This document summarizes cosmological parameters measured from galaxy surveys. It discusses: 1) Direct measurements of the Hubble constant from the Hubble Space Telescope and Planck, finding values of 72-74 km/s/Mpc and 67.3 km/s/Mpc respectively. 2) Supernova surveys finding evidence for an accelerating universe with matter density of ~30% and dark energy density of ~70%. 3) Measurements of cosmic microwave background from COBE, WMAP and Planck, determining ages and densities of the universe. 4) Galaxy clustering surveys like SDSS detecting baryon acoustic oscillations to measure dark energy properties.

1. COSMOLOGICAL PARAMETERS :
GALAXY SURVEY
SUBHASIS SHIT
15PH40040
INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR

2. INTRODUCTION
 The term ‘cosmological parameters’ is forever increasing in its scope, and nowadays often
includes the parameterization of some functions, as well as simple number describing properties
of the Universe.
 The original usage referred to the parameters describing the global dynamics of the Universe,
such as its expansion rate and curvature. Also now of great interest is how the matter budget of
the Universe is built up from its constituents: baryons, photons, neutrinos, dark matter, and dark
energy.
 There may also be parameters describing the physical state of the Universe, such as the
ionization fraction as a function of time during the era since recombination.

3. 1. Direct measures of the Hubble Constant:
 The slope of the relation between the distance and recession velocity is
defined to be the Hubble constant H0.
 The Hubble Space Telescope project found by using the empirical period-
luminosity relations for Cepheid variable stars to obtain distances to 31
galaxies, and calibrated a number of secondary distance indicators—Type
Ia Supernovae (SNe Ia), the Tully–Fisher relation, surface-brightness
fluctuations, and Type II Supernovae—measured over distances of 400 to
600 Mpc. They estimated H0 = 72 ± 3 (statistical) ± 7 (systematic)
kms−1Mpc−1.
 A recent study of over 600 Cepheids in the host galaxies of eight recent
SNe Ia, observed with an improved camera on board the Hubble Space
Telescope, was used to calibrate the magnitude–redshift relation for 240
SNe Ia. This yielded an even more precise figure, H0 = 73.8 ± 2.4
kms−1Mpc−1 (including both statistical and systematic errors).
 The indirect determination of H0 by the Planck Collaboration found a lower
value, H0 = 67.3 ± 1.2 kms−1Mpc−1.

4. 2. Supernovae as cosmological probe:
 Two major studies, the Supernova Cosmology Project and the High-z Supernova Search
Team, found evidence for an accelerating Universe, interpreted as due to a cosmological
constant or a dark energy component.
 Combined with the CMB data (which indicates flatness, i.e., Wm + WL = 1), the best-fit
values were Wm ≈ 0.3 and WL ≈ 0.7.
 Taking w = −1, the SNLS3 team found, by combining their SNIa data with baryon acoustic
oscillation (BAO) and WMAP7 data, Wm = 0.279+0.019
−0.015 and WL = 0.724+0.017
−0.016,
including both statistical and systematic errors.

5. 3. Cosmic Microwave Background:
 The CMB is the electromagnetic radiation left over from the time of recombination in Big-Bang
cosmology.
 It is the oldest light of the Universe.
 This CMB was discovered by Penzias and Wilson in 1964 accidentally.

6.  Black body curve of the CMB.
 The DMR was able to detect the anisotropy of cosmic
background radiation, but the fluctuations are extremely faint.
 The DIRBE instrument was able to conduct studies on
interplanetary dust (IPD) and determine if its origin was from
asteroid or cometary particles.
 The second contribution DIRBE made was a model of the
Galactic disk as seen edge-on from our position.
COBE: FIRAS-DMR-DIRBE

7.  The age of the Universe: 13.772±0.059 billion-year.
 Hubble constant:69.32 ± 0.80 km s-1 Mpc-1
 Baryon density (Wb): 0.04628±0.00093
 Cold dark matter density (Wc): 0.2402+0.0088
−0.0087
 Dark energy density (WL):0.7135+0.0095
-0.0096
 The curvature of space is less than 0.4 percent of "flat" and
the universe emerged from the cosmic Dark Ages "about
400 million years" after the Big Bang.
WMAP:

