A thorough investigation of the prospects of eLISA in addressing the Hubble tension: Fisher Forecast, MCMC and Machine Learning (2301.12708v2)

Abstract: We carry out an in-depth analysis of the capability of the upcoming space-based gravitational wave mission eLISA in addressing the Hubble tension, with a primary focus on observations at intermediate redshifts ($3<z<8$). We consider six different parametrizations representing different classes of cosmological models, which we constrain using the latest datasets of cosmic microwave background (CMB), baryon acoustic oscillations (BAO), and type Ia supernovae (SNIa) observations, in order to find out the up-to-date tensions with direct measurement data. Subsequently, these constraints are used as fiducials to construct mock catalogs for eLISA. We then employ Fisher analysis to forecast the future performance of each model in the context of eLISA. We further implement traditional Markov Chain Monte Carlo (MCMC) to estimate the parameters from the simulated catalogs. Finally, we utilize Gaussian Processes (GP), a machine learning algorithm, for reconstructing the Hubble parameter directly from simulated data. Based on our analysis, we present a thorough comparison of the three methods as forecasting tools. Our Fisher analysis confirms that eLISA would constrain the Hubble constant ($H_0$) at the sub-percent level. MCMC/GP results predict reduced tensions for models/fiducials which are currently harder to reconcile with direct measurements of $H_0$, whereas no significant change occurs for models/fiducials at lesser tensions with the latter. This feature warrants further investigation in this direction.

• The paper uses Fisher analysis, MCMC, and Gaussian Processes to assess eLISA's capability in constraining the Hubble constant.
• The study finds that eLISA can achieve sub-percent precision in H0 estimates, highlighting nuanced shifts in tension levels.
• The integration of machine learning with traditional methods offers a promising route to reconcile discrepancies in the ΛCDM model.

A Thorough Investigation of the Prospects of eLISA in Addressing the Hubble Tension

The paper under review conducts a comprehensive analysis of the potential of the upcoming eLISA (evolved Laser Interferometer Space Antenna) mission in addressing the Hubble tension, focusing on intermediate redshift observations in the range $3 < z < 8$. To assess eLISA's capabilities, the authors employ three methodologically distinct approaches: Fisher forecast, Markov Chain Monte Carlo (MCMC) analyses, and the use of Gaussian Processes (GP) within a machine learning framework.

Theoretical Context and Motivation

The Hubble tension refers to the significant discrepancy between the Hubble constant ($H_0$) values derived from cosmic microwave background (CMB) observations and local measurements using Cepheid-calibrated Type Ia supernovae (SNIa). This long-standing problem poses challenges for the standard $\Lambda$CDM cosmological model, potentially necessitating new physics or methodologies to reconcile these differences.

Methodology and Approach

The paper introduces six cosmological models, i.e., $\Lambda$CDM, Phenomenologically Emergent Dark Energy (PEDE), Vacuum Metamorphosis (VM), Elaborated Vacuum Metamorphosis (VM-VEV), Chevallier-Polarski-Linder (CPL), and Jassal-Bagla-Padmanabhan (JBP), to explore the capabilities of eLISA. The models span simple to more complex scenarios with varying parameters to address the current tensions effectively.

1. Fisher Forecast: The authors utilize Fisher matrix analysis to predict how eLISA might constrain the values of cosmological parameters. This technique highlights eLISA's ability to constrain $H_0$ to sub-percent precision, although it inherits the limitation of assuming the likelihoods are Gaussian.
2. MCMC: This widely-used Bayesian approach provides insights into both the mean and error distributions for the various cosmological parameters, given the simulated data from different fiducials based on the six models.
3. Gaussian Processes: The machine learning strategy leverages GP to non-parametrically reconstruct the Hubble parameter $H(z)$, allowing the mean and error bounds to adapt based on the simulated datasets without assuming a specific cosmological model.

Results and Implications

• Fisher Analysis: Confirms that eLISA can constrain $H_0$ at sub-percent levels, although this comes with an increased tension due to reduced error margins when compared to current datasets.
• MCMC Outcomes: Indicate marginal shifts and generally reduced tensions in $H_0$ estimates, pointing to the subtleties introduced by model assumptions in data analysis.
• Reconstruction via GP: Suggests that GP can shift reconstructed $H_0$ values closer to local measurements, emphasizing the role of non-parametric techniques in potentially resolving existing tensions without inherent model biases.

The implications of this paper are profound for both cosmology and gravitational wave astronomy. If realized, eLISA might distinctly augment our understanding of $H_0$, fostering potential shifts in the standard cosmological model or affirming the necessity for novel theoretical frameworks.

Future Directions

The potential future improvements outlined in the paper include refining catalog generation processes, further analysis of other gravitational wave missions like DECIGO and ET, and expanding the machine learning toolkit beyond GP to encompass more sophisticated neural networks. Additionally, the exploration of gravitational wave implications in theories beyond General Relativity might offer fresh insights into both $H_0$ tension and fundamental physics.

In summary, this paper provides a nuanced evaluation of potential synergies between future gravitational wave observations and traditional cosmological probes, advancing the discourse on one of the central challenges in contemporary cosmology.