  We present Tolman IV spacetime representing compact fluid sphere in
bigravity. Here we have explored the effect of scale parameter $k$ in the local
matter distribution of compact stars. We have model for three well-known
compact stars and it shows that for lower values of $k$ leads to stiffer EoS.
This claim is also supported by the graphical analysis. It can be observed that
the sound speed and the adiabatic index are more for lower values of $k$. It is
also seen that all the solutions of Einstein's field equations are still
satisfying the field equations in the presence of a background metric
$\gamma_{\mu \nu}$. However, the density and pressure does modified by extra
term from the constant curvature background, thus affecting the EoS. One can
also think that the parameter $\alpha \equiv 1/k^2$ as coupling constant
between the $g_{\mu \nu}$ and $\gamma_{\mu \nu}$ and consequently more the
coupling stiffer is the EoS. As $k\rightarrow \infty$, the background de-Sitter
spacetime reduces to Minkowski's spacetime and the coupling vanishes. The
solution satisfy the causality condition, all the energy conditions and
equilibrium under gravity and hydrostatic forces. The stability of the local
stellar structure is enhanced by reducing the scalar curvature of the
background spacetime.
