Reconstructing the Hubble parameter with future Gravitational Wave missions using Machine Learning (2303.05169v2)

Abstract: We study the prospects of Gaussian processes (GP), a ML algorithm, as a tool to reconstruct the Hubble parameter $H(z)$ with two upcoming gravitational wave missions, namely the evolved Laser Interferometer Space Antenna (eLISA) and the Einstein Telescope (ET). Assuming various background cosmological models, the Hubble parameter has been reconstructed in a non-parametric manner with the help of GP using realistically generated catalogs for each mission. The effects of early-time and late-time priors on the reconstruction of $H(z)$, and hence on the Hubble constant ($H_0$), have also been focused on separately. Our analysis reveals that GP is quite robust in reconstructing the expansion history of the Universe within the observational window of the specific missions under consideration. We further confirm that both eLISA and ET would be able to provide constraints on $H(z)$ and $H_0$ which would be competitive to those inferred from current datasets. In particular, we observe that an eLISA run of $\sim10$-year duration with $\sim80$ detected bright siren events would be able to constrain $H_0$ as good as a $\sim3$-year ET run assuming $\sim 1000$ bright siren event detections. Further improvement in precision is expected for longer eLISA mission durations such as a $\sim15$-year time-frame having $\sim120$ events. Lastly, we discuss the possible role of these future gravitational wave missions in addressing the Hubble tension, for each model, on a case-by-case basis.

• The paper demonstrates that Gaussian Processes robustly reconstruct the expansion history H(z) from simulated GW data.
• It compares realistic catalogs from eLISA (80 events over 10 years) and ET (1000 events in 3 years) to refine H0 estimates.
• The approach highlights ML's potential in resolving the Hubble tension and advancing precision cosmology with future GW missions.

Overview of the Reconstruction of the Hubble Parameter using Gravitational Waves and Machine Learning

The paper, "Reconstructing the Hubble parameter with future Gravitational Wave missions using Machine Learning", presents a comprehensive analysis of using Gaussian Processes (GP) as a machine learning approach to reconstruct the Hubble parameter $H(z)$ by leveraging future gravitational wave (GW) missions, the evolved Laser Interferometer Space Antenna (eLISA) and the Einstein Telescope (ET), as potential sources. This research is significant in the field of cosmology as it probes the potential of GPs and future GW datasets to address existing tensions in the value of the Hubble constant $H_0$.

Methodological Approach

The authors adopt a non-parametric technique facilitated by GPs to perform the reconstruction task. They simulate catalogs using realistic expectations for GW events from eLISA and ET based on various cosmological models. These models include extensions or variations of the standard $\Lambda$CDM model such as the Chevallier-Polarski-Linder (CPL) and Jassal-Bagla-Padmanabhan (JBP) parametrizations to address the notorious Hubble tension.

Key computational steps include:

1. Generating mock GW catalogs for eLISA and ET, incorporating measurement errors and mission-specific parameters.
2. Employing GPs to reconstruct $H(z)$ from these simulated catalogs.
3. Analyzing early-time versus late-time prior dependency by using different fiducial parameter sets derived from present cosmological constraints on each model.
4. Evaluating the precision of $H_0$ estimation with increasing mission duration and detection count.

Main Findings and Analysis

The paper finds that Gaussian processes are robust tools for reconstructing the Hubble parameter from future GW mission data. Key findings include:

• GPs can non-parametrically predict the universe's expansion history with error margins competitive with current datasets.
• For a $\sim10$-year eLISA mission with 80 detected events, the reconstructions of $H_0$ are nearly as robust as those for a $\sim3$-year ET mission with 1000 events, attributed to eLISA's higher redshift probe range.
• Increasing the mission duration improves $H_0$ constraints, suggesting a promising future for extended GW observations in cosmology.
• The variance of reconstructed $H_0$ does not significantly depend on the fiducial choice, though the mean values are sensitive to these priors.

Implications and Speculation

The implications of this research are profound for observational cosmology and methodologies used therein. By demonstrating the utility of GPs in tangent with GW data, this work lays a foundation for more precise cosmological measurements independent of existing tensions between early- and late-time universe observations. Moreover, this approach provides a valuable complementary method to traditional electromagnetic observations, potentially resolving the discrepancies, known as the Hubble tension, in future decades.

In terms of AI developments, this research highlights the applicability of machine learning, particularly GPs, in handling non-parametric regression tasks within complex datasets. This can further inspire other interdisciplinary applications in sharp intersection with astrophysics, opening doors for hybrid methods that combine ML's flexibility with astrophysical insights to tackle unresolved cosmological questions.

Future Directions

The exploration of other machine learning techniques beyond Gaussian processes, considering their success here, could yield even more optimized strategies for cosmological inference. Additionally, the synthesis of data from multiple future GW detectors promises enhanced statistical power. The fusion of eLISA, ET, and next-generation missions in analyzing cosmological signals warrants a detailed investigation to enhance data reliability and cross-validation of results in an era of numerous forthcoming detection capabilities.