Two new diagnostics of dark energy (0807.3548v3)

Abstract: We introduce two new diagnostics of dark energy (DE). The first, Om, is a combination of the Hubble parameter and the cosmological redshift and provides a "null test" of dark energy being a cosmological constant. Namely, if the value of Om(z) is the same at different redshifts, then DE is exactly cosmological constant. The slope of Om(z) can differentiate between different models of dark energy even if the value of the matter density is not accurately known. For DE with an unevolving equation of state, a positive slope of Om(z) is suggestive of Phantom (w < -1) while a negative slope indicates Quintessence (w > -1). The second diagnostic, "acceleration probe"(q-probe), is the mean value of the deceleration parameter over a small redshift range. It can be used to determine the cosmological redshift at which the universe began to accelerate, again without reference to the current value of the matter density. We apply the "Om" and "q-probe" diagnostics to the Union data set of type Ia supernovae combined with recent data from the cosmic microwave background (WMAP5) and baryon acoustic oscillations.

• The paper introduces two diagnostic tools that reduce reliance on prior assumptions in modeling dark energy.
• It demonstrates the Om diagnostic's capability to differentiate between a cosmological constant and evolving dark energy using observational data.
• The acceleration probe estimates the transition redshift for cosmic acceleration, promising enhanced constraints with future high-precision data.

Analysis of "Two New Diagnostics of Dark Energy"

The paper "Two New Diagnostics of Dark Energy" by Varun Sahni, Arman Shafieloo, and Alexei A. Starobinsky introduces novel methodologies aimed at improving our understanding of dark energy (DE) through the introduction of two diagnostic tools: the $Om$ diagnostic and the acceleration probe $\bar{q}$. These tools provide new dimensions in the paper of DE without over-reliance on prior assumptions, thus potentially avoiding some pitfalls in model dependency.

Overview of the Om Diagnostic and Its Application

The $Om$ diagnostic is a function composed of the Hubble parameter and redshift, offering a method to test the hypothesized static nature of dark energy as a cosmological constant $\Lambda$. It is defined mathematically as:

$Om(x) \equiv \frac{h^2(x) - 1}{x^3 - 1},$

where $h(x)$ is the normalized Hubble parameter. The distinct utility of $Om$ lies in its ability to serve as a null test for the cosmological constant model. Specifically, in a flat cosmological constant plus cold dark matter (LCDM) model, $Om(x)$ should be constant over different redshifts if DE indeed acts as a cosmological constant. The paper highlights that this diagnostic can differentiate between quintessence ($w > -1$) and phantom types of DE ($w < -1$) by examining its slope over redshift. Notably, $Om$ can function independently of the present matter density parameter, $\Omega_{0m}$, thus circumventing one of the significant uncertainties in cosmological reconstructions.

When applied to the Union data set of type Ia supernovae, along with cosmic microwave background (CMB) and baryon acoustic oscillation (BAO) data, the $Om$ diagnostic demonstrated compatibility with LCDM, while also permitting the possibility of dynamical DE models. The authors assert that forthcoming data could improve the robustness of $Om$, making it a promising tool for differentiating between static and evolving DE scenarios.

The Acceleration Probe $\bar{q}$

The second diagnostic, the acceleration probe $\bar{q}$, estimates the mean deceleration parameter over a select redshift range. This diagnostic is defined as:

$$1+\bar{q} = \frac{1}{\Delta t}\left(\frac{1}{H_1} - \frac{1}{H_2}\right),$$

where $\Delta t$ is the time interval between two redshifts. The ability of $\bar{q}$ to reveal when the universe began accelerating provides an avenue for studying the transition from deceleration to acceleration, again without needing the precise current matter density value. The application of $\bar{q}$ indicates an acceleration redshift in the range $0.4 \leq z_a \leq 0.8$.

Implications and Future Directions

The introduction of $Om$ and $\bar{q}$ marks a significant methodological innovation by reducing the dependency on matter density assumptions and leveraging the expansion history. Consequently, these diagnostics are particularly advantageous in the context of high-precision cosmological data. Their independence from certain uncertainties makes them highly adaptable for application with current and forthcoming datasets, potentially providing a more discerning look at the nature and behavior of dark energy.

Looking forward, the effective use of these diagnostics could support discerning the characteristics of DE, thereby narrowing down viable models or adjustments to the basic LCDM framework. Additionally, as data quality and volume enhance with upcoming telescopic observations and missions, the precision of these tools in constraining DE models will improve. Further research could also explore the robustness of these diagnostics in spatially curved universes and their integration with other cosmological measures.

Conclusion

This paper contributes to the body of work tackling the enigmatic nature of dark energy by offering new, less assumption-dependent diagnostics. The $Om$ diagnostic and acceleration probe $\bar{q}$ are poised to significantly impact the trajectory of observational cosmology and theoretical analyses, assisting in clarifying whether the current cosmological observations mandate a cosmological constant-centric model or something altogether different.