New $H(z)$ measurement at Redshift = 0.12 with DESI Data Release 1

1. Problem Statement

The paper addresses the Hubble Tension, a significant discrepancy between the value of the Hubble constant ($H_0$) derived from early-universe observations (Cosmic Microwave Background, $\Lambda$CDM model) and late-universe measurements (Type Ia Supernovae). To resolve whether this tension stems from systematic errors or new physics, independent probes of the expansion history of the universe are required.

Specifically, the authors aim to measure the Hubble parameter $H(z)$ at low redshift ($z \approx 0.12$) using the Cosmic Chronometers (CC) method. This method relies on measuring the differential age of passively evolving galaxies ($dt/dz$) to calculate $H(z) = -\frac{1}{1+z} \frac{dz}{dt}$ without relying on a specific cosmological model (unlike BAO methods which require sound horizon calibration). The challenge lies in selecting a robust sample of "cosmic clocks" (massive, quiescent galaxies) and accurately determining their ages using modern spectroscopic data.

2. Methodology

Data Source

• DESI DR1: The study utilizes the first major public data release from the Dark Energy Spectroscopic Instrument (DESI), covering observations from May 2021 to June 2022.
• Legacy Surveys: Photometric data from the DESI Legacy Imaging Surveys (g, r, z, W1-W4 bands) are used for target selection and spectral energy distribution (SED) fitting.
• Catalogs: The authors use the Stellar Mass and Emission Line Catalog (based on CIGALE and STARLIGHT) and retrieve spectra from SPARCL and Astro Data Lab.

Sample Selection

A rigorous selection process was applied to isolate massive, passively evolving galaxies suitable for CC analysis:

1. Morphology: Selection of early-type galaxies (MORPHTYPE == DEV).
2. Mass and Activity: Stellar mass $\log_{10}(M_*/M_\odot) > 11$ and specific star formation rate $\log_{10}(\text{sSFR}) < -11$.
3. Emission Line Cuts: Equivalent width (EW) of [O II], [H$\beta$], [H$\alpha$] $< 4$ Å and S/N $< 3$ to ensure quiescence.
4. Spectral Indices: Ratio of Ca II H/K absorption lines $< 1.3$.
5. Redshift and Quality: $z < 0.2$ and FLUX_SCALE $> 3$ to ensure high signal-to-noise ratios.

• Final Sample: 3,429 galaxies after applying strict mass and velocity dispersion ($\sigma_{vel} > 100$ km/s) thresholds.

Spectral Fitting (BAGPIPES)

The authors employed a modified version of BAGPIPES (Bayesian Analysis of Galaxies for Physical Inference and Parameter EStimation) to perform full-spectrum fitting on both spectra and photometry.

• Cosmological Independence: The cosmological prior in BAGPIPES was removed to ensure the age derivation is model-independent.
• Star Formation History (SFH): Two SFH models were tested:
  1. Delayed Exponentially Declining (DED): $SFR(t) \propto (t-T_0)e^{-(t-T_0)/\tau}$.
  2. Double Power-Law (DPL): $SFR(t) \propto [(t/\tau)^\alpha + (t/\tau)^{-\beta}]^{-1}$.
• Physical Components: The model included stellar population synthesis (BC03 with Kroupa IMF), dust attenuation (Calzetti law), nebular emission (CLOUDY), and a Gaussian Process (GP) noise model to account for correlated noise in the spectra.
• Age Definition: For DED, age is defined as $t_U(z_{obs}) - T_0$. For DPL, the mass-weighted age is used.

$H(z)$ Calculation

1. Binning: The sample was divided into redshift and stellar mass bins (split at median mass $\log_{10}(M_*) = 11.16$).
2. Derivative Estimation: The age-redshift relation ($t(z)$) was constructed. To minimize covariance, a non-adjacent differencing approach was used to calculate $dz/dt$.
3. Systematics: Systematic uncertainties were assessed by varying binning strategies (fixed vs. quantile, 2 vs. 4 bins) and SFH models.

3. Key Contributions

• First DESI DR1 CC Measurement: This is one of the first studies to utilize the massive DESI DR1 dataset to derive a cosmic chronometer measurement, significantly increasing the sample size compared to previous works.
• Full-Spectrum Fitting: The application of BAGPIPES with a removed cosmological prior provides a robust, model-independent derivation of stellar ages and star-formation histories.
• Systematic Error Quantification: The paper explicitly quantifies systematic errors arising from binning strategies ($\Delta H_{bin} \approx \pm 1.71$ km/s/Mpc) and SFH model choices ($\Delta H_{SFH} \approx \pm 1.67$ km/s/Mpc).
• Validation of "Mass-Downsizing": The results confirm that at fixed redshift, more massive galaxies are older, consistent with the mass-downsizing scenario.

4. Results

• Sample Properties: The selected 3,429 galaxies have high stellar masses ($\log_{10}(M_*/M_\odot) \approx 11.16$), low dust attenuation ($A_V \approx 0.1$ mag), and super-solar metallicities ($Z/Z_\odot \approx 1.33$).
• Age-Redshift Relation: The derived stellar ages show a clear declining trend with increasing redshift, consistent with the $\Lambda$CDM model prediction.
• Primary Measurement:
  $$H(z = 0.12) = 71.33 \pm 3.45 \text{ (stat.)} \pm 1.71 \text{ (bin)} \pm 1.67 \text{ (SFH)} \text{ km s}^{-1} \text{ Mpc}^{-1}$$
  Combining errors in quadrature yields the final result:
  $$H(z = 0.12) = 71.33 \pm 4.20 \text{ km s}^{-1} \text{ Mpc}^{-1}$$
• Consistency: This value is consistent with other cosmic chronometer measurements and the $\Lambda$CDM prediction from Planck 2018, falling within the error bars of current literature.

5. Significance

This work demonstrates the power of the DESI survey in refining the cosmic expansion history. By providing a precise, model-independent measurement of $H(z)$ at low redshift, it contributes to the ongoing effort to resolve the Hubble Tension. The methodology establishes a robust framework for using full-spectrum fitting on large spectroscopic surveys to calibrate cosmic chronometers. The result supports the standard $\Lambda$CDM model at low redshift but highlights the need for continued precision measurements at higher redshifts ($z > 1$) with future surveys like Euclid and the Wide-field Spectroscopic Telescope to fully map the expansion history and constrain dark energy properties.