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New on the tutorial:

- A discussion of the history of the CMB dipole discovery.
- A history of COBE, the COsmic Background Explorer, in pictures.
- A cool rollover page that blinks between a color image constructed from 3 WMAP bands and the WMAP ILC reduced galaxy map
- A calculator that takes light travel time and computes the redshift. There is also an advanced version of my Cosmology Calculator.

Cosmology is the study of the origin, current state, and future of our Universe. This field has been revolutionized by many discoveries made during the past century. My cosmology tutorial is an attempt to summarize these discoveries. It will be "under construction" for the foreseeable future as new discoveries are made. I will attempt to keep these pages up-to-date as a resource for the cosmology courses I teach at UCLA. The tutorial is completely non-commercial, but tax deductible donations to UCLA are always welcome.

Astronomy and cosmology are very much mathematical sciences, but I have attempted to avoid higher math in these pages. I do use high school algebra and geometry - courses required for admission to UCLA - but I have also included some animations [1, 2, 3, 4, 5, 6, 7], some Java applets [1, 2], and many illustrations in the tutorials, the ABC's of Distances, and the answers to some of the Frequently Asked Questions.

In addition to the cosmology tutorial, there is also a relativity tutorial and extensive discussions on the age, density and size of the Universe. There is also a bibliography of books at a range of levels, and a Javascript calculator of the many distances involved in cosmology.

Slides for recent talks:

- Slides
for the
105
^{th}Faculty Research Lecture at UCLA, 28 Oct 2008. - Colloquium at the Geneva Observatory, 10 Nov 2006.
- Public talk at the 20 Oct 2006 meeting of the Ventura County Astronomical Society
- 27 Sep 2006 colloquium at the Arizona State University School of Earth and Space Exploration.
- 24 Sep 2006 Talk at the Mt. Wilson Observatory Association
- Invited talk at Einstein's Legacy: Relativistic Astrophysics and Cosmology, 7-11 Nov 2005.
- Presentation at the International Symposium on Particle Physics, Astrophysics and Cosmology
- Lectures at the International Summer Institute on Particle physics, Astrophysics and Cosmology, Hangzhou China, 2005 August 15, 16, 18.
- "Fact and Fiction in Cosmology", a public lecture at the Cal State Northridge planetarium.
- 13 March 2005 AFHU Einstein Symposium Talk
- 3 March 2005 Director's Distinguished Lecture at LLNL
- 27 May 2004 Ohio State Colloquium
- 11 Oct 2003 UCLA Extension Course
- September, 2003 NATO ASI in Cargese lectures (1, 2, 3)
- lectures at the July, 2003 winter school in Argentina
- "Are We Likely to Be Alone" at the 4 April 2003 CSEOL Symposium
- Astrophysics Fact Sheet

The course notes (131 pages, 403 equations, 51 figures) for the upper division undergraduate Stellar Systems and Cosmology course, Astronomy 140, that I last taught in spring 2008 are available on the Web. And for a much more technical discussion of cosmology see my graduate course Astro 275 lecture notes (141 pages, 441 equations, 48 figures). This course was last taught in the spring of 2015.

06 Sep 2018 -
Birrer *et al.* report the
time delay distance to the double
imaged quasar SDSS 1206+4332 which also has an Einstein ring image of
its host galaxy. They report H_{o} 68.8 ± 5.25
km/sec/Mpc for this object, and a weighted mean of the 4 objects
studied by the H0LiCOW collaboration of 72.5 ± 2.2 km/sec/Mpc.

01 Mar 2018 -
Bowman *et al.* (2018, Nature, 555, 67-70)
[$]
claim the detection of an absorption dip centered at 78 MHz
with a width of 19 MHz and a depth of 0.5 K due to 21 cm absorption
by neutral hydrogen at
redshifts from 15 to 20.
This is much deeper than expected for standard physics so
Fialkov *et al.*
[arxiv:1802.10577] have proposed dark matter scattering from baryons
which has led to a lot of press interest.
But the foreground fitting process is quite correlated with the fitted signal
so the devil is in these details. The foreground at 78 MHz is 3000 times
higher than the claimed signal.

06 Dec 2017 - Banados et al in Nature describe a new quasar at z=7.54. This was found using IR survey data as an IR source that was very faint optically due to absorption by neutral hydrogen at 122 nm, redshifted to a wavelength of about 1036 nm. Its designation in the AllWISE catalog is WISEA J134208.05+092837.8.

