Curing singularities in cosmological evolution of F(R) gravity (0909.1737v3)

Abstract: We study $F(R)$ modified gravity models which are capable of driving the accelerating epoch of the Universe at the present time whilst not destroying the standard Big Bang and inflationary cosmology. Recent studies have shown that a weak curvature singularity with $|R|\to\infty$ can arise generically in viable $F(R)$ models of present dark energy (DE) signaling an internal incompleteness of these models. In this work we study how this problem is cured by adding a quadratic correction with a sufficiently small coefficient to the $F(R)$ function at large curvatures. At the same time, this correction eliminates two more serious problems of previously constructed viable $F(R)$ DE models: unboundedness of the mass of a scalar particle (scalaron) arising in $F(R)$ gravity and the scalaron overabundance problem. Such carefully constructed models can also yield both an early time inflationary epoch and a late time de Sitter phase with vastly different values of $R$. The reheating epoch in these combined models of primordial and present dark energy is completely different from that of the old $R + R^{2}/6M^{2}$ inflationary model, mainly due to the fact that values of the effective gravitational constant at low and intermediate curvatures are different for positive and negative $R$. This changes the number of e-folds during the observable part of inflation that results in a different value of the primordial power spectrum index.

• The paper demonstrates that incorporating a quadratic term in F(R) gravity cures curvature singularities and resolves scalaron overabundance.
• It rigorously extends previous F(R) models to manage high curvature regimes while unifying early inflation with late-time de Sitter acceleration.
• The study offers a robust framework for parameter tuning that aligns modified gravity theories with current cosmological observations.

Overview of "Curing Singularities in Cosmological Evolution of F(R) Gravity"

The research paper titled "Curing singularities in cosmological evolution of F(R) gravity" by Stephen A. Appleby, Richard A. Battye, and Alexei A. Starobinsky offers a detailed investigation into F(R) modified gravity models. These models are pivotal for explaining the present accelerated expansion of the Universe while preserving the successes of the Big Bang and inflationary cosmology. The paper primarily addresses the issues of singularities and scalaron overabundance in F(R) gravity models, proposing solutions that also support early Universe inflation.

Key Problems and Solutions

The authors identify a significant problem in viable F(R) models of present dark energy: the emergence of a weak curvature singularity characterized by $|R| \to \infty$. This singularity highlights internal incompleteness within these models. Additionally, issues regarding the unbounded mass of the scalaron and the overabundance of scalarons in the early universe are addressed. The paper proposes to introduce a quadratic correction to the F(R) function at large curvatures. This approach not only cures the singularities but also resolves the mass and overabundance concerns associated with the scalaron.

Numerical Insights and Model Improvement

The paper rigorously develops mathematical formulations and analyses to substantiate the proposed solutions. It demonstrates that by incorporating a quadratic term in the form $R^2$, with a small coefficient, the singularity is effectively removed. The authors extend previous models (HSS and AB models) to include this correction, allowing them to handle high curvature regimes without encountering singularities.

Implications for Inflation and Dark Energy

By integrating quadratic corrections, the corrected F(R) models can simultaneously account for an early inflationary epoch and a late-time de Sitter phase—a remarkable feature showing vastly different curvature values. The inflationary phase is shown to transition naturally into a reheating period, distinct from the classical models like $R + R^2/6M^2$.

Theoretical and Practical Implications

Theoretically, this paper provides a framework for refining modified gravity theories. It ensures the models are consistent with observed Universe dynamics without singularities, enhancing the robustness of F(R) gravity as an alternative to $\Lambda$CDM for explaining dark energy. Practically, it underscores the potential for F(R) gravity to unify the descriptions of both primordial and present dark energy phases with adequate parameter tuning, demonstrating compatibility with current observational constraints.

Future Directions

The paper suggests future research could focus on exploring different functional forms of F(R) that incorporate these insights, assessing their implications on cosmic structure formation and testing against precise cosmological observations. Additionally, the interrelation between the introduced quadratic terms and quantum gravity might provide deeper insights into the fundamental physics instigating cosmic acceleration.

In conclusion, this paper makes a significant contribution to the field of cosmological modeling by providing a method to resolve longstanding issues in F(R) gravity models. It demonstrates the potential for these theories to provide a comprehensive picture of the Universe's evolution from inflation to its current accelerated expansion.