A New Model of Agegraphic Dark Energy

Abstract: In this note, we propose a new model of agegraphic dark energy based on the K\'{a}rolyh\'{a}zy relation, where the time scale is chosen to be the conformal time $\eta$ of the Friedmann-Robertson-Walker (FRW) universe. We find that in the radiation-dominated epoch, the equation-of-state parameter of the new agegraphic dark energy $w_q=-1/3$ whereas $\Omega_q=n^2a^2$; in the matter-dominated epoch, $w_q=-2/3$ whereas $\Omega_q=n^2a^2/4$; eventually, the new agegraphic dark energy dominates; in the late time $w_q\to -1$ when $a\to\infty$, and the new agegraphic dark energy mimics a cosmological constant. In every stage, all things are consistent. The confusion in the original agegraphic dark energy model proposed in arXiv:0707.4049 disappears in this new model. Furthermore, $\Omega_q\ll 1$ is naturally satisfied in both radiation-dominated and matter-dominated epochs where $a\ll 1$. In addition, we further extend the new agegraphic dark energy model by including the interaction between the new agegraphic dark energy and background matter. In this case, we find that $w_q$ can cross the phantom divide.

• The paper introduces a novel computation method by adopting conformal time to yield consistent agegraphic dark energy behavior across cosmic epochs.
• The model analytically describes evolution from radiation to matter and late-time dominated epochs with specific equations of state.
• Interaction dynamics with background matter allow phantom divide crossing, offering potential insights into the universe's accelerated expansion.

A New Model of Agegraphic Dark Energy

This paper introduces a novel model for agegraphic dark energy, building upon the foundational Károlyházy relation. The researchers present a model where the time scale is chosen to be the conformal time of the Friedmann-Robertson-Walker (FRW) universe, providing a route to address the challenges seen in earlier models of agegraphic dark energy. This study's framework distinguishes itself by offering an intuitively consistent development over various epochs, including radiation-dominated, matter-dominated, and late-time phases.

The central innovation resides in replacing the conventional time scale with conformal time, which aligns more naturally with the causal structure of spacetime in an FRW universe. In essence, using the conformal time as the basis for computing the energy density of dark energy achieves a consistent behavior across the universe's evolution. The modified model successfully sidesteps the contradictions and limitations faced by the original agegraphic model, such as its inability to naturally dominate near current times and its inconsistent tracking behavior.

Detailed Examination of Model Dynamics

Comparatively, in the radiation-dominated epoch, the new model posits an equation of state (EoS) for agegraphic dark energy as $w = -1/3$ with the fractional energy density evolving as $\Omega_q = n^2a^2$. During the matter-dominated epoch, the model suggests $w = -2/3$ with $\Omega_q = n^2a/4$. Eventually, as the universe approaches late times with $a \to \infty$, the agegraphic dark energy mimics a cosmological constant, transitioning to $w \to -1$. These transitions are mathematically consistent and reflect realistic cosmological scenarios.

Strong numerical demonstrations support the longevity and robustness of this model over cosmic evolution, particularly the natural state of $\Omega_q \ll 1$ in early epochs, validating the parameter choice across large-scale universe dynamics. Furthermore, the model suggests that it shares evolutionary similarities with the holographic dark energy model, yet it maintains fundamental differences, such as being free from causality concerns prominent in the latter.

Integration and Interaction Considerations

Expansion on the model details includes the interaction between new agegraphic dark energy and background matter. When interaction terms (denoted as $Q$) are integrated, the energy exchange dynamics significantly alter the EoS, allowing crossings of the phantom divide, an intriguing theoretical possibility previously unattainable in the absence of interaction. This implies that under specific interactions, the agegraphic dark energy can exhibit w values lower than -1, offering insights into dark energy behaviors that potentially lead to the accelerated expansion of the universe.

Implications and Future Prospects

The proposed model offers practical advantages and resolution to issues linked with both agegraphic and holographic dark energy models. The use of conformal time is particularly notable for its elegance in sidestepping previous challenges and aligning with concepts of causal time in cosmological metrics.

From a theoretical perspective, this model encourages further exploration of quantum gravity's universal features, continuing the dialogue about the cosmological constant problem and encouraging new investigations into dark matter and dark energy coupling dynamics to reconcile challenges like compatibility with Big Bang Nucleosynthesis (BBN) constraints.

The numerical fidelity to observed cosmological data, along with the simplicity of being a single-parameter model, paves the way for further empirical examination. Nonetheless, instabilities within this model remain a critical area for future research, comparable to those in alternate dark energy models. Continued research could deepen our understanding and resolve outstanding questions surrounding cosmic acceleration, dark energy behavior, and interaction dynamics within the universe.