Cosmology Day July 2018

Lecture 2: Cosmic Microwave Background

Dr Erminia Calabrese


(Credit: Stefania Pandolfi)

Dr Calabrese is an STFC Ernest Rutherford Fellow and Lecturer at the School of Physics and Astronomy of Cardiff University. She obtained her PhD in Rome at Sapienza University and then moved to the UK in 2011. She spent 4 years in Oxford as postdoctoral research associate and Beecroft Fellow, moved to Princeton University during fall and winter 2015/2016 as Spitzer Fellow and then back to Oxford to start the Rutherford Fellowship. In May 2017 she moved to Cardiff University to join the Astronomy Instrumentation and Astronomy & Astrophysics groups. Dr Calabrese works at the intersection of cosmological theory and data analysis of the Cosmic Microwave Background signals, and combines the CMB with galaxy surveys to obtain state-of-the-art constraints on cosmological scenarios, including limits on neutrino physics, dark energy and inflation. She also works on the modelling of secondary CMB emissions (e.g., thermal and kinematic Sunyaev-Zeldovich effects) and extra-galactic sources present in CMB data, with the aim of obtaining unbiased cosmology and interesting astrophysics. She is an active member of the Planck satellite and Atacama Cosmology Telescope collaborations and of many other future CMB and galaxy experiments.


The use of the Cosmic Microwave Background radiation (CMB) to study the physics of the Universe is one of the greatest success stories of modern cosmology. Over the last two decades, the astonishing agreement between theory and increasingly-precise observations of CMB temperature and polarisation has led to the establishment of a concordance cosmological model. Stringent constraints on the cosmological parameters of this model are currently set by a combination of data from CMB satellite and ground-based experiments. In this talk Dr Calabrese presented state-of-the-art CMB cosmology from current experiments and introduced the plans for the next decade. She highlighted how current astrophysical and cosmological data support the presence of a non-baryonic, dark, matter component dominating the matter content of the Universe. Dark Matter is considered to be a necessary ingredient for galaxy formation and is thought to be composed of weakly interacting massive particles which interact almost solely via gravity and which, as of today, are eluding laboratory searches.

My notes from the lecture (if they don’t make sense then it is entirely my fault)

The current view of the Universe (WMAP and Planck)


NASA / WMAP Science Team –

CMB Images IMAGES > CMB IMAGES > NINE YEAR MICROWAVE SKY Nine Year Microwave Sky The detailed, all-sky picture of the infant universe created from nine years of WMAP data. The image reveals 13.77 billion year old temperature fluctuations (shown as colour differences) that correspond to the seeds that grew to become the galaxies. The signal from our galaxy was subtracted using the multi-frequency data. This image shows a temperature range of ± 200 microKelvin. Credit: NASA / WMAP Science Team WMAP # 121238 Image Caption 9 year WMAP image of background cosmic radiation (2012)


The Cosmic Microwave Background – as seen by Planck. Credit: ESA and the Planck Collaboration

Sequence of all-sky views obtained by ESA’s Planck mission at increasing frequencies, from 30 to 857 GHz. For each frequency, the animation shows the map of temperature fluctuations in the cosmic microwave background, or CMB, and three measures of the CMB polarisation. In the case of the two highest frequency channels (545 and 857 GHz), which were not sensitive to polarization, only the CMB temperature fluctuations are shown.

These images are based on data from the Planck Legacy release, the mission’s final data release, published in July 2018.


Planck was a space observatory operated by the European Space Agency (ESA) from 2009 to 2013, which mapped the anisotropies of the cosmic microwave background (CMB) at microwave and infra-red frequencies, with high sensitivity and small angular resolution.


Artist’s impression of the Planck spacecraft

Planck Power Spectrum


This graph shows the temperature fluctuations in the Cosmic Microwave Background detected by Planck at different angular scales on the sky, starting at ninety degrees on the left side of the graph, through to the smallest scales on the right hand side.

The red dots are measurements made with Planck; these are shown with error bars that account for measurement errors as well as for an estimate of the uncertainty that is due to the limited number of points in the sky at which it is possible to perform measurements. This so-called cosmic variance is an unavoidable effect that becomes most significant at larger angular scales.

The green curve represents the best fit of the ‘standard model of cosmology’ – currently the most widely accepted scenario for the origin and evolution of the Universe – to the Planck data. The pale green area around the curve shows the predictions of all the variations of the standard model that best agree with the data.

While the observations on small and intermediate angular scales agree extremely well with the model predictions, the fluctuations detected on large angular scales on the sky – between 90 and six degrees – are about 10 per cent weaker than the best fit of the standard model to Planck data. At angular scales larger than six degrees, there is one data point that falls well outside the range of allowed models. These anomalies in the Cosmic Microwave Background pattern might challenge the very foundations of cosmology, suggesting that some aspects of the standard model of cosmology may need a rethink.

Microwave background radiation predictions and measurements

1941 – Andrew McKellar detected the cosmic microwave background as the coldest component of the interstellar medium by using the excitation of CN doublet lines measured by W. S. Adams in a B star, finding an “effective temperature of space” (the average bolometric temperature) of 2.3 K

1946 – George Gamow calculates a temperature of 50 K (assuming a 3-billion year old universe), commenting it “… is in reasonable agreement with the actual temperature of interstellar space”, but does not mention background radiation.

