitational theory based on Lyra geometry and the general relativity theory is not suitable for explaining the entropy as an increasing function of 𝑡. An alternative gravitational theory that can give a good explanation for the entropy as an increasing function of t in the case of a perfect fluid is the second self-creation theory [12], [43], and [44]. Due to the additional term β introduced by Lyra, the behaviors of the thermodynamic functions obtained in Lyra geometry are differs from those obtained in the general relativity theory as indicated in figures ( 5), (6), and (7).…”

“…Roy and Narain [11] investigated the inhomogeneous Bianchi type 𝑉𝐼 0 model. Bianchi type 𝑉𝐼 0 in the theory of self-creation and Lyra geometry was studied by Hegazy and Rahaman [12]. Priyanka et al [13] presented dark energy Bianchi type 𝐼 0 , cosmological models, with the equation of state parameters as a constant and time-dependent.…”