03 Dec 2017 - The WMAP science team won the 2018 Breakthrough Prize in Fundamental Physics. Chuck, David, Gary, Lyman and Norm looked good in tuxes.

04 Aug 2017 - The first cosmological results of the
DES have been
released. The
basic results paper gives limits on parameters for
ΛCDM
and wCDM models with variable equation
of state, w.
The headline results combine the
lensing and galaxy clustering
data from the DES with CMB data from Planck,
BAO data,
, and
supernova data. The combined data give
Ω_{m} = 0.299(8), Ω_{b} = 0.0479(14),
H_{o} = 68.3 ± 1 km/sec/Mpc, and w = -1.00 ± 0.05.
This is consistent with ΛCDM. The ratio of CDM to baryons
is 5.24 ± 0.21.
A flat Universe is assumed.

21 Oct 2016 -
Nielsen, Guffanti & Sarkar have claimed that an improved treatment
of statistics leads to a reduction of the statistical significance of
the supernova evidence for an accelerating Universe, from 4 sigma
using the standard analysis to 3 sigma in their new analysis. In their
Figure 2, the non-accelerating Universe line touches the 3 sigma contour.
In the standard analysis a similar Figure (3rd figure on my
Supernova Cosmology page) shows the
4 sigma contour hitting the non-accelerating Universe line. This is
not a big deal in any case, but more importantly the new statistical
analysis is wrong. It assumes that the intrinsic luminosities of the
supernovae *in the observed sample* are not correlated with their
redshifts, and this assumption is easily shown to be false. The high
redshift part of the JLA sample is on average brighter than the low
redshift part, because distant low luminosity objects are harder to find,
an effect long known to astronomers as the
Malmquist bias.

07 Jul 2016 - The H0LiCOW project has
announced a new determination of the
Hubble constant
from the time delays
seen in strongly lensed quasars. They
find H_{0} = 71.9+2.4-3.0 km/sec/Mpc based on three systems.

25 Feb 2016 - Keane *etal.*
identified the host galaxy of a Fast Radio Burst, and obtained a redshift of
0.492 ± 0.008. This plus the dispersion measure gives a density
for the intergalactic medium of Ω = 0.049 ± 0.013, consistent with
ΛCDM expectation of 0.041.

15 Feb 2016 -
Connaughton *et al.* report a 1 second burst of
gamma-rays occuring 0.4 seconds after the gravitational wave
burst GWB 091416. This burst of radiation had one millionth
as much energy as the gravitational wave burst.
The false alarm probablity is 0.22 percent.

11 Feb 2016 - LIGO, the Laser
Interferometer Gravitational-Wave Observatory, has made the first
direct detection of the gravitational radiation predicted by Einstein
100 years ago. Rainer Weiss was working on the technology for LIGO
when I first came to MIT in 1976. The technical
paper
shows that a merger of two black holes of 36 and 29 solar
masses occurred 410 Megaparsecs away leaving a 62 solar mass remnant,
with 3 solar masses radiated away in gravitational waves. The peak
strain was 10^{-21}, and the last cycle of the signal was 7
milliseconds long.
The peak luminosity was equivalent to annihilating 200 solar masses
per second.
The peak energy flux was about 8 erg/cm^{2}/sec, equivalent
to magnitude -14 (a little brighter than the full Moon)
if this energy had come as light.
The signal was seen 14 Sep 2015 at 9:50:42 UTC by
both Hanford and Livingston, with a 7 ms time difference pointing to a
localization on the sky covering hundreds of square degrees in the
Southern hemisphere. A new window on the Universe has been opened.
Papers describing the
event rate based on
two events, the
astrophysical implications,
and many other analyses are all on arxiv.org for 12 Feb 2016.
They are also on the LIGO website.
Press coverage:
NY Times lead story with a big picture above the fold on the front page
12 Feb 2016,
Washington Post,
Los Angeles Times,
New Yorker,
CNN,
NBC.

15 Jul 2015 -
Zitrin *et al*
have found a redshifted Lyman α
line at a wavelength of 1178 nm which implies a
redshift of 8.68 in the spectrum of
galaxy with colors that suggested a redshift of 8.57. This now the
highest spectroscopically confirmed redshift.

27 Mar 2015 - Many press articles about dark matter, many with titles like "Dark matter is darker than once thought" or "Dark matter is apparently darker than we thought". Actually that depends on what you mean by "we", since the result confirms the default opinion that dark matter does not interact with itself, although some theorists hoped that it did. There is a nice study behind it, and a press release with a reasonable title: "NASA's Hubble, Chandra Find Clues that May Help Identify Dark Matter". Many more examples like the "Bullet Cluster" have been found, where the dark matter in two colliding clusters passes right through the collision without interacting. These systems are also trouble for MOND theories, since the source of gravity is not following the normal matter.

