Joint constraints on $$R_h=ct$$ cosmology from DESI DR2 BAO, CC, and SNIa Pantheon$$^+$$ sample

Abstract We carry out a comparative analysis of the standard $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM cosmological model and the alternative $$R_h=ct$$ <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> framework using recent observational data from cosmic chronometers (CC), Type Ia supernova, and baryon acoustic oscillations. The study evaluates the ability of each model to reproduce the observed expansion history of the Universe through a joint statistical assessment based on $$\chi ^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>χ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> statistics, Akaike Information Criterion ( AIC ), Bayesian Information Criterion ( BIC ), and Bayes factor. While both models yield acceptable fits, $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM consistently attains lower information-criterion values and higher likelihood, indicating a superior overall performance. An examination of the redshift evolution of the Hubble parameter H ( z ) and the deceleration parameter q ( z ) shows that $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM naturally captures the transition from early-time deceleration to late-time acceleration, whereas $$R_h=ct$$ <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> predicts a strictly linear expansion. We also estimate the age of the Universe within both models, obtaining $$t_0^{\Lambda CDM}= 13.676_{-0.81}^{+0.92}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>t</mml:mi> <mml:mn>0</mml:mn> <mml:mrow> <mml:mi>Λ</mml:mi> <mml:mi>C</mml:mi> <mml:mi>D</mml:mi> <mml:mi>M</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>13</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>676</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.81</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.92</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> Gyr and $$t_0^{R_h=ct}= 16.035_{-0.98}^{+1.09}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>t</mml:mi> <mml:mn>0</mml:mn> <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:msubsup> <mml:mo>=</mml:mo> <mml:mn>16</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>035</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.98</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.09</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> Gyr. The posterior-derived age in the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM framework is broadly consistent with the Planck 2018 CMB result. This agreement is interpreted as a validation of the analysis pipeline and the reliability of the DESI DR2, CC, and supernova constraints, rather than as a new result for $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM, and serves as a benchmark for assessing the viability of 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>