Current observations indicate that, on a large enough scale, the universe is homogeneous and isotropic. However, this does not preclude the possibility of some anisotropy having occurred during the early stages of the evolution of the universe, which could then have been damped out later. This idea has aroused interest in the Bianchi models, which are homogeneous but anisotropic. Secondly, there is much interest in modified gravity these days due to the problems that the usual ΛCDM model faces in general relativity. Hence, in this paper, a study was conducted on the Bianchi type-I cosmological model in f(R,T)-modified gravity. Following some ideas from cosmography, a specific form of the deceleration parameter was assumed, leading to a model that exhibited a transition from early deceleration to late-time acceleration. The derived model approached isotropy at late times. The physical properties of the model were discussed, and expressions for the various parameters of the model were derived. It is also possible to make progress towards solving the cosmological constant problem, since in this model in f(R,T) gravity, a variable cosmological-type parameter arose, which was large early on but decreased to a constant value in later times.
Although the present universe is believed to be homogeneous and isotropic on large scales, there is some evidence of some anisotropy at early times, Hence, there is interest in the Bianchi models, which are homogeneous, but anisotropic. In this presentation, the Bianchi type-I spacetime in the framework of the f(R,T) modified theory of gravity has been investigated for the specific choice of f(R,T) = R + 2f(T), where f(T) = -mT, m = constant. The solution of the modified gravity field equations has been generated by assuming that the deceleration parameter q is a function of the Hubble parameter H, i.e., q = b -n/H, (where b and n are constants, and n > 0) which yields the scale factor a = k[exp(dt) -1] 1/(1+b) (where k is a constant). The model exhibits deceleration at early times, and is currently accelerating. It is also seen that the model approaches isotropy at late times. Expressions for the Hubble parameter in terms of red-shift, luminosity distance, and state-finder parameter are derived and their significance is described in detail. The physical properties of the cosmological model are also discussed. An interesting feature of the model is that it has a dynamic cosmological parameter, which is large during the early universe, decreases with time, and approaches a constant at late times. This may help in solving the cosmological constant problem.
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