In this paper, we study cosmic evolutionary stages in the background of
modified theory admitting non-minimal coupling between Ricci scalar, trace of
the energy-momentum tensor, contracted Ricci and energy-momentum tensors. For
dust distribution, we consider isotropic, homogeneous and flat cosmic model to
determine symmetry generators, conserved integrals and exact solutions using
Noether symmetry scheme. We find maximum symmetries for non-minimally
interacting Ricci scalar and trace of the energy-momentum tensor but none of
them correspond to any standard symmetry. For rest of the models, we obtain
scaling symmetry with conserved linear momentum. The graphical analysis of
standard cosmological parameters, squared speed of sound, viability conditions
suggested by Dolgov-Kawasaki instability and state-finder parameters identify
realistic nature of new models compatible with Chaplygin gas model,
quintessence and phantom regions. The fractional densities relative to ordinary
matter and dark energy are found to be consistent with Planck 2018
observational data. It is concluded that the constructed non-minimally coupled
models successfully explore cosmic accelerated expansion.

In this paper, the authors study cosmic evolutionary stages in the background of a modified theory that allows for non-minimal coupling between various quantities. Specifically, they consider a dust distribution in an isotropic, homogeneous, and flat cosmic model.

Using the Noether symmetry scheme, the authors determine symmetry generators, conserved integrals, and exact solutions for the system. They find maximum symmetries for the non-minimally interacting Ricci scalar and trace of the energy-momentum tensor, but none of these symmetries correspond to any standard symmetry. For the remaining models, they obtain a scaling symmetry with conserved linear momentum.

The authors then conduct a graphical analysis of various cosmological parameters, including squared speed of sound and viability conditions suggested by the Dolgov-Kawasaki instability. They also examine state-finder parameters to identify realistic characteristics of the new models. They find that these models are compatible with the Chaplygin gas model, as well as quintessence and phantom regions.

Finally, the authors compare the fractional densities relative to ordinary matter and dark energy in their models to Planck 2018 observational data. They conclude that the constructed non-minimally coupled models successfully explore cosmic accelerated expansion.

Future Roadmap

Potential Challenges

  1. Further investigation is needed to understand the implications of the non-standard symmetries found in the non-minimally interacting Ricci scalar and trace of the energy-momentum tensor.
  2. Verification and validation of the exact solutions using other methods or numerical simulations would provide additional confidence in their results.
  3. The compatibility of these models with observational data should be further tested using additional cosmological observations.

Potential Opportunities

  1. The scaling symmetry with conserved linear momentum discovered in the remaining models may have implications for the understanding of cosmic evolution and could be further explored in future research.
  2. The compatibility of these models with the Chaplygin gas model, quintessence, and phantom regions opens up new possibilities for understanding the nature of dark energy and its role in cosmic expansion.
  3. The successful exploration of cosmic accelerated expansion in these non-minimally coupled models may inspire the development of new theoretical frameworks or alternative cosmological models.

Overall, this study presents interesting findings regarding cosmic evolutionary stages in modified theories with non-minimal coupling. While there are challenges to address and opportunities for further research, the results offer new insights into the dynamics of the universe and its accelerated expansion.

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