1948 – Ralph Alpher and Robert Herman estimate “the temperature in the universe” at 5 K. Although they do not specifically mention microwave background radiation, it may be inferred.

1949 – Ralph Alpher and Robert Herman re-re-estimate the temperature at 28 K

1953 – George Gamow estimates 7 K

1956 – George Gamow estimates 6 K

1955 – Émile Le Roux of the Nançay Radio Observatory, in a sky survey at l = 33 cm, reported a near-isotropic background radiation of 3 kelvins, plus or minus 2.

1957 – Tigran Shmaonov reports that “the absolute effective temperature of the radioemission background … is 4±3 K”. It is noted that the “measurements showed that radiation intensity was independent of either time or direction of observation … it is now clear that Shmaonov did observe the cosmic microwave background at a wavelength of 3.2 cm”

1960s – Robert Dicke re-estimates a microwave background radiation temperature of 40 K

1964 – A. G. Doroshkevich and Igor Dmitrievich Novikov publish a brief paper suggesting microwave searches for the black-body radiation predicted by Gamow, Alpher, and Herman, where they name the CMB radiation phenomenon as detectable.

1964–65 – Arno Penzias and Robert Woodrow Wilson measure the temperature to be approximately 3 K. Robert Dicke, James Peebles, P. G. Roll, and D. T. Wilkinson interpret this radiation as a signature of the big bang.

1966 – Rainer K. Sachs and Arthur M. Wolfe theoretically predict microwave background fluctuation amplitudes created by gravitational potential variations between observers and the last scattering surface

1968 – Martin Rees and Dennis Sciama theoretically predict microwave background fluctuation amplitudes created by photons traversing time-dependent potential wells

1969 – R. A. Sunyaev and Yakov Zel’dovich study the inverse Compton scattering of microwave background photons by hot electrons

1983 – Researchers from the Cambridge Radio Astronomy Group and the Owens Valley Radio Observatory first detect the Sunyaev-Zel’dovich effect from clusters of galaxies

1983 – RELIKT-1 Soviet CMB anisotropy experiment was launched.

1990 – FIRAS on the Cosmic Background Explorer (COBE) satellite measures the black body form of the CMB spectrum with exquisite precision, and shows that the microwave background has a nearly perfect black-body spectrum and thereby strongly constrains the density of the intergalactic medium.

January 1992 – Scientists that analysed data from the RELIKT-1 report the discovery of anisotropy in the cosmic microwave background at the Moscow astrophysical seminar.

1992 – Scientists that analysed data from COBE DMR report the discovery of anisotropy in the cosmic microwave background.

1995 – The Cosmic Anisotropy Telescope performs the first high resolution observations of the cosmic microwave background.

1999 – First measurements of acoustic oscillations in the CMB anisotropy angular power spectrum from the TOCO, BOOMERANG, and Maxima Experiments. The BOOMERanG experiment makes higher quality maps at intermediate resolution, and confirms that the universe is “flat”.

2002 – Polarization discovered by DASI

2003 – E-mode polarization spectrum obtained by the CBI. The CBI and the Very Small Array produces yet higher quality maps at high resolution (covering small areas of the sky)

2003 – The Wilkinson Microwave Anisotropy Probe spacecraft produces an even higher quality map at low and intermediate resolution of the whole sky (WMAP provides no high-resolution data, but improves on the intermediate resolution

maps from BOOMERanG).

2004 – E-mode polarization spectrum obtained by the CBI

2004 – The Arcminute Cosmology Bolometer Array Receiver produces a higher quality map of the high resolution structure not mapped by WMAP.

2005 – The Arcminute Microkelvin Imager and the Sunyaev-Zel’dovich Array begin the first surveys for very high redshift clusters of galaxies using the Sunyaev-Zel’dovich effect.

2005 – Ralph A. Alpher is awarded the National Medal of Science for his groundbreaking work in nucleosynthesis and prediction that the universe expansion leaves behind background radiation, thus providing a model for the Big Bang theory.

2006 – The long-awaited three-year WMAP results are released, confirming previous analysis, correcting several points, and including polarization data.

2006 – Two of COBE’s principal investigators, George Smoot and John Mather, received the Nobel Prize in Physics in 2006 for their work on precision measurement of the CMBR

2006–2011 – Improved measurements from WMAP, new supernova surveys ESSENCE and SNLS, and baryon acoustic oscillations from SDSS and WiggleZ, continue to be consistent with the standard Lambda-CDM model.

2010 – The first all-sky map from the Planck telescope is released.

2013 – An improved all-sky map from the Planck telescope is released, improving the measurements of WMAP and extending them to much smaller scales.

2014 – On March 17, 2014, astrophysicists of the BICEP2 collaboration announced the detection of inflationary gravitational waves in the B-mode power spectrum, which if confirmed, would provide clear experimental evidence for the theory of inflation. However, on 19 June 2014, lowered confidence in confirming the cosmic inflation findings was reported.

