### 7. The 2dF Galaxy Redshift Survey (2dFGRS)

To actually measure the two-point correlation function $\xi(r)$ and identify the Baryon Acoustic Oscillation (BAO) scale, cosmologists require massive, three-dimensional maps of the universe. One of the pioneering efforts to build such a map was the Two-degree-Field Galaxy Redshift Survey (2dFGRS).

Conducted between 1997 and 2002 by the Anglo-Australian Observatory (AAO), the 2dFGRS was a watershed moment in observational cosmology. Alongside the Sloan Digital Sky Survey (SDSS), it ushered in the era of precision cosmology by mapping the local universe on an unprecedented scale.

#### 7.1 The Instrument and Methodology Prior to the late 1990s, measuring the redshift of a galaxy (to determine its distance) was a painstaking, one-at-a-time process. The 2dFGRS utilized a revolutionary multi-object spectrograph mounted on the 3.9-meter Anglo-Australian Telescope.

The instrument possessed a 2-degree field of view on the sky (roughly four times the diameter of the full moon) and utilized a robotic arm to position 400 optical fibers onto the focal plane. Each fiber was aligned with a pre-selected target galaxy. This allowed astronomers to capture the spectra—and thus the redshifts—of 400 galaxies simultaneously in a single observation.

#### 7.2 Survey Scope and Geometry The survey ultimately obtained reliable redshifts for 221,414 galaxies. To avoid the obscuring dust and stars of our own Milky Way galaxy, the survey targeted two primary regions: * An equatorial strip near the North Galactic Pole. * A contiguous strip near the South Galactic Pole.

The survey probed galaxies out to a redshift of $z \approx 0.3$, with a median redshift of $z \approx 0.11$. This provided a comprehensive snapshot of the large-scale structure of the relatively local, modern universe.

#### 7.3 Cosmological Significance and Key Results The 2dFGRS provided the astrophysics community with several foundational results that cemented the standard $\Lambda$CDM (Cold Dark Matter with a Cosmological Constant) model:

1. Mapping the Cosmic Web: The 2dF slice maps provided stunning visual confirmation of the “cosmic web.” Galaxies were not distributed uniformly, nor were they clumped randomly; they formed a vast network of dense nodes (superclusters), long connecting filaments, and vast, empty voids. 2. Matter Density: By analyzing the way galaxies clustered and incorporating redshift-space distortions (the apparent squashing of galaxy clusters due to their peculiar velocities), the 2dF team precisely constrained the total matter density parameter of the universe, $\Omega_m$, finding it to be roughly 30% of the critical density. 3. Upper Limit on Neutrino Mass: The survey placed some of the first stringent cosmological limits on the total mass of neutrino species, as massive neutrinos would “free-stream” in the early universe and wash out the formation of structure on small scales.

#### 7.4 2dFGRS and Baryon Acoustic Oscillations Crucially for this lecture, the 2dFGRS was one of the first two surveys to definitively detect the BAO signal.

In 2005, two independent papers were published nearly simultaneously: one analyzing data from SDSS (Eisenstein et al.), and one analyzing the power spectrum $P(k)$ of the 2dFGRS data (Cole et al.). The 2dFGRS team measured the power spectrum of their hundreds of thousands of galaxies and identified the subtle, wiggles in $P(k)$ that correspond to the Fourier-space equivalent of the BAO peak in the correlation function.

This detection proved that the sound waves generated in the primordial plasma (seen in the Cosmic Microwave Background at $z \approx 1100$) had successfully translated into the physical clustering of galaxies billions of years later at $z \approx 0.11$.