In this work we consider the realization of a variant emergent Universe
scenario in the context of $f(R)$ gravity. We use well-known reconstruction
techniques existing in the literature, and we find the approximate form of the
vacuum $f(R)$ that reproduces the specific variant emergent Universe scale
factor in the large curvature approximation. As we show, in the variant
emergent Universe scenario, the Hubble horizon shrinks primordially and the
Universe undergoes in an accelerated expansion era. In a perturbation theory
approach, the scalar and tensor curvature perturbations can be expressed in
terms of the phenomenological indices $epsilon_i , i=1,3,4$, usually used for
inflationary phenomenology, and we extract the spectral indices for the scalar
and tensor perturbations, along with the tensor-to-scalar ratio expressed in
terms of the perturbation indices. Using a powerful genetic algorithm we
investigate in depth the parameter space of the model, quantified by several
free parameters, in order to study the viability of the model when this is
compared with the Planck 2018 data. We also investigate the implications of the
vacuum $f(R)$ gravity we found on the Big Bang nucleosynthesis.
Conclusions
The author considers the realization of a variant emergent Universe scenario in the context of $f(R)$ gravity. They use reconstruction techniques existing in the literature to find the approximate form of the vacuum $f(R)$ that reproduces the specific variant emergent Universe scale factor in the large curvature approximation. In this scenario, the Hubble horizon shrinks primordially and the Universe undergoes an accelerated expansion era. They also express the scalar and tensor curvature perturbations in terms of phenomenological indices and extract the spectral indices and tensor-to-scalar ratio.
Using a genetic algorithm, they investigate the parameter space of the model to study its viability compared to the Planck 2018 data. They also examine the implications of the vacuum $f(R)$ gravity on Big Bang nucleosynthesis.
Future Roadmap: Challenges and Opportunities
Looking ahead, there are several potential challenges and opportunities for further research in this field:
- Refining the Model: The current study provides an approximate form of the vacuum $f(R)$ that reproduces the emergent Universe scenario. Future research can focus on refining this model to improve its accuracy and capture a wider range of observations.
- Understanding the Parameter Space: The investigation of the parameter space using a genetic algorithm is a promising approach. However, further exploration is needed to fully understand the implications and constraints on these parameters, especially in comparison with more recent data.
- Testing Against Experimental Data: The study compares the model with Planck 2018 data, but future experiments and observations may provide more precise and comprehensive data on the Universe. Researchers should continue to test and validate the model against new data to ensure its viability.
- Exploring Cosmological Implications: The implications of the vacuum $f(R)$ gravity on Big Bang nucleosynthesis are briefly mentioned. Researchers can delve deeper into this aspect and investigate other cosmological implications of the model, such as the formation and evolution of structures in the Universe.
Overall, this work presents a variant emergent Universe scenario in the context of $f(R)$ gravity and lays the groundwork for future research in understanding the Universe’s expansion and its implications.