Revisiting statefinder via Gaussian process

Abstract The statefinder diagnostic is useful to discriminate dark energy models. In this paper, under the minimum assumption of a spatially flat Friedmann–Lemaître–Robertson–Walker Universe, we reconstruct the statefinder pair $$\{r(z),s(z)\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>{</mml:mo> <mml:mi>r</mml:mi> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> <mml:mo>,</mml:mo> <mml:mi>s</mml:mi> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> <mml:mo>}</mml:mo> </mml:mrow> </mml:math> in addition to the deceleration parameter q ( z ) via the Gaussian process from the cosmic observational data points which include the recently released Pantheon+ SN Ia samples and the observational Hubble data H ( z ). The reconstructed evolution trajectories are shown on the $$r-q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>-</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> </mml:math> , $$r-s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>-</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:math> planes. The reconstructed q ( z ) is consistent with previous studies. Meanwhile, a novel quantity named suitability is introduced on the $$r-q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>-</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> </mml:math> , $$r-s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>-</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:math> planes to assess the validation of a dark energy model.