Nonlocal Cosmology (0706.2151v2)

Abstract: We explore nonlocally modified models of gravity, inspired by quantum loop corrections, as a mechanism for explaining current cosmic acceleration. These theories enjoy two major advantages: they allow a delayed response to cosmic events, here the transition from radiation to matter dominance, and they avoid the usual level of fine tuning; instead, emulating Dirac's dictum, the required large numbers come from the large time scales involved. Their solar system effects are safely negligible, and they may even prove useful to the black hole information problem.

• The paper demonstrates that nonlocal operators yield a delayed temporal response to cosmic events, effectively modeling the transition from radiation to matter dominance.
• The paper reveals that these models reduce fine tuning by deriving key parameters from extended cosmic durations rather than relying on arbitrary adjustments.
• The paper supports its claims with numerical analyses that validate the nonlocal modifications as a robust framework for explaining cosmic acceleration and related phenomena.

Nonlocal Modifications in Cosmological Models

Overview

The paper explores nonlocally modified models of gravity as inspired by quantum loop corrections. It primarily seeks to address the observed cosmic acceleration, which poses significant challenges to classical explanations rooted in Einstein's General Relativity. The authors identify two desirable attributes of nonlocal models: the capacity for a delayed temporal response to cosmic events and the minimization of fine tuning, both of which circumvent issues prevalent in other theories like scalar fields or $f(R)$ gravity.

Key Contributions

1. Delayed Response Mechanism: The paper elucidates how nonlocal models can naturally incorporate a delayed response to significant cosmological transitions, notably the shift from radiation to matter dominance. This delay is conceptualized via nonlocal operators, which effectively allow adjustments to reflect cosmic changes occurring at earlier epochs.
2. Reduction in Fine Tuning: Traditional models often involve significant fine tuning to account for the small observed value of the cosmological constant $\Lambda$. By reducing reliance on tuning large parameters, these nonlocal models derive large numbers naturally from historical cosmic durations, resonating with Dirac's hypotheses about large numbers.
3. Nonlocal Operators: The use of nonlocal differential operators, such as the inverse d'Alembertian, enables a mathematical framework where the time lag between significant historical cosmic events can be accommodated. The models discussed yield promising results without resorting to extreme parameter assumptions.
4. Potential for Broader Cosmological Application: Beyond addressing cosmic acceleration, nonlocal models might provide insights into unresolved issues such as the black hole information paradox, by retaining information about matter infall in a nonlocal fashion.

Results and Implications

The paper presents numerical analyses showing the feasibility of these models in evoking non-fine-tuned cosmic acceleration. Specifically, terms such as $G[R]$ effectively serve to modify the Einstein tensor in a manner that demands delay yet avoids complexity or excessive parameter tuning:

• The inverse operator produces quantifiable lags measurable in cosmic transitions.
• The reliance on the dimensionless coupling constants $C$ and $k$ demonstrates that models can reconcile observations with theoretical predictions without excessive adjustments from known physics.

The implications of these findings are substantial. Practically, they offer an alternative cosmological model potentially more robust to empirical tests against observed cosmic backgrounds. Theoretically, they suggest a framework that integrates quantum corrections more seamlessly with cosmological observations, potentially impacting ongoing debates on cosmological constants, dark energy modifications, and gravitational theory.

Future Directions

Given the findings, several avenues for future research arise:

• Further Exploration of Operator Classes: Extending beyond the simple operators explored could yield richer cosmological dynamics or address other phenomena presently challenging to reconcile within standard paradigms.
• Derivation from Quantum Field Theories: A firmer theoretical underpinning for these models could involve linking the nonperturbative quantum corrections with observed nonlocal effects more rigorously.
• Addressing Solar System Constraints: While nonlocal effects in the solar system framework appear negligible due to higher order terms, boundaries of validity remain a key area of exploration.
• Black Hole Physics: Employing nonlocal models to solve aspects of the black hole information paradox remains speculative but could bridge currently disparate theoretical frameworks.

The research in this paper highlights the ongoing evolution of cosmological modeling, strongly indicating the role of nonlocality in advancing our understanding of universe dynamics without dismissing standard cornerstones of gravitational theory.