05 Feb 2015 - Planck released its latest cosmology results today. Technical preprints are available on the arxiv. The 6 parameter Λ CDM model is an excellent fit to the Planck data.

The parameters of the 6-parameter ΛCDM model
fit to Planck TT power spectrum plus the Planck measured
CMB lensing are given in
paper I as :
Ω_{Λ} = 0.692 ± 0.012;
the baryon density = 0.4181 ± 0.0043 yoctograms per cubic meter;
the cold dark matter density = 2.228 ± 0.038
yoctograms per cubic meter;
CDM:baryon density ratio = 5.36 ± 0.10;
dark energy density = 3352 ± 125 eV/cc;
H_{0} = 67.80 ± 0.9 km/sec/Mpc;
and the age of the Universe = 13.799 ± 0.038 Gyr.
The above values are from CMB data alone.
Parameters fit to the Planck data plus external datasets
(BAO, SNe) are given in the last column of Table 4 in
paper XIII as:
Ω_{Λ} = 0.6911 ± 0.0062;
the baryon density = 0.4189 ± 0.0026 yoctograms per cubic meter;
the cold dark matter density = 2.232 ± 0.019
yoctograms per cubic meter;
CDM:baryon density ratio = 5.33 ± 0.06;
dark energy density = 3349 ± 67 eV/cc;
H_{0} = 67.74 ± 0.46 km/sec/Mpc;
and the age of the Universe = 13.799 ± 0.021 Gyr.
The baryon density is known to 0.63% precision
and the cold dark matter density is known to 0.84% precision.

The dark energy density is known to 2.0% precision, assuming
a flat ΛCDM Universe. For theorists who
set hbar and c to 1, it works out to (2.252 meV)^{4}. We still
have no good theory to explain this value.

Limits on 1 parameter extension to the 6 parameter model are

- Ω = 0.9992 ± 0.002 so the data are consistent with a flat Universe
- sum of the neutrino masses is < 0.19 eV with 95% confidence
- the number of neutrino species is 3.04 ± 0.17 which is consistent with the expected 3.046 (slightly larger than 3 because of the way this parameter is defined and the fact that the electron neutrinos were only 99% decoupled when the positrons annihilated).
- The tensor:scalar ratio is < 0.11

Planck data is available at the InfraRed Science Archive (IRSA).

30 Jan 2015 - A
joint analysis of Planck & BICEP data shows that the
previously reported
detection of CMB B-mode polarization has the spectrum
expected from dust in the Milky Way. Their new limit on the
tensor to scalar ratio is *r < 0.12* which is
consistent with the limits from WMAP9 and Planck based on the
angular power spectrum of the temperature anisotropy.
The B-modes from lensing are well detected, and the primordial
B-modes from inflation are not yet seen.

06 June 2014 -
Bennett *et al.* give a concordance value for the
Hubble constant
with a precision of one percent: H_{o} = 69.6
± 0.7 km/sec. This is based on
CMB data,
BAO data, and
direct measurements of the Hubble constant. They also find
the matter density
Ω_{M} = 0.286 ± 0.008.
The Cosmology Calculator
has been updated to use these as default values.

29 May 2014 - Alan Guth, Andrei Linde, and Alexei Starbinsky have won the 2014 Kavli Prize in Astrophysics for their theoretical work on the inflationary scenario in cosmology.

27 May 2014 - Daniel Eisenstein, Shaun Cole, and John Peacock have won the 2014 Shaw Prize in Astronomy for their work on baryon acoustic oscillations, which provide one of the most precise measures of the evolution of the Universe in modern cosmology.

17 Mar 2014 - The BICEP2 experiment has announced a detection of a primordial polarization signal from the inflationary epoch.

Marsh etal already have a paper using this result to constrain axion dark matter on the arxiv preprint server, posted less than 5 hours after the announcement.

Update: More papers on arxiv.org discussing this result: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 & 14; all posted within 2 days.

But I have some concerns about this result. The experimenters switched from a two frequency design to a single frequency design in order to get the highest possible signal to noise. This leaves them vulnerable to polarized foregrounds. In addition, both WMAP and Planck have placed upper limits on this signal that are lower than the claimed detection. But these upper limits are based on subtle features in the CMB angular power spectrum, so it may be the case that other parameters can be adjusted to accommodate all of these experiments.