2015 – On January 30, 2015, the same team of astronomers from BICEP2 withdrew the claim made on the previous year. Based on the co

combined data of BICEP2 and Planck, the European Space Agency announced that the signal can be entirely attributed to dust in the Milky Way.

Chronology of the universe

The chronology of the universe describes the history and future of the universe according to Big Bang cosmology. The earliest stages of the universe’s existence are estimated as taking place 13.8 billion years ago, with an uncertainty of around 21 million years at the 68% confidence level.



In cosmology, decoupling refers to a period in the development of the universe when different types of particles fall out of thermal equilibrium with each other. This occurs as a result of the expansion of the universe, as their interaction rates decrease (and mean free paths increase) up to this critical point. The two verified instances of decoupling since the Big Bang which are most often discussed are photon decoupling and neutrino decoupling, as these led to the cosmic microwave background and cosmic neutrino background, respectively.

The photon epoch started after most leptons and anti-leptons were annihilated at the end of the lepton epoch, about 10 seconds after the Big Bang. Atomic nuclei were created in the process of nucleosynthesis which occurred during the first few minutes of the photon epoch. For the remainder of the photon epoch, the universe contained a hot dense plasma of nuclei, electrons and photons. A sort of cosmic soup. At this point the temperature was around 3000K and gamma radiation was emitted.

In cosmology, recombination refers to the epoch at which charged electrons and protons first became bound to form electrically neutral hydrogen atoms. Photons are no longer in thermal equilibrium with matter and the Universe first becomes transparent. The photons of the cosmic microwave background radiation originate at this time (temperature of 2.7K). Recombination occurred about 378,000 years after the Big Bang.

Photon decoupling is closely related to recombination, which occurred about 378,000 years after the Big Bang, when the universe was a hot opaque (“foggy”) plasma. During recombination, free electrons became bound to protons (hydrogen nuclei) to form neutral hydrogen atoms.

Because direct recombinations to the ground state (lowest energy) of hydrogen are very inefficient, these hydrogen atoms generally form with the electrons in a high energy state, and the electrons quickly transition to their low energy state by emitting photons.

Photons are free to travel.

Then come the dark ages

After recombination and decoupling, the universe was transparent and had cooled enough to allow light to travel long distances, but there were no light-producing structures such as stars and galaxies. During this time, the only source of photons was hydrogen emitting radio waves at the hydrogen line. Freely propagating CMB photons quickly (within about 3 million years) red-shifted to infrared, and Universe was devoid of visible light.

Stars and galaxies are formed when dense regions of gas form due to the action of gravity, and this takes a long time within a near-uniform density of gas and on the scale required, so it is estimated that stars did not exist for perhaps hundreds of millions of years after recombination.

In the field of Big Bang theory, and cosmology, reionization is the process that caused the matter in the universe to reionise after the lapse of the “dark ages”.

The most distant astronomical objects observable with telescopes date to this period; as of 2016, the most remote galaxy observed is GN-z11. The earliest “modern” Population III stars are formed in this period.

Investigating the chronology of the Universe

Look at the temperature fluctuations caused by the expansion of the Universe

Look at acoustic wave behaviour

In cosmology, baryon acoustic oscillations (BAO) are fluctuations in the density of the visible baryonic matter (normal matter) of the universe, caused by acoustic density waves in the primordial plasma of the early universe.

Look at Thomson scattering

The CMB photons are scattered by free charges such as electrons that are not bound in atoms. In an ionised universe, such charged particles have been liberated from neutral atoms by ionising (ultraviolet) radiation. Today these free charges are at sufficiently low density in most of the volume of the universe that they do not measurably affect the CMB. However, if the IGM was ionised at very early times when the universe was still denser, then there are two main effects on the CMB:

1) Small-scale anisotropies are erased. (Just as when looking at an object through fog, details of the object appear fuzzy.)

2) The physics of how photons are scattered by free electrons (Thomson scattering) induces polarisation anisotropies on large angular scales. This broad angle polarisation is correlated with the broad angle temperature perturbation.

Both of these effects have been observed by the WMAP spacecraft, providing evidence that the universe was ionized at very early times

Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism.

Anisotropy is the property of being directionally dependent, which implies different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material’s physical or mechanical properties (absorbance, refractive index, conductivity, tensile strength, etc.)

An example of anisotropy is light coming through a polariser. Another is wood, which is easier to split along its grain than across it.

Primordial fluctuations are density variations in the early universe which are considered the seeds of all structure in the universe. Currently, the most widely accepted explanation for their origin is in the context of cosmic inflation.

The statistical properties of the primordial fluctuations can be inferred from observations of anisotropies in the cosmic microwave background and from measurements of the distribution of matter, e.g., galaxy redshift surveys. Since the fluctuations are believed to arise from inflation, such measurements can also set constraints on parameters within inflationary theory.


