Generalized almost schouten solitons on perfect fluid spacetimes under f (ℛ)-gravity

In this study we investigate generalized almost Schouten soliton (GASS) and gradient generalized almost Schouten soliton (GGASS) by taking the potential vector field as a concircular vector field (CVF) in a perfect fluid spacetime (PFS) under [Formula: see text]-gravity. Also, it is proven that the GASS in a PFS under [Formula: see text]-gravity with constant Ricci scalar greenestablishes Poisson’s equation and Laplace’s equation. Moreover, we deduce the Schrödinger equation for the potential function [Formula: see text] on a PFS coupled with [Formula: see text]-gravity admitting GASS. As a consequence, it is proved that if a PFS within the context of [Formula: see text]-gravity admits a GGASS with constant Ricci scalar satisfies [Formula: see text], then either perfect fluid has vanishing expansion scalar, or the spacetime green represents a dark matter era. Also, we examine two models [Formula: see text] and [Formula: see text] (here [Formula: see text] is the Ricci scalar of the spacetime; [Formula: see text] and [Formula: see text] are constants; [Formula: see text] and [Formula: see text] are positive dimensionless constants; and [Formula: see text], [Formula: see text] are positive parameters), various energy conditions with respect to the Ricci scalar are examined red and stated that the expansion of the universe is decelerate and the system exhibits stable, classic attractive gravitational characteristics in this zone and voilate the no exotic matter, or dark energy behavior.