Constraints on dark energy from TDCOSMO & SLACS lenses

Abstract: Problems with the cosmological constant model of dark energy motivate the investigation of alternative scenarios. I make the first measurement of the dark energy equation of state using the hierarchical strong lensing time delay likelihood provided by TDCOSMO. I find that the combination of seven TDCOSMO lenses and 33 SLACS lenses is only able to provide a weak constraint on the dark energy equation of state, $w < -1.75$ at 68% confidence, which nevertheless implies the presence of a phantom dark energy component. When the strong lensing time delay data is combined with a collection of cosmic microwave background, baryon acoustic oscillation and Type Ia supernova data, I find that the equation of state is $w = -1.025\pm 0.029$.

• The paper constrains dark energy by using a hierarchical Bayesian approach on 40 strong lensing systems to estimate the equation-of-state parameter.
• It refines the Hubble constant to 68.7 km/s/Mpc by combining TDCOSMO and SLACS data with other cosmological probes.
• The study mitigates the mass-sheet degeneracy issue by employing a population-level inference method, setting a benchmark for future surveys.

Analysis of Dark Energy Constraints through Strong Lensing Observations

The paper by Natalie B. Hogg presents an important examination of dark energy dynamics by utilizing the strong lensing TDCOSMO and SLACS datasets—a total of 40 cosmological lenses. This analysis is groundbreaking as it attempts to constrain the dark energy equation of state parameter $w$ using a hierarchical Bayesian approach, basing inferences on time delay measurements from strong gravitational lensing.

The study targets a longstanding issue in cosmology regarding the nature of dark energy, particularly whether its influence corresponds to a cosmological constant with a fixed equation of state $w = -1$, or if it exhibits dynamic properties that vary over time. The hierarchical Bayesian framework used in this research endeavors to mitigate model dependencies, especially concerning the mass profile of typical lens galaxies, that often introduce significant uncertainties into determinations of the Hubble parameter $H_0$.

Key Findings

1. Dark Energy Constraints:

- Utilizing the combined datasets from TDCOSMO and SLACS, the study offers a weak constraint on the dark energy equation of state with $w < -1.75$ at 68% confidence level. This result suggests the potential presence of a 'phantom' dark energy component where $w < -1$.

- When integrating the strong lensing constraints with other cosmological observations such as those from the cosmic microwave background (CMB), baryon acoustic oscillations (BAO), and Type Ia supernovae, the study finds a more refined constraint of $w = -1.025 \pm 0.029$, consistent with the cosmological constant model, indicating no substantial evolution in dark energy density.

2. Hubble Constant Estimates:

- The analysis also assesses the estimation of the Hubble constant $H_0$, presenting a measured value of $H_0 = 68.7^{+3.4}_{-3.9}$ km/s/Mpc using the combined datasets, which concurs with other recent determinations.

3. Implications of Mass Sheet Degeneracy:

- One significant challenge addressed in this paper is the mass-sheet degeneracy problem in gravitational lensing, an issue that complicates the interpretation of lensing data in relation to cosmological parameters. The study attempts to minimize this by employing a population-level inference method through additional data from the SLACS lenses.

Implications and Future Outlook

The implications of this research extend into both theoretical understanding and observational strategies in cosmology:

• Theoretical Insights: By tightly constraining $w$, these findings bolster the robustness of the cosmological constant model $\Lambda$CDM and have potential implications on theories extending standard cosmology, especially those engaging with evolving dark energy scenarios.
• Observational Strategies: The integration with multiple observational datasets underscores the importance of comprehensive, multi-probe analysis in cosmology. Upcoming large-scale surveys such as LSST and Euclid are anticipated to greatly enhance the precision and breadth of these constraints through more expansive lensing datasets.
• Toward Evolving $\Omega_{\rm DE}$: While current results lean towards a constant $w$, future surveys could further probe evolving dark energy models by expanding data precision and reach, potentially illuminating shifts in $\Omega_{\rm DE}$ over cosmological time scales.

In conclusion, Hogg's study represents a methodologically careful advancement in the investigation of dark energy's nature. By employing a rigorous statistical framework aligned with strong observational data, it provides an insightful benchmark against which future cosmic surveys can be calibrated and highlights the significance of carefully unified datasets in constraining fundamental cosmic parameters.