The primordial fluctuations in hot and cold dark matter gave rise to two completely different distributions of cosmic structure. In hot dark matter models, the first structures to form were the most massive, that subsequently fragment into smaller and smaller structures. This has been discarded on the basis of observations of galaxies in the early Universe: since the first objects that are seen to emerge in cosmic history have low mass (light elements), and they gradually evolve into more massive structures, cosmologists have established that the bulk of dark matter in the Universe is cold. However, a small fraction of hot dark matter is present in the Universe as neutrinos. Depending on the mass of neutrinos (which has not been determined yet) the effect of hot dark matter can be more or less evident in the distribution of cosmic structure on different scales, since neutrinos tend to smooth out the formation of small‐scale structures.

When temperatures were so high random motions of particles were at relativistic speeds, and particle–antiparticle pairs of all kinds were being continuously created and destroyed in collisions.

From what we know today, a majority of the neutrinos floating around were born around 15 billion years ago, soon after the birth of the universe. Since this time, the universe has continuously expanded and cooled, and neutrinos have just kept on going. Theoretically, there are now so many neutrinos that they constitute a cosmic background radiation whose temperature is 1.9 degree Kelvin (-271.2 degree Celsius). Other neutrinos are constantly being produced from nuclear power stations, particle accelerators, nuclear bombs, general atmospheric phenomenae, and during the births, collisions, and deaths of stars, particularly the explosions of supernovae.

Of all high-energy particles, only weakly interacting neutrinos can directly convey astronomical information from the edge of the universe – and from deep inside the most cataclysmic high-energy processes and as far as we know, there are three different types of neutrinos, each type relating to a charged particle.

The study of galaxy formation and evolution is concerned with the processes that formed a heterogeneous universe from a homogeneous beginning, the formation of the first galaxies, the way galaxies change over time, and the processes that have generated the variety of structures observed in nearby galaxies. Galaxy formation is hypothesized to occur from structure formation theories, as a result of tiny quantum fluctuations in the aftermath of the Big Bang. The simplest model in general agreement with observed phenomena is the Lambda-CDM model—that is, that clustering and merging allows galaxies to accumulate mass, determining both their shape and structure.

ESA’s Planck satellite has delivered its first all-sky image of the Cosmic Microwave Background (CMB), bringing with it new challenges about our understanding of the origin and evolution of the cosmos. The image has provided the most precise picture of the early Universe so far.

Initial conditions of the Universe

Time = 0 seconds (13.799 ± 0.021 Gya): Planck Epoch begins: earliest meaningful time. The Big Bang occurs in which ordinary space and time develop out of a primeval state (possibly a virtual particle or false vacuum) described by a quantum theory of gravity or “Theory of Everything”. All matter and energy of the entire visible universe is contained in an unimaginably hot, dense point (gravitational singularity), a billionth the size of a nuclear particle. This state has been described as a particle desert. Other than a few scant details, conjecture dominates discussion about the earliest moments of the universe’s history since no effective means of testing this far back in space-time is presently available. WIMPS (weakly interacting massive particles) or dark matter and dark energy may have appeared and been the catalyst for the expansion of the singularity. The infant universe cools as it begins expanding outward. It is almost completely smooth, with quantum variations beginning to cause slight variations in density.

In Big Bang cosmology, the Planck epoch or Planck era is the earliest stage of the Big Bang, before the time passed was equal to the Planck time, or approximately 10−43 seconds.

It is generally assumed that quantum effects of gravity dominate physical interactions at this timescale. At this scale, the unified force of the Standard Model is assumed to be unified with gravitation.

The Big Bang theory is the prevailing cosmological model for the observable universe from the earliest known periods through its subsequent large-scale evolution

Probing the cosmic neutrino background

The cosmic neutrino background (CNB, CνB) is the universe’s background particle radiation composed of neutrinos. They are sometimes known as relic neutrinos.

According to the Big Bang theory, neutrinos decoupled from other particles earlier than Cosmic Microwave Background (CMB).

The CνB is a relic of the big bang; while the cosmic microwave background radiation (CMB) dates from when the universe was 379,000 years old, the CνB decoupled (separated) from matter when the universe was just one second old. It is estimated that today, the CνB has a temperature of roughly 1.95 K.

As neutrinos rarely interact with matter, these neutrinos still exist today. They have a very low energy, around 10−4 to 10−6 eV. Even high energy neutrinos are notoriously difficult to detect, and the CνB has energies around 10−10 times smaller, so the CνB may not be directly observed in detail for many years, if at all. However, Big Bang cosmology makes many predictions about the CνB, and there is very strong indirect evidence that the CνB exists.

Confirmation of the existence of these relic neutrinos may only be possible by directly detecting them using experiments on Earth. This will be difficult as the neutrinos which make up the CνB are non-relativistic, in addition to interacting only weakly with normal matter, and so any effect they have in a detector will be hard to identify.

Future cosmological measurements should enable the sum of neutrino masses to be determined indirectly through their effects on the expansion rate of the Universe and the clustering of matter.

Apparatus used for detecting the Cosmic Microwave Background

These include satellites, balloons and ground-based experiments


The telescope being readied for launch

In astronomy and observational cosmology, The BOOMERanG experiment (Balloon Observations Of Millimetric Extragalactic Radiation ANd Geophysics) was an experiment which measured the cosmic microwave background radiation of a part of the sky during three sub-orbital (high-altitude) balloon flights. It was the first experiment to make large, high-fidelity images of the CMB temperature anisotropies, and is best known for the discovery in 2000 that the geometry of the universe is close to flat, with similar results from the competing MAXIMA experiment.

