Traversable wormholes, tunnel like structures introduced by Morris & Thorne [1], have a significant role in connection of two different space-times or two different parts of the same space-time. The characteristics of these wormholes depend upon the redshift and shape functions which are defined in terms of radial coordinate. In literature, several shape functions are defined and wormholes are studied in f (R) gravity with respect to these shape functions [55,57,60]. In this paper, two shape functions (i) b(r) = r 0 log(r + 1) log(r 0 + 1) and (ii) b(r) = r 0 ( r r 0 ) γ , 0 < γ < 1 are considered. The first shape function is newly defined, however the second one is collected from the literature [77]. The wormholes are investigated for each type of shape function in f (R) gravity with f (R) = R + αR m − βR −n , where m, n, α, and β are real constants. Varying parameters α or β, f (R) model is studied in five subcases for each type of shape function. In each case, the energy density, radial & tangential pressures, energy conditions that include null energy condition, weak energy condition, strong energy condition & dominated energy condition, and anisotropic parameter are computed. The energy density is found to be positive and all energy conditions are obtained to be violated which supports the existence of wormholes. Also, the equation of state parameter is obtained to possess values less than -1, that shows the presence of the phantom fluid and leads towards the expansion of the universe.

In this work, wormholes, tunnel like structures introduced by Morris & Thorne [1], are explored within the framework of f (R) gravity. Using the shape function b(r) = r 0where 0 < γ < 1, and the equation of state p r = ωρ, the f (R) function is derived and the field equations are solved. Then null, weak, strong and dominated energy conditions are analyzed and spherical regions satisfying these energy conditions are determined. Furthermore, we calculated the range of the radius of the throat of the wormhole, where the energy conditions are satisfied.

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In this work, the study of traversable wormholes in f (R) gravity with the function f (R) = R + αR n , where α and n are arbitrary constants, is taken into account. The shape function b(r) = r exp(r−r 0 ) , proposed by Samanta et al. [71], is considered. The energy conditions with respect to both constant and variable redshift functions are discussed and the existence of wormhole solutions without presence of exotic matter is investigated.

We propose a novel shape function, on which the metric that models traversable wormholes is dependent. With this shape function, the energy conditions, equation of state and anisotropy parameter are analyzed in f (R) gravity, f (R, T ) gravity and general relativity. Furthermore, the consequences obtained with respect to these theories are compared. In addition, the existence of wormhole geometries is investigated.

Morris & Thorne [12] proposed geometrical objects called traversable wormholes that act as bridges in connecting two spacetimes or two different points of the same spacetime. The geometrical properties of these wormholes depend upon the choice of the shape function. In literature, these are studied in modified gravities for different types of shape functions. In this paper, the traversable wormholes having shape function b(r) = r 0 tanh(r) tanh(r 0 ) are explored in f (R) gravity with f (R) = R + αR m − βR −n , where α, β, m and n are real constants.For different values of constants in function f (R), the analysis is done in various cases. In each case, the energy conditions, equation of state parameter and anisotropic parameter are determined.

In the present paper, the modelling of traversale wormholes, proposed by Morris & Thorne [1], is performed within the f (R) gravity with particular viable case f (R) = R − µR c R Rc p , where µ, R c > 0 and 0 < p < 1. The energy conditions are analyzed using the shape function b(r) = r log(r+1) log(r 0 +1) defined by Godani and Samanta [64] and geometric nature of wormholes is analyzed.

In this paper, we considered the study of Friedmann–Robertson–Walker (FRW) model in the framework of [Formula: see text] gravity, an extension of symmetric teleparallel gravity, recently defined by Xu et al. [[Formula: see text] gravity, Eur. Phys. J. C 79 (2019) 708]. The nonlinear model [Formula: see text], where [Formula: see text] and [Formula: see text] are constants, is taken into account. The equation of state of perfect fluid is assumed and 31 points of Hubble data are used to constrain the value of model parameter. To explore the evolution of the universe, the numerical solutions of cosmological implications, such as Hubble parameter, deceleration parameter, apparent magnitude and luminosity distance, are determined and the energy conditions are examined. The theoretical results of Hubble parameter are compared with [Formula: see text]CDM model. Further, 57 Supernova data (42 from Supernova cosmology project and 15 from Calán/Tolono supernova survey) are also used to have consistent results of apparent magnitude and luminosity distance.