Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models (1011.0544v4)

Abstract: Classical generalization of general relativity is considered as gravitational alternative for unified description of the early-time inflation with late-time cosmic acceleration. The structure and cosmological properties of number of modified theories, including traditional $F(R)$ and Ho\v{r}ava-Lifshitz $F(R)$ gravity, scalar-tensor theory, string-inspired and Gauss-Bonnet theory, non-local gravity, non-minimally coupled models, and power-counting renormalizable covariant gravity are discussed. Different representations and relations between such theories are investigated. It is shown that some versions of above theories may be consistent with local tests and may provide qualitatively reasonable unified description of inflation with dark energy epoch. The cosmological reconstruction of different modified gravities is made in great detail. It is demonstrated that eventually any given universe evolution may be reconstructed for the theories under consideration: the explicit reconstruction is applied to accelerating spatially-flat FRW universe. Special attention is paid to Lagrange multiplier constrained and conventional $F(R)$ gravities, for last theory the effective $\Lambda$CDM era and phantom-divide crossing acceleration are obtained. The occurrence of Big Rip and other finite-time future singularities in modified gravity is reviewed as well as its curing via the addition of higher-derivative gravitational invariants.

• The paper demonstrates that modified gravity models, particularly F(R)-based approaches, unify early-time inflation with late-time cosmic acceleration.
• The study employs cosmological reconstruction techniques to replicate a spatially flat FRW universe’s evolution without invoking dark energy.
• The analysis validates advanced models—including Gauss-Bonnet, non-local, and Horava-Lifshitz theories—as viable frameworks for addressing singularities and quantum gravity challenges.

Overview of "Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models"

This academic paper explores an extensive range of modified gravity theories in an effort to provide a comprehensive explanation for the universe's historic and projected evolution, specifically addressing the early-time inflation and the late-time acceleration phenomena. The paper evaluates various theoretical models, including $F(R)$ gravity, Hořava-Lifshitz $F(R)$ gravity, scalar-tensor theories, string-inspired and Gauss-Bonnet theories, non-local gravity, non-minimal coupling models, and power-counting renormalizable covariant gravity.

The authors, Shin'ichi Nojiri and Sergei D. Odintsov, delve into the structure and potential cosmological implications of these theories, asserting that many modified gravity models offer viable frameworks to unify different cosmic epochs without necessitating additional dark components. They emphasize the cosmological reconstruction analyses, which demonstrate that virtually any given universe evolution can be reconstructed within these modified gravities, applying particularly to the acceleration of a spatially flat Friedmann-Robertson-Walker (FRW) universe.

Key Findings and Claims

1. $F(R)$ Gravity Models: The paper investigates $F(R)$ gravity extensively, highlighting its potential for unifying early-time inflation and late-time acceleration. It discusses various models such as power-law $F(R)$, the exponential-type modifications, and viable models that can cohesively evolve across cosmic history without flat space solutions. These models can reproduce the observed cosmic acceleration or inflationary anomalies, encapsulating the effective energy conditions necessary to achieve such expansions.
2. Gauss-Bonnet and Non-local Gravity: The exploration extends to Gauss-Bonnet gravity, including stringy inspired models, and the formulations involving non-local terms. The paper underscores non-local models' capacity for reconstructing inflationary and cosmic acceleration phases, presenting scenarios that can avoid finite-time singularities traditionally observed in phantom cosmologies.
3. Horava-Lifshitz and Covariant Power-Counting Renormalizable Gravity: These approaches introduce new dynamics by breaking Lorentz invariance or utilizing a covariant framework, aiming for a renormalizable quantum gravity theory. The authors contend that these frameworks can still produce the desired cosmological effects, notably through higher-order gravitational action terms.
4. Cosmological Reconstruction: The authors propose reconstruction techniques to attain specific cosmological evolutions by tailoring the functional forms of modified gravity, specifically addressing the transition from non-phantom to phantom regimes. They utilize these reconstruction techniques across various modified gravity frameworks, demonstrating their versatility in producing desired cosmic history outcomes.

Implications and Future Directions

The paper asserts substantial theoretical extensions for understanding and simulating cosmic phenomena beyond what is achievable with standard General Relativity. Practically, the models offer frameworks that imply potential observational deviations, notably through the verification against dark energy dynamics and the matching of cosmological parameters with observational data.

Theoretically, understanding the interplay of different higher-order gravitational terms, non-local operators, and their cosmological implications could advance proposals for a theory of quantum gravity. The connections with string-inspired models and their broad domain of influence offer fertile ground for deeper exploration, especially regarding gravitational interaction at quantum scales.

Future avenues, as suggested by the authors, could focus on the development of covariant higher-derivative cosmological perturbation theories, capable of evaluative expansions in a way consistent with standard cosmology but enhanced for more intricate structural formations such as black holes or anti-de Sitter spaces. Emphasis on tackling singularities through dynamic stabilization techniques or higher-order corrections could further stabilize reconstructed models against theoretical inconsistencies or observational discrepancies.

In summary, this paper contributes significantly to the field of modified gravity, presenting comprehensive approaches to alternate cosmic evolutionary scenarios while addressing both practical implications and complex theoretical challenges inherent in modeling universal expansion through different gravity modifications.