$5 σ$ tension between Planck cosmic microwave background and eBOSS Lyman-alpha forest and constraints on physics beyond $Λ$CDM

Abstract: We find that combined Planck cosmic microwave background, baryon acoustic oscillations and supernovae data analyzed under $\Lambda$CDM are in 4.9$\sigma$ tension with eBOSS Ly$\alpha$ forest in inference of the linear matter power spectrum at wavenumber $\sim 1 h\,\mathrm{Mpc}^{-1}$ and redshift = 3. Model extensions can alleviate this tension: running in the tilt of the primordial power spectrum ($\alpha_\mathrm{s} \sim -0.01$); a fraction $\sim (1 - 5)\%$ of ultra-light axion dark matter (DM) with particle mass $\sim 10^{-25}$ eV or warm DM with mass $\sim 10$ eV. The new DESI survey, coupled with high-accuracy modeling, will help distinguish the source of this discrepancy.

• The paper reports a 4.9σ tension in the linear matter power spectrum between Planck CMB and eBOSS Lyman-α observations.
• It employs MCMC and a compressed likelihood approach using CLASS-based Boltzmann codes to test extensions of the ΛCDM model.
• Findings indicate that modifications, such as a negative spectral index running or alternative dark matter candidates, may resolve the discrepancy.

Analyzing the Tension Between Planck CMB and eBOSS Lyman-alpha Forest Data

The paper investigates the notable discrepancies between different cosmological datasets, specifically between the Planck Cosmic Microwave Background (CMB) data and the eBOSS Lyman-alpha forest observations. These datasets offer insights into the linear matter power spectrum, which is pivotal for understanding the large-scale structure (LSS) of the Universe and testing the standard $\Lambda$CDM model's validity.

Main Findings

The authors report a $4.9\sigma$ tension when comparing the inferred linear matter power spectrum at a wavenumber around $1 \, h\,\mathrm{Mpc}^{-1}$ and a redshift of 3 between these datasets. This suggests a systematic deviation that might point either to unidentified systematics in the data or to physics beyond the $\Lambda$CDM framework. Several extensions to the $\Lambda$CDM model are proposed to resolve this tension, including:

1. Running of the Spectral Index ($\alpha_\mathrm{s}$): Introducing a negative running of the spectral index ($\alpha_\mathrm{s} \approx -0.01$) aligns the datasets by modifying the tilt of the primordial power spectrum.
2. Ultra-light Axion Dark Matter (ULA DM): A small fraction ($\sim 1 - 5\%$) of the Universe's dark matter content may consist of ultra-light axions with a mass around $10^{-25}$ eV, which could reconcile the differences observed in the datasets.
3. Warm Dark Matter (WDM): Another possibility is the existence of warm dark matter with a mass near $90$ eV, which similarly alters the matter power spectrum in a way that could alleviate the observed discrepancies.

Methodology

The study leverages a compressed likelihood approach that effectively summarizes the cosmic information captured in the eBOSS Lyman-alpha forest data. This method focuses on two key parameters: the amplitude and tilt of the linear matter power spectrum at the specified redshift and wavenumber. The parameters are subjected to various cosmological models, such as mixed neutrino masses, incorporation of running in spectral indices, and alternative dark matter candidates, to explore potential resolutions for the observed tension.

For inference, the authors utilize Markov chain Monte Carlo (MCMC) methods interfaced with established Boltzmann codes like CLASS and capably accommodate the physics of extensions like ultra-light axions through the AxiCLASS modifications.

Implications

The implications of this research are significant for cosmology, as they hint at potential physics beyond the $\Lambda$CDM model. The resolution of such tension, whether through correcting systematic biases or redefining cosmological paradigms, could lead to a deeper understanding of fundamental physical processes governing the Universe.

The insight that the Lyman-alpha forest provides, especially given its sensitivity to small-scale quasi-linear modes, reinforces its utility as an independent probe complementary to the CMB. Future datasets, notably from upcoming surveys like DESI, will play a crucial role in further clarifying these discrepancies and testing the credence of new physics models proposed here.

Conclusion

This paper underscores the importance of integrating large-scale cosmic datasets to test the limits of our current cosmological models. It illustrates how incorporating extensions to the $\Lambda$CDM model fine-tunes our grasp on the Universe's attributes. The results call for a methodical refinement of astrophysical models and an anticipation for next-generation data to rigorously test potential resolutions to observed parameter tensions.