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 $Λ(t)$.The cosmological constant tends to have a tiny positive value in the current epoch.The scalar field pressure $p_ϕ$ shows a sign reversal for a normal scalar field. For the phantom field, the scalar potential $V(ϕ)$ is negative and the energy density $ρ_ϕ=E_k+V$ takes negative values when the equation of state parameter $ω_ϕ$ is less than $-1$. While the weak energy condition WEC implies that the total energy density $ρ=\sum_iρ_i\geq 0$, we still can have a negative $ρ$ term as long as the total $ρ$ is positive. In the current work we argue that the WEC, $ρ=\sum_i ρ_i \geq 0$ and $p_i+ρ_i \geq 0$, is not violated but with an instability for the second model at late-times. For a scalar field $ϕ$, The condition $ρ_ϕ+p_ϕ=ρ_ϕ (1+ω_ϕ)=2E_k\geq 0$ allows for $ρ_ϕ<0$ if $ω_ϕ<-1$. 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.