Easing the Hubble Tension in <i>f</i>(<i>R</i>,<i>L</i>_m) Gravity: A Bayesian MCMC Analysis with CC and Pantheon Plus & SH0ES Datasets

In this study, we explored the cosmological implications of the modified gravity framework <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi>L</mi><mi>m</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula>, taking the specific form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi>L</mi><mi>m</mi></msub><mo>)</mo></mrow><mo>=</mo><mstyle scriptlevel="0" displaystyle="false"><mfrac><mi>R</mi><mn>2</mn></mfrac></mstyle><mo>+</mo><msubsup><mi>L</mi><mi>m</mi><mi>n</mi></msubsup><mo>,</mo></mrow></semantics></math></inline-formula> where <i>n</i> denotes the model parameter. The analysis was carried out within a spatially flat FLRW background by adopting the Barboza–Alcaniz (BA) parametrization for the dark energy equation of state, expressed as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ω</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>w</mi><mn>0</mn></msub><mo>+</mo><msub><mi>w</mi><mn>1</mn></msub><mstyle scriptlevel="0" displaystyle="false"><mfrac><mrow><mi>z</mi><mo>(</mo><mn>1</mn><mo>+</mo><mi>z</mi><mo>)</mo></mrow><mrow><mn>1</mn><mo>+</mo><msup><mi>z</mi><mn>2</mn></msup></mrow></mfrac></mstyle><mo>.</mo></mrow></semantics></math></inline-formula> Based on this setup, an expression for the Hubble parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>(</mo><mi>z</mi><mo>)</mo></mrow></semantics></math></inline-formula> was derived. The parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>H</mi><mn>0</mn></msub><mo>,</mo><mi>n</mi><mo>,</mo><msub><mi>w</mi><mn>0</mn></msub><mo>,</mo><msub><mi>w</mi><mn>1</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula> were estimated using a Bayesian Markov Chain Monte Carlo (MCMC) technique, implemented via the <i>emcee</i> package, with Cosmic Chronometers (CC), Pantheon Plus & SH0ES (PPS) and DESI BAO datasets. For the CC+PPS+DESI BAO combination, the best-fit Hubble constant was obtained as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mn>0</mn></msub><mo>=</mo><msubsup><mn>72.08</mn><mrow><mo>−</mo><mn>0.24</mn></mrow><mrow><mo>+</mo><mn>0.30</mn></mrow></msubsup><mspace width="0.166667em"></mspace><mi>km</mi><mspace width="0.166667em"></mspace><msup><mi mathvariant="normal">s</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mspace width="0.166667em"></mspace><msup><mi>Mpc</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>,</mo></mrow></semantics></math></inline-formula> which shows better consistency with the local SH0ES measurement than with the Planck <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM result, thereby reducing the Hubble tension. Furthermore, the dynamical evolution of the equation of state parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>, the deceleration parameter, the impact of various energy conditions, and the optimal model parameters were thoroughly examined. The study also investigated the behavior of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>O</mi><mi>m</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> diagnostic and determined the present age of the universe predicted by this model.