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The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration (0804.3519v4)

Published 22 Apr 2008 in hep-th and gr-qc

Abstract: We study the future evolution of quintessence/phantom dominated epoch in modified $F(R)$-gravity which unifies the early-time inflation with late-time acceleration and which is consistent with observational tests. Using the reconstruction technique it is demonstrated that there are models where any known (Big Rip, II, III or IV Type) singularity may classically occur. From another side, in Einstein frame (scalar-tensor description) only IV Type singularity occurs. Near the singularity the classical description breaks up, it is demonstrated that quantum effects act against the singularity and may prevent its appearance. The realistic $F(R)$-gravity which is future singularity free is proposed. We point out that additional modification of any $F(R)$-gravity by the terms relevant at the early universe is possible, in such a way that future singularity does not occur even classically.

Citations (229)

Summary

  • The paper shows that finite-time singularities in F(R)-gravity differ between Jordan and Einstein frames, with the Einstein frame yielding only Type IV singularity.
  • Its rigorous reconstruction technique reveals that quantum corrections via the conformal anomaly can mitigate the progression of singularities.
  • The proposed non-linear F(R)-gravity model successfully unifies early inflation with late-time cosmic acceleration while satisfying Solar System constraints.

Analysis of Future Evolution and Singularities in F(R)-Gravity Framework

The paper authored by Shin’ichi Nojiri and Sergei D. Odintsov provides an in-depth examination of the cosmological implications of F(R)-gravity, a modified gravity theory proposed as a viable alternative to the standard model of cosmology. The focus of this paper is on addressing finite-time future singularities that may arise in the context of quintessence and phantom dark energy models within the framework of F(R)-gravity. Drawing upon a rigorous mathematical reconstruction technique, the authors explore the full spectrum of singularity types, including Big Rip, Type II, III, and IV singularities, which potentially threaten the stability of cosmic evolution.

Core Findings and Methodology

The authors demonstrate that the classification of finite-time singularities is highly dependent on the frame—Jordan or Einstein—in which the F(R)-gravity is expressed. Crucially, they find that, regardless of the singularity type observed in the Jordan frame, the corresponding Einstein frame restricts the occurrence solely to Type IV singularity. This indicates that the physical nature of singularities is intricately tied to the mathematical formulation used to describe gravitational interactions.

The research emphasizes the significant role of quantum mechanical effects in the vicinity of singularities. By incorporating quantum corrections through the conformal anomaly, they discover that such effects can fundamentally alter the progression towards singularities, potentially averting them. This highlights a need to consider quantum gravity effects that are not yet fully understood or formulated.

An innovative aspect of the paper is the authors' proposal of a realistic non-linear F(R)-gravity model, designed to avoid future singularities while unifying the inflationary period with late-time acceleration. The model maintains consistency with local tests within the Solar System, a critical criterion for any viable cosmological theory.

Implications and Future Directions

The research holds several critical implications for both theoretical and observational cosmology. Practically, the exploration of F(R)-gravity provides an impetus for reconsidering the fundamental rules governing dark energy and cosmic inflation, possibly offering alternative pathways to address these unresolved phenomena. Theoretically, the potential for quantum corrections to forestall singularities supports the view that a complete understanding of quantum gravity is indispensable for resolving the long-term fate of the universe.

The paper encourages further exploration of modified gravity theories, particularly in the context of other extended models like Gauss-Bonnet gravity and string-inspired alterations, to comprehensively uncover their ability to explain and predict cosmic evolution.

Conclusion

In conclusion, the paper presents a thorough investigation into the cosmological behavior and singularities within the F(R)-gravity framework. By elucidating how modified gravity models can potentially unify inflationary and late-time cosmic acceleration without succumbing to singularities, the paper broadens the scope of gravitational theory and offers fertile ground for future inquiry into the intricacies of our universe’s evolution. Continued research in this domain could yield significant breakthroughs in our understanding of gravity, possibly reshaping our conception of the cosmos itself.