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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:

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.

News of the Universe

News from the Dark Energy Survey

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 Ωm = 0.299(8), Ωb = 0.0479(14), Ho = 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.

Non-news about the accelerating Universe

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.

Hubble Constant from Lensing Time Delay

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 H0 = 71.9+2.4-3.0 km/sec/Mpc based on three systems.

FRB redshift found

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.

Short GRB from GWB?

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.

LIGO Detects Black Hole Merger 1.3 Billion Lightyears Away

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/cm2/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.

A New Galaxy Redshift Record

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.

Darker Dark Matter?

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.

Cosmology Results from the full Planck mission.

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 : ΩΛ = 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; H0 = 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: ΩΛ = 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; H0 = 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

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

CMB Swirls Turn to Dust

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.

A One Percent Hubble Constant

06 June 2014 - Bennett et al. give a concordance value for the Hubble constant with a precision of one percent: Ho = 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 ΩM = 0.286 ± 0.008. The Cosmology Calculator has been updated to use these as default values.

Inflation Pioneers Win the Kavli Prize in Astrophysics

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.

2014 Shaw Prize in Astronomy for Baryon Acoustic Oscillations

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.

First Detection of Primordial B-mode CMB Polarization

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.

Notes from the BOSS

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.

The thumbnail on the right is my simplified way of showing how these data, combined with the CMB measurement of the acoustic scale length at z = 1089, and the supernova measurement of the acceleration of the expansion of the Universe, provide enough information to simultaneously determine the current matter density, the current dark energy density and the rate of change of the dark energy density. The figure is labeled with the "Equation of State" w = P/ρc2 but I think a better way to think of this is in terms of the "cosmic interest rate" on dark energy density. The percentage change per unit time in the dark energy density is less than 1/3 of the Hubble rate and could well be zero, as expected for a cosmological constant.

Steady State Disproved Again and Again

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 TCMB 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 TCMB = To(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.

First detection of CMB B-mode Polarization

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.

2013 Gruber Prize

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

Herschel out of Helium

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.

First Cosmology Results from Planck

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 ΩΛ = 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; H0 = 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

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

Not the Mayan Apocalypse - WMAP 9 Year Data Released

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+H0 are ΩΛ = 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; H0 = 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 Ωtot = 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 Neff = 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.

HST Claims it has Uncovered the Most Robust Sample of Distant Galaxies

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.:

To summarize, most previous claims were proven wrong, but a new sample based on the same kind of data is now presented. To be clear, the previous objects still exist but now have smaller estimated redshifts. One previously claimed object is seen again but with the redshift increased by 1.6 to 11.9. I am sure the JWST will sort this out in several years.

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.

New CMB Anisotropy Results from the South Pole

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

Inaugural Milner Prizes to Guth & Linde

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.

No change in fundamental constants

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 = gp α2 me/ mp 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 x by 20 parts per million.

Planck warms up

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 3He. The Low Frequency Instrument continues to operate at 4 K. The first announcement of cosmological results from Planck is scheduled for Jan 2013.

2011 Nobel Prize for Supernova Cosmology

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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