Investigating the hyperbolic and hybrid scalar field cosmologies with varying cosmological constant in $f(R,T)$ gravity

Abstract

This paper investigated two scalar field cosmological models in $f(R,T)$ gravity with cosmic transit and varying cosmological constant $\Lambda (t)$.The cosmological constant tends to have a tiny positive value in the current epoch.The scalar field pressure $p_{\varphi }$ shows a sign reversal for a normal scalar field. For the phantom field, the scalar potential $V(\varphi )$ is negative and the energy density ${\rho }_{\varphi }=E_k+V$ takes negative values when the equation of state parameter ${\omega }_{\varphi }$ is less than $-1$. While the weak energy condition WEC implies that the total energy density $\rho ={\sum }_i{\rho }_i\ge 0$, we still can have a negative $\rho$ term as long as the total $\rho$ is positive. In the current work we argue that the WEC, $\rho ={\sum }_i{\rho }_i\ge 0$ and $p_i+{\rho }_i\ge 0$, is not violated but with an instability for the second model at late-times. For a scalar field $\varphi$, The condition ${\rho }_{\varphi }+p_{\varphi }={\rho }_{\varphi }(1+{\omega }_{\varphi })=2E_k\ge 0$ allows for ${\rho }_{\varphi }<0$ if ${\omega }_{\varphi }<-1$. The causality and energy conditions have been discussed for both models. The cosmology in both models was studied using a given function $a(t)$ derived from the desired cosmic behavior, which is the opposite of the traditional view.