This work proposes a stellar model under Gauss-Bonnet $f(\mathcal{G},T)$ gravity with the conjecture theorized by Mazur and Mottola, well known as the gravitational vacuum stars (gravastars). By taking into account the $f(\mathcal{G},T)$ stellar model, the structure of the gravastar with its exclusive division of three different regions, namely, (i) the core interior region, (ii) the junction region (shell), and (iii) the exterior region, has been investigated with reference to the existence of energy density, pressure, ultrarelativistic plasma, and repulsive forces. The different physical features, like the equation of state parameter, length of the shell, entropy, and energy-thickness relation of the gravastar shell model, have been discussed. Also, some other physically valid aspects have been presented with the connection to nonsingular and event-horizon-free gravastar solutions, which in contrast to a black hole solution, might be stable without containing any information paradox.

We explore the recently introduced modified Gauss–Bonnet gravity (Sharif and Ikram in Eur Phys J C 76:640, 2016 ), \(f(\mathcal {G},T)\) pragmatic with \(\mathcal {G}\), the Gauss–Bonnet term, and T, the trace of the energy-momentum tensor. Noether symmetry approach has been used to develop some cosmologically viable \(f(\mathcal {G},T)\) 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 \(f(\mathcal {G},T)\) gravity model.

Using the Noether symmetry approach, we investigate \(f( \mathcal{R} , \varphi ,\chi)\) theories of gravity, where \( \mathcal{R} \) is the scalar curvature, \( \varphi \) is the scalar field, and \(\chi\) is the kinetic term of \( \varphi \). Based on the Lagrangian for \(f( \mathcal{R} , \varphi ,\chi)\) gravity, we obtain the determining equations. We consider \(f( \mathcal{R} , \varphi ,\chi)\) models of a flat Friedmann–Robertson–Walker universe. Using the obtained solutions, we find conserved quantities. In the framework of this scenario, the continuity equation is extremely important for analyzing the energy density and pressure. Using the first integral of motion, we present a graphical analysis of the energy density, pressure component, and parameter of the equation of state. The negativity of the pressure observed in the considered cases in fact suggests that this theory can describe a Noether universe with dark matter.

The possible emergence of compact stars has been investigated in the recently introduced modified Gauss–Bonnet $$f(\mathcal {G},T)$$f(G,T) gravity, where $$\mathcal {G}$$G is the Gauss–Bonnet term and