High-z candles

A Bayesian Python code to confront the quasar data set with models beyond the standard model of elementary particle physics and models beyond the $\Lambda$CDM standard cosmology.

Abstract

The Hubble diagram of quasars, as candidates to ``standardizable" candles, has been used to measure the expansion history of the Universe at late times, up to very high redshifts ($z \sim 7$). It has been shown that this history, as inferred from the quasar dataset, deviates at $\gtrsim 3 \sigma$ level from the concordance ($\Lambda$CDM) cosmology model preferred by the cosmic microwave background (CMB) and other datasets. In this article, we investigate whether new physics beyond $\Lambda$CDM (B$\Lambda$CDM) or beyond the Standard Model (BSM) could make the quasar data consistent with the concordance model. We first show that an effective redshift-dependent relation between the quasar UV and X-ray luminosities, complementing previous phenomenological work in the literature, can potentially remedy the discrepancy. Such a redshift dependence can be realized in a BSM model with axion-photon conversion in the intergalactic medium (IGM), although the preferred parameter space could be in mild tension with various other astrophysical constraints on axions, depending on the specific assumptions made regarding the IGM magnetic field. We briefly discuss a variation of the axion model that could evade these astrophysical constraints. On the other hand, we show that models beyond $\Lambda$CDM such as one with a varying dark energy equation of state ($w$CDM) or the phenomenological cosmographic model with a polynomial expansion of the luminosity distance, cannot alleviate the tension.

How to run

Requirements

1. Python
2. numpy
3. scipy
4. emcee
5. corner

How to run the MCMC

In the terminal:

$ python cosmo_axions_run.py -L likelihoods/ -o path/to/your/chain/output/ -i inputs/the_param_file.param -N number_of_points -w number_of_walkers

As a rule of thumb, a good number to start most runs is -N 40000 -w 100. You can adjust the number depending on the convergence test during analysis. Be careful that analyzing an unfinished chain will likely break the run. Therefore, it is better to copy the unfinished chain to a different folder and analyze from there.

How to analyze the chain

After the runs are finished, you can analyze them with:

$ python cosmo_axions_analysis.py -i path/to/your/chain/output/

Once the analysis is done, if you wanna output the contours in ma-ga space from the frequentist likelihood ratio test, do:

$ python bin_chi2.py -c path/to/your/chain/output/ -b number_of_ma-ga_bins

where the argument with flag -b bins the ma-ga parameter space in order to minimize the chi2 in each bin. A value of ~50 is good enough.

For the best fit point, it can be extracted by the parse() from bin_chi2.py. A sample is given below:

(bf_chi2,
 x_mesh,
 y_mesh,
 chi2_mins,
 idx_mins_global,
 x_arr, y_arr,
 delta_arr,
 _,
 pts, 
 blobs) = parse(directory="path_to_chain",
					chain_name="chain_1.h5",
					x_name="OmL",
					y_name="h0",
					bins=10)

The specific location of the best fit in the chain is output, which can then be located in the flat chain with pts[<index_of_best_fit>.

Cosmographic Model

The master branch can fit $\Lambda$CDM, wCDM, axion, step function $\beta(z)$, and smooth $\beta(z)$. Due to the very different functions, the cosmographic model (a2-a3-a4 expansion) is implemented as a separate branch cosmo_inde_model.

Bibtex entry

If you use this code or find it in any way useful for your research, please cite Sun, Buen-Abad, Fan (2023). The BibTeX entry is:

@article{Sun:2023wqq,
    author = "Sun, Chen and Buen-Abad, Manuel A. and Fan, JiJi",
    title = "{Probing New Physics with High-Redshift Quasars: Axions and Non-standard Cosmology}",
    eprint = "2309.07212",
    archivePrefix = "arXiv",
    primaryClass = "astro-ph.CO",
	reportNumber = "LA-UR-23-29579",
    month = "09",
    year = "2023"
}

The main routine and the routine of fitting SNIa is based on Buen-Abad, Fan, & Sun (2020). Please also consider citing this publication with the following BibTeX entry:

@article{Buen-Abad:2020zbd,
    author = "Buen-Abad, Manuel A. and Fan, JiJi and Sun, Chen",
    title = "{Constraints on Axions from Cosmic Distance Measurements}",
    eprint = "2011.05993",
    archivePrefix = "arXiv",
    primaryClass = "hep-ph",
    month = "11",
    year = "2020"
}