Solving the $$H_{0}$$ tension in f(T) gravity through Bayesian machine learning
Muhsin Aljaf, E. Elizalde, Martiros Khurshudyan, Kairat Myrzakulov, A. Zhadyranova
Abstract
Abstract Bayesian Machine Learning (BML) and strong lensing time delay (SLTD) techniques are used in order to tackle the $$H_{0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> tension in f ( T ) gravity. The power of BML relies on employing a model-based generative process which already plays an important role in different domains of cosmology and astrophysics, being the present work a further proof of this. Three viable f ( T ) models are considered: a power law, an exponential, and a squared exponential model. The learned constraints and respective results indicate that the exponential model, $$f(T)=\alpha T_{0}\left( 1-e^{-p T / T_{0}}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>α</mml:mi> <mml:msub> <mml:mi>T</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mfenced> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mi>p</mml:mi> <mml:mi>T</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>T</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:msup> </mml:mfenced> </mml:mrow> </mml:math> , has the capability to solve the $$H_{0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> tension quite efficiently. The forecasting power and robustness of the method are shown by considering different redshift ranges and parameters for the lenses and sources involved. The lesson learned is that these values can strongly affect our understanding of the $$H_{0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> tension, as it does happen in the case of the model considered. The resulting constraints of the learning method are eventually validated by using the observational Hubble data (OHD).