Together with experiments like the Saskatoon experiment, TOCO, MAXIMA, and others, the BOOMERanG data from 1997 and 1998 determined the angular diameter distance to the surface of last scattering with high precision. When combined with complementary data regarding the value of Hubble’s constant, the Boomerang data determined the geometry of the Universe to be flat, supporting the supernova evidence for the existence of dark energy.

The Millimeter Anisotropy eXperiment IMaging Array (MAXIMA) experiment was a balloon-borne experiment funded by the U.S. NSF, NASA and Department of Energy, and operated by an international collaboration headed by the University of California, to measure the fluctuations of the cosmic microwave background.

Compared to MAXIMA’s competitor the BOOMERanG experiment, MAXIMA’s data covers a smaller part of the sky but with much more detail. By the end of the year 2000 the experiment provided the most accurate measurements of the cosmic background radiation (CMB) fluctuations on small angular scales. With this data it is possible to calculate the first three acoustic peaks from the CMB power spectrum. These greatly confirm the standard cosmological model by measuring a baryon density of about 4%, which agrees with the density calculated from Big Bang nucleosynthesis. The measurement of the flatness of the Universe also confirms a major prediction of inflationary cosmology, although BOOMERang was the first to discover this.

The E and B Experiment (EBEX) will measure the cosmic microwave background radiation of a part of the sky during two sub-orbital (high-altitude) balloon flights. It is an experiment to make large, high-fidelity images of the CMB polarization anisotropies. By using a telescope which flies at over 42,000 metres high, it is possible to reduce the atmospheric absorption of microwaves to a minimum. This allows massive cost reduction compared to a satellite probe, though only a small part of the sky can be scanned and for a shorter duration than a typical satellite mission such as WMAP.

Spider is a balloon-borne experiment designed to search for primordial gravitational waves imprinted on the cosmic microwave background (CMB). Measuring the strength of this signal puts limits on inflationary theory.


POLARBEAR is a cosmic microwave background polarisation experiment located in the Atacama Desert of northern Chile in the Antofagasta Region. The POLARBEAR experiment is mounted on the Huan Tran Telescope (HTT) at the James Ax Observatory in the Chajnantor Science Reserve. The HTT is located near the Atacama Cosmology Telescope on the slopes of Cerro Toco at an altitude of nearly 5,200 m.

LiteBIRD ((Light) satellite for the studies of B-mode polarization and Inflation from cosmic background Radiation Detection) is a proposed small space observatory that aims to detect the footprint of the primordial gravitational wave on the cosmic microwave background (CMB) in a form of polarization pattern called B-mode.

RELIKT-1 (sometimes RELICT-1 from Russian: РЕЛИКТ-1) – a Soviet cosmic microwave background anisotropy experiment on board the Prognoz 9 satellite (launched 1 July 1983) gave upper limits on the large-scale anisotropy.

The Cosmic Background Explorer (COBE ), also referred to as Explorer 66, was a satellite dedicated to cosmology, which operated from 1989 to 1993. Its goals were to investigate the cosmic microwave background radiation (CMB) of the universe and provide measurements that would help shape our understanding of the cosmos.

Archeops was a balloon-borne instrument dedicated to measuring the Cosmic microwave background (CMB) temperature anisotropies. The study of this radiation is essential to obtain precise information on the evolution of the Universe: density, Hubble constant, age of the Universe, etc.

Absolute Radiometer for Cosmology, Astrophysics, and Diffuse Emission (ARCADE) is a program which utilizes high-altitude balloon instrument package intended to measure the heating of the universe by the first stars and galaxies after the big bang and search for the signal of relic decay or annihilation.

QMAP is a balloon experiment to measure the anisotropy of the Cosmic microwave background.

TopHat was a scientific experiment launched from McMurdo Station in January 2001 to measure the cosmic microwave background radiation produced 300,000 years after the Big Bang.

Other ground-based experiments:




Tenerife; VSA

Bibliography of WMAP Science Team Publications

Gary F. Hinshaw (born in San Rafael, California) is an astronomer and astrophysicist. Hinshaw worked on the Wilkinson Microwave Anisotropy Probe (WMAP) whose observations of Cosmic Microwave Background (CMB) have provided significant insights into cosmology.

Planck intermediate results XXIV. Constraints on variations in fundamental constants?

Polarisation measurements produce fresh and independent information on the primordial density perturbations and cosmological parameters, and offer the potential to detect primordial gravity waves, constrain dark energy and measure the neutrino mass scale.

Gravitational lensing of the CMB as measured by Planck; the path of photons is altered by the presence of matter. If you look at the CMB in a given direction on the sky, most likely the light did not come from that direction originally. It came from another direction, not too far off (~2 arcminutes), and was deflected along its way to us by the intervening large-scale structure. This effect is known as weak gravitational lensing.

While the CMB depicts our Universe when it was about 380,000 yrs old, CMB lensing is caused by the intervening matter and thus allows us to retrieve information about the evolution of the Universe. Observationally, it causes a correlation between the temperature on the sky and its gradient, or how quickly the temperature changes from one place to another. By measuring this correlation, one can reconstruct the “lensing potential”, which is related to the total mass along the line-of-sight.

