Fast radio bursts as cosmological proxies: estimating the hubble constant

One of the most challenging problems in modern cosmology is the Hubble tension, a discrepancy in the predicted expansion rate of the Universe with different observational techniques that results in two conflicting values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . We leverage the sensitivity of the Dispersion Measure (DM) from Fast Radio Bursts (FRBs) with the Hubble factor to investigate the Hubble tension. We build a catalog of 98 localized FRBs and an independent mock catalog and employ three methods to calculate the best value of the Hubble constant: i) the median value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> derived from direct computation combined with bootstrap resampling, ii) the Maximum Likelihood Estimate (MLE), and iii) the reconstruction of the cosmic expansion history <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi>z</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> using two DM- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"> <mml:mrow> <mml:mi>z</mml:mi> </mml:mrow> </mml:math> relations previously explored in the literature. The values found vary between 53 and 80 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m5"> <mml:mrow> <mml:mtext>km/s/Mpc</mml:mtext> </mml:mrow> </mml:math> . The result with the best statistical precision (6.0%) is the one obtained through MLE: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m6"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>70.1</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>3.63</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>4.19</mml:mn> </mml:mrow> </mml:msubsup> <mml:mtext> km/s/Mpc</mml:mtext> </mml:mrow> </mml:math> . On the other hand, when using 100 mock catalogs of 500 simulated FRBs in each realization, we obtain a value for the Hubble constant changes to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m7"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>67.3</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.85</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.98</mml:mn> </mml:mrow> </mml:msubsup> <mml:mtext> km/s/Mpc</mml:mtext> </mml:mrow> </mml:math> . More importantly, the latter result notably increases the statistical precision to 1.5% (the same level of precision as reports from the SH0ES collaboration). Ultimately, the rapid increase in the number of confirmed FRBs will provide us with a robust prediction of the value of the Hubble parameter today, which, in combination with other cosmological observations, will allow us to alleviate (to a certain degree) the current Hubble tension and make inference of other cosmological observables.