More blogs with discussions of this result include Lumps'n'Bumps and Of Particular Significance.

23 Jan 2014 - I have been running a bit behind in posting news,
but a big dataset has returned very good information about the Universe.
This is from the
BOSS:
Baryon Oscillation Spectroscopic Survey which is working to
get redshifts
for 1.5 million Luminous Red Galaxies out to
redshift *z = 0.7*.
They have a strong 10σ detection of the
BAO
signal and measurements of the acoustic scale length in two redshift bins
centered at *z = 0.32* and *0.57*.
These results are detailed in a paper by
Anderson *et al.*

11 Dec 2013 - A new preprint
by Saro *et al.*
reports on South Pole Telescope
observations of the Sunyaev-Zeldovich
effect cross-over frequency
for cluster of galaxies versus their redshifts. The cross-over frequency
is proportional to the temperature of the blackbody background that is
being scattered. So if T_{CMB} scale like (1+z) as expected, then
the cross-over frequency at the cluster scales likes (1+z), but it gets
redshifted which divides by (1+z), so the net effect is that the
observed cross-over frequency is constant. They find that
T_{CMB} = T_{o}(1+z)^{1-α}
with α = 0.017 ± 0.029 from the SPT data alone which is
32 standard deviations away from the
Steady State prediction of α = 1.

This result is very similar to a
paper by Hurier *et al.*
which used
Planck
data on clusters of galaxies, and obtained
α = 0.009 ± 0.017 which is 58 standard deviations away from
the Steady State prediction
Planck has a wide range of frequencies from 30 to 857 GHz, so the
cross-over at 217 GHz is easy to find, while the SPT only has 90 and 150
GHz and has to extrapolate to find the cross-over frequency but the SPT
is a much bigger telescope and reaches much higher redshifts.
All these results are consistent with the Big Bang model.

23 July 2013 - Hanson *et al.*
announce the first detection of the B-mode polarization signal in the
CMB.
B-modes have a swirling pattern like a pinwheel.
The result is at very small angular scales using the
South Pole Telescope,
and the signal is produced by
gravitational lensing
distorting the polarization produced by electron scattering (the E-mode).
A distorted E-mode pattern contains a B-mode component.
So this is not the primordial B-mode signal from the era of inflation,
but a foreground pattern whose shape and amplitude can be definitely predicted.
That prediction is now confirmed.

14 July 2013 - The Gruber Prize in Cosmology goes to Viatcheslav Mukhanov and Alexei Starobinsky. Starobinsky was a pioneer in studying the inflationary scenario.

29 April 2013 - The European Space Agency's Herschel Space Observatory has run out of liquid helium coolant, nearly 4 years after its launch. This means that there are currently no space infrared telescopes operating at wavelengths longer than the 4.5 μm channel of the Spitzer Space Telescope.

31 March 2013 - Planck released its first cosmology results today. Technical preprints are available here. The 6 parameter Λ CDM model is an excellent fit to the Planck data, and also to the Planck plus ACT, SPT and WMAP polarization extended CMB data, and to the CMB plus supernovae, Hubble constant and baryon acoustic oscillation data.

The parameters of the 6-parameter ΛCDM model
fit to Planck+WMAP polarization+SPT+ACT+BAO are
Ω_{Λ} = 0.692 ± 0.010;
the baryon density = 0.416 ± 0.0045 yoctograms per cubic meter;
the cold dark matter density = 2.23 ± 0.032
yoctograms per cubic meter;
CDM:baryon density ratio = 5.36 ± 0.10;
dark energy density = 3352 ± 125 eV/cc;
H_{0} = 67.80 ± 0.77 km/sec/Mpc;
and the age of the Universe = 13.798 ± 0.037 Gyr.
The baryon density is known to 1.1% precision
and the cold dark matter density is known to 1.4% precision.

The dark energy density is known to 3.7% precision. For theorists who
set hbar and c to 1, it works out to (2.25 meV)^{4}. We still
have no good theory to explain this value.

Limits on 1 parameter extension to the 6 parameter model are

- Ω = 0.9995 ± 0.0034 so the data are consistent with a flat Universe
- sum of the neutrino masses is < 0.23 eV
- the number of neutrino species is 3.3 ± 0.28 which is consistent with the expected 3.046 (slightly larger than 3 because of the way this parameter is defined and the fact that the electron neutrinos were only 99% decoupled when the positrons annihilated).
- The tensor:scalar ratio is < 0.111

Planck data is available at the InfraRed Science Archive (IRSA).