8.  The Universe is 13.798±0.037 billion
years old.
 It is currently theorised that these
ripples gave rise to the present vast
cosmic web of galactic clusters and
dark matter.
 It contains 4.82 ± 0.05% ordinary
matter, 25.8 ± 0.4% dark matter and
69 ± 1% dark energy.
 The Hubble constant was also
measured to be 67.80±0.77
(km/s)/Mpc.
PLANCK (Spacecraft):

9. Cosmic Microwave Background comparison

10. 4. Galaxy Clustering:
 BAO: In cosmology, baryon acoustic oscillations (BAO) are regular, periodic
fluctuations in the density of the visible baryonic matter (normal matter) of the
universe. The power spectra of the 2-degree Field (2dF) Galaxy Redshift Survey and
the Sloan Digital Sky Survey (SDSS) both surveys showed evidence for BAOs. The
Baryon Oscillation Spectroscopic Survey (BOSS) of Luminous Red Galaxies (LRGs) in
the SDSS found consistency with the dark energy equation of state w = −1 ± 0.06.
 Redshift Survey: In astronomy, a redshift survey is a survey of a section of the sky
to measure the redshift of astronomical objects: usually galaxies, but sometimes
other objects such as galaxy clusters or quasars. These observations are used to
measure properties of the large-scale structure of the universe. The Great Wall, a
vast supercluster of galaxies over 500 million light-years wide, provides a dramatic
example of a large-scale structure that redshift surveys can detect.

11. 5. Cluster of Galaxies:
 A cluster of galaxies is a large collection of galaxies held together by their mutual gravitational
attraction.
 Clusters are an ideal application in the present Universe. They are usually used to constrain the
fluctuation amplitude σ8.
 A theoretical prediction for the mass function of clusters can come either from semi-analytic
arguments or from numerical simulations. The same approach can be adopted at high redshift
(which for clusters means redshifts of order one) to attempt to measure σ8 at an earlier epoch.
The evolution of σ8 is primarily driven by the value of the matter density Wm, with a sub-
dominant dependence on the dark energy properties.
 The Planck observations were used to produce a sample of 189 clusters selected by the SZ
effect. For an assumed flat LCDM model, the Planck Collaboration found σ8 = 0.77±0.02 and -
Wm = 0.29±0.02.

12. Bringing all the observations together:
 The CMB data gives the age of the universe is 13.798 ± 0.037 billion years old which is in good
agreement with the ages of the globular cluster and radioactive dating.
 Inclusion of BAO data, plus the assumption that the dark energy is a cosmological constant, with
the CMB data yields a constraint on Wtot = Wi + WL =1.0005±0.0033.
 From the CMB and BAO data the cosmological constant w = −1.13+0.13
−0.11 .
 The data provide strong support for the main predictions of the simplest inflation models: spatial
flatness and adiabatic, Gaussian, nearly scale-invariant density perturbations. But it is
disappointing that there is no sign of primordial gravitational waves.

13. Outlook For the Future:
In the future developments we can expect the one of two directions. Either the existing
parameter set will continue to prove sufficient to explain the data, with the parameters subject
to ever-tightening constraints, or it will become necessary to deploy new parameters.
There are many possibilities on offer for striking discoveries,
 Detection of primordial non-Gaussianities would indicate that non-linear processes influence
the perturbation generation mechanism,
 Detection of variation in the dark-energy density (i.e., w ≠ −1) would provide much-needed
experimental input into the nature of the properties of the dark energy.
There are many proposals for the nature of the dark matter, but no consensus as to which is
correct. The nature of the dark energy remains a mystery. Even the baryon density, now
measured to an accuracy of a percent, lacks an underlying theory able to predict it within orders
of magnitude.

14. THANK YOU