Exploring cosmological constraints on galaxy formation time

TL;DR

The paper tackles how to constrain the galaxy formation time $t_f(z)$ in a largely model-independent way by applying two non-parametric reconstructions—Gaussian Processes and High-performance Symbolic Regression—to age data of 32 old passive galaxies and the Pantheon+ SN sample. It explores two pathways: (i) in a $\Lambda$CDM framework with two $H_0$ values (Planck and SH0ES) to obtain $t_f = t_u - t_g$, and (ii) a cosmology-free lookback-time reconstruction from SN distances to infer $t_f$; both methods yield consistent redshift trends. The results reveal that $t_f$ is not constant, with medians around $0.72$–$1.26$ Gyr depending on the $H_0$ prior and consistent cross-methods, and show larger $t_f$ at higher $z$ and noticeable variation at $z \lesssim 0.5$. The study also highlights that the well-known $H_0$ tension propagates into cosmological estimates of $t_f(z)$, underscoring the need for independent, non-parametric probes of galaxy formation timing and its cosmological implications.

Abstract

The Universe consists of a variety of objects that formed at different epochs, leading to variations in the formation time which represents the time elapsed from the onset of structure formation until the formation time of a particular object. In this work, we present two approaches to reconstruct and constrain the galaxy formation time $t_f(z)$ using non-parametric reconstruction methods, such as Gaussian Processes (GP) and High-performance Symbolic Regression (SR). Our analysis uses age estimates of 32 old passive galaxies and the Pantheon+ type Ia supernova sample, and considers two different values of the Hubble constant $H_0$ from the SH0ES and Planck Collaborations. When adopting the $Λ$CDM model and the GP reconstructions, we find $\left<t_f\right>=0.72_{-0.16}^{+0.14}$ Gyr (SH0ES) and $\left<t_f\right>=1.26_{-0.11}^{+0.10}$ Gyr (Planck). Without considering a specific cosmological model, we obtain $\left<t_f\right>=0.71 \pm {0.19}$ Gyr (SH0ES) and $\left<t_f\right> = 1.35_{-0.23}^{+0.21}$ Gyr (Planck). Similar values are obtained from the SR reconstructions, with both methods (GP and SR) indicating the same behavior regarding the time evolution of $t_f(z)$. The results also show significant differences in the formation time from SH0ES and Planck values, highlighting the impact of the $H_0$ tension on the cosmological estimates of $t_f(z)$. In particular, the different approaches used in the analysis agree with each other, demonstrating the robustness and consistency of our results. Overall, this study suggests that galaxies have different evolutionary timescales and that $t_f$ is not constant, with noticeable variations at lower redshifts ($z \lesssim 0.5$).

Figures (4)

• Figure 1: GP and SR reconstructions of the age-redshift relation from age estimates of 32 old passive galaxies (black points) simon2005constraints. The contours show the reconstruction at $1\sigma$ level while the solid black line represents the mean of the reconstructions.
• Figure 2: Left: The age-redshift relation assuming a flat, $\Lambda$CDM model and the values of $H_0$ and $\Omega_m$ provided by the SH0ES collaboration. Middle: The same as in the previous Panel for the values of $H_0$ and $\Omega_m$ provided by the Plank collaboration. In both panels, the dark blue region corresponds to the reconstructed age-redshift relation shown in Fig. \ref{['fig:agegapp']}. Right: Evolution of the galaxy formation time $t_f(z)$ with redshift obtained from the difference between $t_u$ and $t_g$ -- Eq. \ref{['tf']}. The red and blue regions represent the reconstructed $1\sigma$ intervals.
• Figure 3: Same as Fig. \ref{['fig:30']}, but using PySR to reconstruct galaxy ages.
• Figure 4: Left: GP reconstruction of the luminosity distance as a function of redshift using the SH0ES and Planck values discussed in the text. Middle: The lookback-time redshift relation reconstructed from $d_L(z)$ curves, as expressed by Eq. \ref{['eq:lookbacktime']}. Right: Evolution of the galaxy formation time $t_f(z)$ with redshift obtained from Eq. \ref{['principal']}. In all panels, the blue and red regions represent the reconstructed $1\sigma$ intervals assuming SH0ES and Planck parameter values, respectively.