21 Dec 2012 -
Bennett *et al.* presents the basic results,
while
Hinshaw *et al.* presents the cosmological fits.
The 6 parameter Λ
CDM
model is still an excellent fit to the WMAP data, and also to the
WMAP plus ACT
and SPT
extended CMB data, and to the CMB plus
supernovae,
Hubble constant
and
baryon acoustic oscillation data.
The data are available now at
LAMBDA.
This is the last version of WMAP results.
The baton is now passed on to Europe's
Planck.

The parameters of the 6-parameter ΛCDM model
fit to WMAP+BAO+H_{0} are
Ω_{Λ} = 0.712 ± 0.010;
the baryon density = 0.426 ± 0.008 yoctograms per cubic meter;
the cold dark matter density = 2.17 ± 0.04
yoctograms per cubic meter;
CDM:baryon density ratio = 5.11 ± 0.14;
dark energy density = 3607 ± 144 eV/cc;
H_{0} = 69.33 ± 0.88 km/sec/Mpc;
and the age of the Universe = 13.75 ± 0.085 Gyr.
Both the baryon density and the cold dark matter density are known
to 2% precision.

The dark energy density is known to 4% precision. For theorists who
set hbar and c to 1, it works out to (2.3 meV)^{4}. We still
have no good theory to explain this value.

Several extensions to the 6 parameter ΛCDM are considered,
but none are necessary to fit the data.
The non-flat model gives Ω_{tot}
= 1.0027 ± 0.0039. This is perfectly consistent with a
flat Universe.

The sum of the neutrino masses is < 0.44 eV.

The number of neutrino species is N_{eff} = 2.83 ± 0.38
which is consistent with the standard value of 3.04 for 3 neutrino species.
Update 30 Jan 2013: v2 of the papers are posted to
the preprint server. With the helium abundance fixed, the number of
neutrino species for the WMAP+eCMB+BAO+H0 dataset is 3.84 ± 0.40
which is consistent (at 2σ) with the standard value.

12/12/12 - The Hubble Ultra Deep Field has been reobserved to greater depth
in new filters in the infrared. Here are some highlights from the abstract
of Ellis *et al.*:

- none of the previously claimed UDF candidates with 8.5< z < 10 is confirmed
- we find 7 promising z > 8.5 candidates
- the candidate UDFj-39546284 (previously proposed at z=10.3) [...] is undetected in the newly added F140W image, implying it lies at z=11.9

Update 04 Jan 2013: Brammer
*et al.* report a tentative emission line in UDFj-39546284
at 1.599 μm, which they feel is probably [O III] at z=2.19.

29 Oct 2012 - The South Pole Telescope announced new data on the small angular scale anisotropy of the Cosmic Microwave Background. Notable conclusions are:

- the new data and the WMAP 7 year data are both consistent with a 6 parameter, flat ΛCDM model.
- a CMB-only measurement of the flatness of the Universe gives Ω = 1.003±0.017.
- a combined CMB, H
_{0}and baryon acoustic oscillation (BAO) model has 71.5% of the Universe being dark energy, 23.9% dark matter, and 4.6% ordinary matter; with a Hubble constant of 69.6 ± 0.8 km/sec/Mpc. - the combined CMB+H
_{0}+BAO fit is also flat: Ω = 1.006±0.004.

01 Aug 2012 - Inflation cosmology theorists Alan Guth and Andrei Linde are among the 9 winners of the first Milner Prizes to be awarded. This prize amounts to $3,000,000.

12 Jun 2012 - Rahmani *et al.
* report that the ratio of the 21 cm line of hydrogen to optical line
wavelengths has not changed since 9 Gyr ago. Their limit on the change
in a combination
of constants *x = g _{p} α^{2} m_{e}/
m_{p}* is -0.1+/-1.3 parts per million.
This makes earlier claims
unlikely, since the claimed 10 parts per million change in α would
change

13 Jan 2012 - The BBC
reports that the dilution refrigerator that cools the High Frequency
Instrument on the European CMB satellite Planck to 0.1 K
has run out of ^{3}He.
The Low Frequency Instrument continues to operate at 4 K.
The first announcement of cosmological results from Planck is
scheduled for Jan 2013.

04 Oct 2011 -
Saul Perlmutter, Adam Riess & Brian Schmidt have won the
2011 Nobel Prize in Physics
for their work showing the Universe is accelerating
by measuring the brightness of distant supernovae.
This is evidence for an energy density of the vacuum or a
cosmological constant.

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