A cosmological model by gravitational decoupling in a non-minimal coupling theory
A cosmological model by gravitational decoupling in a non-minimal coupling theory
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The accelerating expansion of the universe, the behavior of compact astrophysical objects, and the quest to unify gravity with the other fundamental forces continue to drive modern cosmology into new theoretical territories. One such pathway lies in exploring modified theories of gravity, particularly those involving non-minimal coupling (NMC) between matter and curvature. These theories, by extending the standard formulation of General Relativity (GR), allow for richer dynamics that can accommodate dark energy, explain cosmic inflation, and support more complex stellar configurations.
In this study, we present a cosmological model derived via the gravitational decoupling method within the context of a non-minimally coupled scalar-tensor theory of gravity. The approach taken here is innovative: we employ the Minimal Geometric Deformation (MGD) technique to decouple the Einstein field equations into simpler, tractable forms. This allows us to generate new exact solutions that represent anisotropic configurations in a relativistic background — key features for realistic stellar modeling and early universe cosmologies.
The non-minimal coupling between the scalar field and the Ricci scalar introduces additional degrees of freedom, which are handled effectively through the gravitational decoupling approach. The method splits the total energy-momentum tensor into two sectors: a known isotropic solution and an additional source representing the effects of anisotropy and scalar coupling. By solving the decoupled system, we construct a family of exact solutions describing compact objects embedded in a cosmological fluid with dynamical scalar fields.
Our results show that the model is physically viable, satisfying all energy conditions, and exhibits stability under perturbations. Moreover, the inclusion of the NMC term introduces a repulsive component in the gravitational interaction, which could mimic the effect of dark energy in cosmological settings. The scalar field evolution leads to modified pressure and density profiles that remain regular and finite throughout the stellar configuration.
We also explore the cosmological implications by analyzing the behavior of the effective equation of state (EoS) parameter. The model supports an accelerated expansion phase, consistent with current observational constraints from Type Ia supernovae, CMB anisotropies, and baryon acoustic oscillations. Additionally, we discuss how different choices of the coupling function and scalar potential can lead to a unification of inflation and dark energy mechanisms within a single theoretical framework.
This work contributes to the growing body of research that bridges gravitational decoupling techniques with extended gravitational theories. By combining the MGD approach with non-minimal coupling, we open new possibilities for exact solutions in scenarios where anisotropy and scalar fields play a fundamental role. This has applications not only in theoretical cosmology but also in astrophysics, where exotic compact objects such as quark stars, boson stars, or even gravastars may require such sophisticated models.
Our model provides a fertile ground for further investigations, including thermodynamic analysis, junction conditions for matching interior and exterior solutions, and potential observational signatures in gravitational wave astronomy. As gravitational decoupling continues to prove its versatility, coupling it with non-minimal scalar-tensor frameworks stands out as a promising frontier in modern gravitational research.
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