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We have examined tilted cosmological models by using conformally flat space-time with wet dark fluid in Lyra geometry. In order to solve the field equations we have considered a power law. In this paper we have discussed tilted universe with time-dependent displacement field vector, heat conduction vectors and also discussed big rip singularity. Some physical and geometrical properties are also investigated. We have also extended our work to investigate the consistency of the derived model with observational parameter from the point of astrophysical phenomenon such as look-back time-redshift, proper distance, luminosity distance, angular-diameter distance and distance modulus.

In this work, we have studied LRS Bianchi type I cosmological models in $f(R,T)$ gravity with tilted observers, where $R$ is the Ricci scalar and $T$ is the trace of the stress energy tensor. We have explored a tilted model and determined the solutions of the field equations by assuming special law of variation of Hubble’s parameter, proposed by Berman (1983) that yields constant deceleration parameter. In this scenario, we have used the equation of state $p=(\gamma -1)\rho$ and power law of velocity to describe the different anisotropic physical models such as Dust Universe, Radiation Universe, Hard Universe and Zedovich Universe. We have discussed graphical presentation of all parameters of the derived models with the help of MATLAB. Some physical and geometrical aspects of the models are also discussed.

We have presented the Big Rip singularity in $f(R,T)$ gravity with tilt congruences and creation field. We have solved the field equations by considering a conformally flat universe and the condition $B=A^n$, where $n$ is a constant. The solutions of the field equations have also been investigated by using the method of [J. V. Narlikar and T. Padmanabhan, Phys. Rev. D 32, 1928 (1985)] in which the creation field $C$ is a function of time $t$. Some geometric aspects of the model are also discussed by using MATLAB.

We discuss the difference in views of the universe as seen by two different observers. While one of the observers follows a geodesic congruence defined by the geometry of the cosmological model, the other observer follows the fluid flow lines of a perfect fluid with a linear equation of state. We point out that the information these observers collect regarding the state of the universe can be radically different; while one observes a non-inflating, ever-expanding, ever-lasting universe, the other observer can experience a dynamical behavior reminiscent of that of quintessence or even that of a phantom cosmology leading to a "big rip" singularity within finite time (but without the need for exotic forms of matter).

In this paper, tilted congruence with big rip singularity in f(T) theory of gravity is presented. f(T) theory of gravity is the generalization of the Teleparallel theory of gravity, where $T$ is the torsion scalar. In this work, tilted model is studied in which the three-velocity represents additional degree of freedom and tilted model detected the presence of dissipative processes including gravitational radiation. The solution of the field equations is explored by using the stiff fluid, power law of velocity field and a linear relationship between $H_1$ and $H_3$. In this paper, the big bang and big rip singularity are observed. The cosmological evolution in f(T) model is examined. The physical and geometrical phases of the models are also investigated.