Anchoring the Universe with Characteristic Redshifts using Raychaudhuri Equation Informed Reconstruction Algorithm (REIRA)

TL;DR

We address whether late-time cosmic acceleration requires physics beyond the Planck \,\\Lambda$CDM baseline. The authors develop a model-independent distance reconstruction augmented by a physics-informed prior based on the Raychaudhuri equation (REIRA) to sharpen estimates of $H(z)$ and dark-energy parameters. They identify seven characteristic redshifts that remain robust across DE parameterizations and reconstruction methods, with a minimal Alcock–Paczyński correction at these points, and observe notable low-redshift deviations from Planck \$\\Lambda$CDM at $z_1$–$z_3$. REIRA improves reconstruction precision and tightens DE-parameter constraints, demonstrating a powerful combination of geometric reconstruction and kinematic physics for probing late-time cosmology, with implications for detecting new physics in the DE sector.

Abstract

We study the robustness and physical implications of a set of characteristic redshifts that capture key features of the late-time Universe. Using both model-independent reconstructions as well as different dark energy (DE) parameterizations, we show that these redshifts remain stable across cosmological models and reconstruction algorithm, making them reliable geometric anchors of the expansion history. Moreover, the Alcock-Paczyński corrections at these redshift anchors are found to be unity with high statistical significance, making them natural isotropy points in the comoving distance-redshift relation. We also find that certain redshifts anchors $(z < 1)$ coincide with epochs where strong deviations from the Planck $Λ$CDM baseline are apparent irrespective of DE parametrisation like CPL or reconstruction algorithm, indicating their potential as probes of new physics in cosmological evolution. Finally, we demonstrate, for the first time, that a Raychaudhuri Equation Informed Reconstruction Algorithm, substantially enhances the precision of the inferred distance measures and the Hubble expansion rate as well as results tighter constraints in the DE parameter space. These results demonstrate that combining geometric reconstruction with physics-informed kinematic information offers a powerful and consistent algorithm to probe new physics in the late-time dynamics of our Universe.

Figures (5)

• Figure 1: Characteristic redshifts and their uncertainty for RA and different DE parameterizations.
• Figure 2: $D_M^\prime/D_M$ and its uncertainty at Characteristic redshifts for RA and different DE parameterizations.
• Figure 3: Deviation of the reconstructed Hubble parameter from the $\Lambda$CDM baseline ($\Delta H$) with 1$\sigma$ error-bars at the characteristic redshifts for RA and REIRA with a comparison to CPL shown in \ref{['fig4:sub1']} and \ref{['fig4:sub2']} respectively. The shaded region denotes consistency with the $\Lambda$CDM baseline.
• Figure 4: Comparison of the uncertainty in characteristic redshifts obtained using RA (blue) and REIRA (red).
• Figure 5: Heatmap comparison of the statistical tensions in $D_A$ and $E$ with respect to the $\Lambda$CDM baseline, is shown for three cases: RA, REIRA, and the CPL model in \ref{['fig5:sub1']}. Blue shades denote lower tension, while red shades denote higher tension; lighter and deeper tones within each color represent finer gradations. Evolution of the DE pressure $p_{\rm DE}(z)$ obtained using RA (blue) and REIRA (red), compared to the $\Lambda$CDM baseline (green) is shown in \ref{['fig5:sub2']}. Constraints in the $w_0$–$w_a$ parameter space for the CPL model, obtained from compressed likelihoods based on RA (blue) and REIRA (red) are shown in \ref{['fig5:sub3']}. Deeper and lighter shades in \ref{['fig5:sub2']} and \ref{['fig5:sub3']} correspond to $1\sigma$ and $2\sigma$ confidence levels respectively.