Model-independent Reconstruction of Low-redshift Dark Energy Dynamics

Abstract We reconstruct the late-time expansion history of the Universe in a fully model-independent manner. By combining observations from cosmic chronometers (CCs), the Dark Energy Spectroscopic Instrument (DESI) baryon acoustic oscillation (BAO) Data Release 2, and the Dark Energy Survey 5 yr Type Ia supernova sample (DESY5), we jointly infer the dimensionless Hubble parameter E ( z ), its first derivative <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> , and their full covariance structure. By integrating the reconstructed inverse Hubble function constrained by CC data and calibrating it against DESI measurements of D M / r d , we obtain a model-independent estimate of the sound horizon, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>d</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>146.5</mml:mn> <mml:msubsup> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.55</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.65</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:mi>Mpc</mml:mi> </mml:math> at the 68% confidence level, in agreement with the Planck determination. This calibration enables a coherent comparison across different data combinations. DESI BAO data alone suggest a mildly quintessence-like behavior but exhibit instabilities in higher-order derivatives, whereas the inclusion of DESY5 significantly improves the smoothness and stability of the reconstruction. The combined data set yields an expansion history that remains compatible with ΛCDM within the reconstructed 1 σ uncertainties over the redshift range 0 ≲ z ≲ 1.2, with no statistically significant evidence for phantom crossing or evolving dark energy in our ANN-based reconstruction. Our nonparametric, covariance-aware methodology demonstrates the potential of reconstructions to probe dark energy properties in current and future cosmological surveys.