We explore the recently introduced modified Gauss-Bonnet gravity (Sharif and Ikram in Eur Phys J C 76:640, 2016), f (G, T ) pragmatic with G, the Gauss-Bonnet term, and T , the trace of the energy-momentum tensor. Noether symmetry approach has been used to develop some cosmologically viable f (G, T ) gravity models. The Noether equations of modified gravity are reported for flat FRW universe. Two specific models have been studied to determine the conserved quantities and exact solutions. In particular, the well known deSitter solution is reconstructed for some specific choice of f (G, T ) gravity model.

This paper is devoted to investigate the recently proposed modified Gauss-Bonnet f (G, T ) gravity, with G, the Gauss-Bonnet term, coupled with T , the trace of energy-momentum tensor. We have used the Noether symmetry methodology to discuss some cosmologically important f (G, T ) gravity models with anisotropic background. In particular, the Noether symmetry equations for modified f (G, T ) gravity are reported for locally rotationally symmetric Bianchi type I universe. Explicitly, two models have been proposed to explore the exact solutions and the conserved quantities. It is concluded that the specific models of modified Gauss-Bonnet gravity may be used to reconstruct ΛCDM cosmology without involving any cosmological constant.

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This current study is focussed to discuss the existence of a new family of compact star solutions by adopting the Karmarkar condition in the background of Bardeen black hole geometry. For this purpose, we consider static spherically symmetric spacetime with anisotropic fluid distribution in the presence of electric charge. We consider a specific model of grr metric function, to describe a new family of solutions which satisfies the Karmarkar condition. Further, we investigate the interior solutions for two different models of compact stars with observational mass and radii, i.e., (M = 1.77M⊙, R b = 9.56km) and (M = 1.97M⊙, R b = 10.3km). It is found that these solutions fulfill all the necessary conditions for a charged star. Through graphical discussion, it is noticed that our calculated solutions are physically arguable with a best degree of accuracy for n ∈ [1.8, 7), where parameter n is involved in the model under discussion. However, it is perceived that the presented model violates all the physical conditions for n ∈ {2, 4, 6}. Finally, it is concluded that the parameter n has a strong impact on the obtained solutions in the context of Bardeen stellar structures.

This study explores the Gaussian and the Lorentzian distributed spherically symmetric wormhole solutions in the f(τ,T) gravity. The basic idea of the Gaussian and Lorentzian noncommutative geometries emerges as the physically acceptable and substantial notion in quantum physics. This idea of the noncommutative geometries with both the Gaussian and Lorentzian distributions becomes more striking when wormhole geometries in the modified theories of gravity are discussed. Here we consider a linear model within f(τ,T) gravity to investigate traversable wormholes. In particular, we discuss the possible cases for the wormhole geometries using the Gaussian and the Lorentzian noncommutative distributions to obtain the exact shape function for them. By incorporating the particular values of the unknown parameters involved, we discuss different properties of the new wormhole geometries explored here. It is noted that the involved matter violates the weak energy condition for both the cases of the noncommutative geometries, whereas there is a possibility for a physically viable wormhole solution. By analyzing the equilibrium condition, it is found that the acquired solutions are stable. Furthermore, we provide the embedded diagrams for wormhole structures under Gaussian and Lorentzian noncommutative frameworks. Moreover, we present the critical analysis on an anisotropic pressure under the Gaussian and the Lorentzian distributions.