What do we learn from CMB lensing? It helps determine whether the Universe is flat, it gives evidence of the existence of dark energy just from the CMB, it is crucial for a detection of the integrated Sachs-Wolfe effect and it gives information on the connection between luminous and dark matter.

The Sachs–Wolfe effect, named after Rainer K. Sachs and Arthur M. Wolfe, is a property of the cosmic microwave background radiation (CMB), in which photons from the CMB are gravitationally redshifted, causing the CMB spectrum to appear uneven.

The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a parametrization of the Big Bang cosmological model in which the universe contains a cosmological constant, denoted by Lambda (Greek Λ), associated with dark energy, and cold dark matter (abbreviated CDM). It is frequently referred to as the standard model of Big Bang cosmology because it is the simplest model that provides a reasonably good account of the following properties of the cosmos:

The existence and structure of the cosmic microwave background;

The large-scale structure in the distribution of galaxies;

The abundances of hydrogen (including deuterium), helium, and lithium;

The accelerating expansion of the universe observed in the light from distant galaxies and supernovae

The model assumes that general relativity is the correct theory of gravity on cosmological scales. It emerged in the late 1990s as a concordance cosmology, after a period of time when disparate observed properties of the universe appeared mutually inconsistent, and there was no consensus on the makeup of the energy density of the universe.

The ΛCDM model can be extended by adding cosmological inflation, quintessence and other elements that are current areas of speculation and research in cosmology.

Some alternative models challenge the assumptions of the ΛCDM model. Examples of these are modified Newtonian dynamics, modified gravity, theories of large-scale variations in the matter density of the universe, and scale invariance of empty space.

The ΛCDM Cold Dark Matter Double Dark theory based on this appears to be able to account for all the large scale features of the observable universe, including the details of the heat radiation of the Big Bang and the large-scale distribution of galaxies.

It explains why our universe is geometrically flat

The global shape of the universe can be described with three attributes:

Finite or infinite

Flat (no curvature), open (negative curvature), or closed (positive curvature)

Connectivity, how the universe is put together, i.e., simply connected space or multiply connected.

“pillars of the cosmological standard model”:

The laws of physics: The basic theoretical frameworks that we rely on for building cosmological models. (Includes GR, standard model of particle physics…)

Foundational assumptions: Basic assumptions that we make when constructing theories and interpreting observations. (Includes homogeneity, isotropy, Big Bang, inflation…)

Constituents of the Universe: What the Universe is made of, and how it behaves. (Includes dark energy/vacuum energy, dark matter, inflaton, neutrinos…)

Beyond ΛCDM to go beyond the standard model by modifying or replacing the above pillars in some way, to better explain observations or construct more appealing theories. For example, modified gravity theories replace GR as a law of physics; models of dark energy add a new fluid to the content of the Universe; and so on.

Planck 2015 results show that by combining Planck observations with other astrophysical data we find Neff = 3.15 ± 0.23 for the effective number of relativistic degrees of freedom, consistent with the value Neff = 3.12 ± 0.23 of the Standard Model of particle physics.

From the Planck temperature data combined with Planck lensing, for this cosmology the Hubble constant, H0 = (67.8 ± 0.9) km s-1Mpc-1, a matter density parameter Ωm = 0.308 ± 0.012, and a tilted scalar spectral index with ns = 0.968 ± 0.006.

The sum of neutrino masses is constrained to ∑mν < 0.23 eV.

Universe content and the CMB

There are three ingredients in this universe: normal matter (or atoms), cold dark matter, and dark energy.

Atoms: The amount of ordinary matter (atoms) in your universe, the stuff you see around you: tables, chairs, planets, stars, etc. Expressed as a percentage of the “critical density”.

Cold Dark Matter: The amount of cold dark matter in your universe, as a percentage of the critical density. Cold dark matter cannot be seen or felt, and has not been detected in the laboratory, but it does exert a gravitational pull.

Dark energy: The amount of dark energy in your universe, as a percentage of the “critical density”. Unlike dark matter, dark energy exerts gravitational push (a form of anti-gravity) that is causing the expansion of the universe to accelerate or speed up.

The BAO technique helps constrain cosmological parameters and provide further insight into the nature of dark energy.

The recent discovery of the previously predicted acoustic peaks in the power spectrum has established a working cosmological model: a critical density universe consisting of mainly dark matter and dark energy, which formed its structure through gravitational instability from quantum fluctuations during an inflationary epoch. Wayne Hu and Scott Dodelson

2% constraint on the amplitude of matter fluctuations Z~2

Planck 2015 results XV

Lensing potential map


NILC, fsky (fraction of the sky) = 0.87

NILC CMB map is constructed from all Planck channels from 44 to 857 GHz

Dark matter evidence

The arms of spiral galaxies rotate around the galactic centre. The luminous mass density of a spiral galaxy decreases as one goes from the centre to the outskirts. If luminous mass were all the matter, then we can model the galaxy as a point mass in the centre and test masses orbiting around it, similar to the Solar System. From Kepler’s Second Law, it is expected that the rotation velocities will decrease with distance from the centre, similar to the Solar System. This is not observed. Instead, the galaxy rotation curve remains flat as distance from the centre increases.

