We present models of wormhole under the Finslerian structure of spacetime. This is a sequel of our previous work (Eur Phys J 75:564, 2015) where we constructed a toy model for compact stars based on the Finslerian spacetime geometry. In the present investigation, a wide variety of solutions are obtained, which explore the wormhole geometry by considering different choices for the form function and energy density. The solutions, like in the previous work, are revealed to be physically interesting and viable models for the explanation of wormholes as far as the background theory and literature are concerned.

We construct a toy model for compact stars based on the Finslerian structure of spacetime. By assuming a particular mass function, we find an exact solution of the FinslerEinstein field equations with an anisotropic matter distribution. The solutions are revealed to be physically interesting and pertinent for the explanation of compact stars.

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We consider a very general scenario of our universe where its geometry is characterized by the Finslerian structure on the underlying spacetime manifold, a generalization of the Riemannian geometry. Now considering a general energy-momentum tensor for matter sector, we derive the gravitational field equations in such spacetime. Further, to depict the cosmological dynamics in such spacetime proposing an interesting equation of state identified by a sole parameter γ which for isotropic limit is simply the barotropic equation of state p = (γ − 1)ρ (γ ∈ R being the barotropic index), we solve the background dynamics. The dynamics offers several possibilities depending on this sole parameter as follows − (i) only an exponential expansion, or (ii) a finite time past singularity (big bang) with late accelerating phase, or (iii) a nonsingular universe exhibiting an accelerating scenario at late time which finally predicts a big rip type singularity. We also discuss several energy conditions and the possibility of cosmic bounce. Finally, we establish the first law of thermodynamics in such spacetime. PACS numbers: 98.80.+k; 95.36.+x