Einstein equations with cosmological constant in Super Space-Time
We introduce a new kind of super warped product spaces $\bar{M}_{_{(I)}}=\textbf{I}^{1|0}\times_f M^{m|n}$, $\bar{M}_{_{(II)}}=\textbf{I}^{0|1}\times_{f} M^{m|n}$, and $\bar{M}_{_{(III)}}=\textbf{I}^{1|1}\times_{f} M^{m|n}$, where $M^{m|n}$ is a supermanifold of dimension $m|n$, $\textbf{I}^{δ|δ'}$ is standard superdomain with $\textbf{I}=(0,1)$ and $δ,δ' \in \{0,1\}$, subject to the warp functions $f(t)$, $f(\bar t)$, and $f(t, \bar t)$, respectively. In each super warped product space, $\bar{M}_{_{(I)}}$, $\bar{M}_{_{(II)}}$, and $\bar{M}_{_{(III)}}$, it is shown that Einstein equations $\bar{G}_{AB}=-\barΛ\bar{g}_{AB}$, with cosmological term $\barΛ$ are reducible to the Einstein equations $G_{αβ} = -Λg_{αβ}$ on the super space $M^{m|n}$ with cosmological term $Λ$, where $\barΛ$ and $Λ$ are functions of $f(t)$, $f(\bar t)$, and $f(t, \bar t)$, as well as ($m$, $n$). This dependence points to the origin of cosmological terms which turn out to be within the warped structure of the super space-time. By using the Generalized Robertson-Walker space-time, as a super space-time, and demanding for constancy of $\barΛ$ we can determine the warp functions and $Λ$ which result in finding the solutions for Einstein equations $\bar{G}_{AB}=-\barΛ\bar{g}_{AB}$ and $G_{αβ} = -Λg_{αβ}$. We have discussed the cosmological solutions, for each kind of super warped product space, in the special case of $M^{3|0}$.