If Kepler’s laws are correct, then the obvious way to resolve this discrepancy is to conclude that the mass distribution in spiral galaxies is not similar to that of the Solar System. In particular, there is a lot of non-luminous matter (dark matter) in the outskirts of the galaxy.


Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). Dark matter can explain the ‘flat’ appearance of the velocity curve out to a large radius.

The rotation curve of a disc galaxy (also called a velocity curve) is a plot of the orbital speeds of visible stars or gas in that galaxy versus their radial distance from that galaxy’s centre.

In astronomy, the velocity dispersion (σ) is the statistical dispersion of velocities about the mean velocity for a group of objects, such as an open cluster, globular cluster, galaxy, galaxy cluster, or supercluster.

Stars in bound systems must obey the virial theorem. The theorem, together with the measured velocity distribution, can be used to measure the mass distribution in a bound system, such as elliptical galaxies or globular clusters. With some exceptions, velocity dispersion estimates of elliptical galaxies do not match the predicted velocity dispersion from the observed mass distribution, even assuming complicated distributions of stellar orbits.

As with galaxy rotation curves, the obvious way to resolve the discrepancy is to postulate the existence of non-luminous matter.

Galaxy clusters are particularly important for dark matter studies since their masses can be estimated in three independent ways:

From the scatter in radial velocities of the galaxies within clusters;

From X-rays emitted by hot gas in the clusters. From the X-ray energy spectrum and flux, the gas temperature and density can be estimated, hence giving the pressure; assuming pressure and gravity balance determines the cluster’s mass profile;

Gravitational lensing (usually of more distant galaxies) can measure cluster masses without relying on observations of dynamics (e.g., velocity);

Generally, these three methods are in reasonable agreement that dark matter outweighs visible matter by approximately 5 to 1

Gravitational lensing

One of the consequences of general relativity is that massive objects (such as a cluster of galaxies) lying between a more distant source (such as a quasar) and an observer should act as a lens to bend the light from this source. The more massive an object, the more lensing is observed.

Although both dark matter and ordinary matter are matter, they do not behave in the same way. In particular, in the early universe, ordinary matter was ionized and interacted strongly with radiation via Thomson scattering. Dark matter does not interact directly with radiation, but it does affect the CMB by its gravitational potential (mainly on large scales), and by its effects on the density and velocity of ordinary matter. Ordinary and dark matter perturbations, therefore, evolve differently with time and leave different imprints on the cosmic microwave background (CMB).

In physical cosmology, structure formation is the formation of galaxies, galaxy clusters and larger structures from small early density fluctuations.

If there were only ordinary matter in the universe, there would not have been enough time for density perturbations to grow into the galaxies and clusters currently seen.

Dark matter provides a solution to this problem because it is unaffected by radiation. Therefore, its density perturbations can grow first. The resulting gravitational potential acts as an attractive potential well for ordinary matter collapsing later, speeding up the structure formation process. Gravitational potential wells allow structure formation.

If dark matter does not exist, then the next most likely explanation is that general relativity—the prevailing theory of gravity—is incorrect. The Bullet Cluster, the result of a recent collision of two galaxy clusters, provides a challenge for modified gravity theories because its apparent centre of mass is far displaced from the baryonic centre of mass. Standard dark matter theory can easily explain this observation, but modified gravity has a much harder time, especially since the observational evidence is model-independent.

Type Ia supernovae can be used as standard candles to measure extragalactic distances, which can in turn be used to measure how fast the universe has expanded in the past. The data indicates that the universe is expanding at an accelerating rate, the cause of which is usually ascribed to dark energy.

Sky surveys and baryon acoustic oscillations. Baryon acoustic oscillations (BAO) are fluctuations in the density of the visible baryonic matter (normal matter) of the universe on large scales.

Redshift-space distortions. Large galaxy redshift surveys may be used to make a three-dimensional map of the galaxy distribution.

Lyman-alpha forest

In astronomical spectroscopy, the Lyman-alpha forest is the sum of the absorption lines arising from the Lyman-alpha transition of neutral hydrogen in the spectra of distant galaxies and quasars. Lyman-alpha forest observations can also constrain cosmological models. These constraints agree with those obtained from WMAP data.

