Model comparison of $$\Lambda $$CDM vs $$R_h=ct$$ using cosmic chronometers
Haveesh Singirikonda, Shantanu Desai
Abstract
Abstract In 2012, Bilicki and Seikel (Mon Not R Astron Soc 425:1664, 2012) showed that H ( z ) data reconstructed using Gaussian Process Regression from cosmic chronometers and baryon acoustic oscillations, conclusively rules out the $$R_h=ct$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>h</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>c</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:math> model. These results were disputed by Melia and collaborators in two different works (Melia and Maier in Mon Not R Astron Soc 432:2669, 2013; Melia and Yennapureddy in JCAP 2018:034, 2018), who showed using both an unbinned analysis and Gaussian Process reconstructed H ( z ) data from chronometers, that $$R_h=ct$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>h</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>c</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:math> is favored over $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> CDM model. To resolve this imbroglio, we carry out model comparison of $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> CDM versus $$R_h=ct$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>h</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>c</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:math> by independently reproducing the above claims using the latest chronometer data. We perform model selection between these two models using Bayesian model comparison. We find that no one model between $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> CDM and $$R_h=ct$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>h</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>c</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:math> is decisively favored when uniform priors on $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> CDM parameters are used. However, if we use priors centered around the Planck best-fit values, then $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> CDM is very strongly preferred over $$R_h=ct$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>h</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>c</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:math> .