In this paper, the proposed dark energy, Tsallis holographic dark energy (THDE), infrared cut-off with the Hubble horizon has been investigated in the Bianchi-I (axially symmetric) anisotropic model with a hybrid expansion law. It has been observed that the THDE is in tune with the accelerating Universe with equation of state (EoS) parameter ($\omega_{T}$ < $−1/3$) in the $k$-essence region. We have used the statefinder diagnostic in our model. In addition, we try to accommodate the perspective of dark energy by the avenue of reconstructing the evolution of scalar field potential. We have considered the $k$-essence for the analysis of this reconstruction, showing the accelerated expansion at present.

The current research considers the Tsallis holographic dark energy (THDE) with the Hubble horizon as an IR cut-off with a non-interacting flat Friedmann–Lemaitre–Robertson–Walker (FLRW) Universe. We investigate the evolutionary behaviour of deceleration and the equation of state parameter for the distinct Tsallis exponent δ and noticed appropriate behaviour in the model. The scalar field of the phantom describes the non-interacting Tsallis holographic dark energy when δ > 2, then we demonstrate the phantomic narration when δ > 2 for the Tsallisholographic dark energy and reconstruct the scalar field potential of the phantom.

In the present paper, we investigate wormholes in 4D Einstein–Gauss–Bonnet (EGB) gravity without the requirement of exotic matters.We have taken the radial-dependent red-shift function φ= ln($\frac{r_0}{r + 1}$) and shape function b(r) =$\frac{r_0 ln(r+1)}{ln(r_0+1)}$ as well as anisotropic matter sources through the equation of state (EoS) pr (r ) = ωρ(r ). We examine the energy conditions, flaring-out condition, throat condition and anisotropic parameter. The volume integral quantifier is also analysed to validate the existence and stability of theWHsolution.We find that the negative branch wormhole solutions satisfy the null energy conditions (NEC) throughout the entire space–time and positive branch reduces exactly to Morris–Thorne of GR.