Constraining self-interacting dark matter with cluster mergers

Simulated analogs of merging galaxy clusters constrain the viewing angle

Exploring cosmic origins with CORE: Inflation

Dark matter facts

1. Dark matter is everywhere

2. It’s completely invisible

3. Dark matter binds galaxies together

4. It distorts the appearance of space

5. Scientists have created dark matter ‘maps’

6. We don’t know what dark matter is made of

7. Dark matter might not even exist

8. Spaceships are hunting for signs

9. Some countries have dark matter labs hidden deep, deep underground

10. We are edging closer to the truth about dark matter

US Cosmic Visions: New Ideas in Dark Matter 2017: Community Report

Dark matter laboratory searches

Underground laboratories


Direct WIMP searches

On earth – WIMP interactions in the detector should be:

▸ nuclear recoils

▸ single scatters, uniform throughout detector volume

▸ Spectral shape

Observables – Place detector on Earth; WIMPs interact (σ ≲ 1046 cm2) with the nucleus inducing a nuclear recoil of energy

Indirect WIMP searches

g’s: Cherenkov telescopes (surface), satellites (space)

e+e-: satellites (space)

n’s: neutrino ‘telescopes’ (underground/underwater)

Snomass report 2013

Several strategic goals have emerged from the Snowmass study for dark matter:

Execute a program with the U.S. as host that provides precision tests of the neutrino sector with an underground detector

Identify the particles that make up dark matter through complementary experiments deep underground, on the Earth’s surface, and in space, and determine the properties of the dark sector.

Map the evolution of the universe to reveal the origin of cosmic inflation, unravel the mystery of dark energy, and determine the ultimate fate of the cosmos.

Dark Matter nature

Two dark matter particles could annihilate to produce gamma rays (energy injection) or Standard Model particle-antiparticle pairs or if the dark matter particle is unstable, it could decay into standard model (or other) particles. These processes could be detected indirectly through an excess of gamma rays, antiprotons or positrons emanating from high density regions in our galaxy or others.

Neutrinophilic Axion-Like Dark Matter The axion-like particles (ALPs) are very good candidates of the cosmological dark matter, which can exist in many extensions of the standard model.

The axion is a hypothetical elementary particle postulated by the Peccei–Quinn theory in 1977 to resolve the strong CP problem in quantum chromodynamics (QCD). If axions exist and have low mass within a specific range, they are of interest as a possible component of cold dark matter.

Planck 2015 results XIII. Cosmological parameters

The Planck results offer powerful evidence in favour of simple inflationary models and show that the neutrino sector of the theory is consistent with the assumptions of the base ΛCDM model and that the dark energy is compatible with a cosmological constant.

The non-gravitational interactions of dark matter in colliding galaxy clusters

Constraints on Scattering of keV–TeV Dark Matter with Protons in the Early Universe

Many experiments seek to detect dark matter particles via their elastic scattering interactions with detector nuclei

CMR in the 2020s


The site of the future Simons Observatory, with the Simons Array, Atacama Cosmology Telescope and POLARBEAR.

The Simons Observatory will be located in the high Atacama Desert in Northern Chile inside the Chajnator Science Preserve, at an altitude of 5,200 meters. The Atacama Cosmology Telescope (ACT) and the Simons Array are currently making observations of the Cosmic Microwave Background. Their goals are to study how the universe began, what it is made of, and how it evolved to its current state. The Simons Observatory will add to these several new telescopes and new cameras with state of the art detector arrays. This has been made possible by a combined $40.1 million grant from the Simons Foundation and a number of participating universities (the UK is a partner).

The observatory has begun the design and development of a large (6 meter) diameter telescope. It is envisaged that one of its telescopes would be a precursor for an element of the proposed CMB-S4 array

CMB stage IV

The ‘Stage-4’ ground-based cosmic microwave background (CMB) experiment, CMB-S4, consisting of dedicated telescopes equipped with highly sensitive superconducting cameras operating at the South Pole, the high Chilean Atacama plateau, and possibly northern hemisphere sites, will provide a dramatic leap forward in our understanding of the fundamental nature of space and time and the evolution of the Universe. CMB-S4 will be designed to cross critical thresholds in testing inflation, determining the number and masses of the neutrinos, constraining possible new light relic particles, providing precise constraints on the nature of dark energy, and testing general relativity on large scales.

LiteBIRD ((Light) satellite for the studies of B-mode polarization and Inflation from cosmic background Radiation Detection) is a proposed small space observatory that aims to detect the footprint of the primordial gravitational wave on the cosmic microwave background (CMB) in a form of polarization pattern called B-mode.

Cosmologists predict two types of B-modes, the first generated during cosmic inflation shortly after the big bang, and the second generated by gravitational lensing at later times.

LiteBIRD and OKEANOS are the two finalists for Japan’s second Large

-Class Mission. OKEANOS is a solar sail spacecraft that would explore and possibly return Jupiter Trojan asteroid samples to Earth in the 2050s. The finalist is expected to be announced in December 2018. If selected for development, LiteBird is planned to be launched in the 2020s with an H3 launch vehicle for three years of observations at a Sun-Earth Lagrangian point L2.

In celestial mechanics, the Lagrangian points (also Lagrange points, L-points, or libration points) are positions in an orbital configuration of two large bodies, wherein a small object, affected only by the gravitational forces from the two larger objects, will maintain its position relative to them. The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centripetal force required to orbit at the same angular velocity (essentially, the speed of the orbit) and thus remain in the same relative position.

The science goal of LiteBIRD is to measure the CMB polarization over the entire sky, which allows testing the major single-field slow-roll inflation models experimentally.

Answers to questions

Dark ages occurred when atoms were forming but no stars yet to produce light. The only “light” came from the cosmic microwave background (CMB).

Dark energy could have produced neutrinos. It could be a force but not believed to be made of particles.

Dark energy causes things to accelerate away from each other.

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