# Is there any correlation between the Cosmic Microwave Background (CMB) and the distribution of distant galaxies?

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The Cosmic Microwave Background (CMB) is remarkably isotropic but does exhibit a distinct dipolar Doppler shift and also much smaller but measurable fluctuations in intensity and polarization. Presumably some of these fluctuations should carry over into the subsequent formation of early galaxies and other structures. To what extent is this expected and to what extent has this been observed?

The CMB Doppler shift is attributed to our local velocity with respect to the early universe. Is this Doppler-shift equally observed with respect to distant galaxies and diffuse starlight?

More particularly, is any of the fine structure in the CMB represented in the distribution or properties of the most ancient objects that can be observed optically (infrared)?

### CMB fluctuations

The CMB fluctuations are often analyzed through their power spectrum $$P(k)$$, which is a measure of the extent to which it is "clumpy" on a given scale $$ell$$, with corresponding wavenumber $$k = 2pi/ell$$. The origin of this power spectrum is laid in the very early early Universe, just after the Big Bang, and it is of utmost importance in cosmology, as it specifies how structure subsequently evolves.

Various observations help us constrain $$P(k)$$. For the early Universe, we use the CMB, while at later epochs, the large scale structure of galaxies and, even later, galaxy clusters are helpful. Moreover, absorption lines in the spectra of background quasars enable us to map out the structure via the so-called Lyman $$alpha$$ forest.

The figure below (from Norman 2008) show how a single cosmological model (from Tegmark et al. 2004) fit all epochs.

The power spectrum evolves with time, so to compare difference epochs, the figure shows $$P(k)$$ for the different observations extrapolated to the current epoch (i.e. today).

### CMB dipole

Observing the dipole in the CMB is relatively easy because, to within 1 in ~100,000, it is described by the same Planck temperature in all directions. This is not the case for any astrophysical sources, so measuring the dipole in galaxies is less straightforward. With large samples of galaxies it has nevertheless been attempted. For 1.2 million galaxies in the WISE catalogue, Rameez et al. (2018) find the dipole anisotropy to be consistent with that of the CMB.

## Correlation between large-scale galaxy structure and CMB fluctuations?

During a relatively non-technical astronomy seminar the other day, the speaker displayed the famous WMAP full-sky image as an aid to describing what the CMB is, the scale of its fluctuations, etc. This speaker mentioned that there are correlations between the higher-temperature regions on the map and regions of large-scale galaxy structure seen in deep-sky surveys.

I was surprised to hear this. My understanding is that CMB is an image of events currently about 14 billion light years away, while the observed large-scale filaments of galaxies are at approximately half that distance. I wouldn't have expected any density fluctuation 14 billion light years away to share any correlation with a density fluctuation 7 billion light years away.

When I asked, the speaker admitted to being "mostly a star guy" and continued with his excellent talk.

Is there actually a correlation between the warmer, denser regions of the CMB and the distribution of dense galaxy clusters? Is there a causal reason for these distant objects to be correlated with each other? Is there a lensing effect on the CMB temperature? Or is this "correlation" just an enticing-sounding mistake, slowly working its way into common knowledge?

## ESA Science & Technology - The effect of gravitational lensing on the Cosmic Microwave Background

Date: 01 September 2013
Satellite: Herschel
Depicts: Map of the projected density of matter as observed on a patch of the southern sky
Copyright: Image from G. Holder et al., 2013, The Astrophysical Journal Letters, 771, L16
Show in archive: true

This image shows the density of the large-scale distribution of matter in the Universe as seen projected along the line of sight and estimated using two different types of data.

The grey-scale map (shown in both panels) is based on observations of the Cosmic Microwave Background (CMB) performed with the National Science Foundation&aposs South Pole Telescope (SPT) at a frequency of 150 GHz. White areas indicate regions where the matter density is higher than average, whereas black areas indicate regions with lower than average density.

The colour map (plotted over the grey-scale one in the right panel) is based on observations of the Cosmic Infrared Background (CIB) obtained with ESA&aposs Herschel Space Observatory. The reconstruction is based on data collected at a wavelength of 500 microns using the SPIRE instrument on board Herschel. Red areas indicate regions where the matter density is higher than average, whereas blue areas indicate regions with lower than average density.

In contrast to the CMB, which is the diffuse light that permeated the very early Universe, the CIB is a cumulative background, and arose with the formation of stars and galaxies.

Gravitational lensing, the bending of light caused by massive objects, also affects the CMB as it propagates across the large-scale distribution of structure that started populating the Universe a few hundred million years after the Big Bang. Massive bodies, such as galaxies, galaxy clusters and the dark matter halos in which these are embedded, act as lenses and deflect the path of photons, causing distortions to the image of distant sources. For this reason, there is a very strong correlation between the gravitationally-lensed CMB and the CIB detected by Herschel, as the latter traces the lenses responsible for the deflection.

This correlation is apparent in the right panel, which shows the gravitational potential of the galaxies that are distorting the CMB estimated from the gravitationally-lensed CMB (grey-scale map) and from the distribution of galaxies (colour map).

Like ordinary glass lenses, a gravitational lens is most effective when located half way between the source of light and the observer. In a cosmological context, the galaxies that most contribute to lens the CMB are those located at a redshift z

2. These galaxies are best probed through the longest-wavelength band on the SPIRE instrument on Herschel, which is centred on 500 microns.

## The Event Horizon and Hubble Sphere

As described previously the Universe is expanding. The further away an object is the faster it is receding from us.

There is a clear relationship between the recessional velocity and the distance of a galaxy. This relationship is known as Hubble’s Law and is written as

• v is the velocity an object is moving away from us
• D is the object’s distance
• Ho is a constant known as the Hubble constant. If v is measured in kilometres per second and D is in megaparsecs (Mpc) (1 Mpc =3.26 million light years) then Ho is approximately 70 km/s per Mpc. The Hubble constant measures how fast the Universe is expanding. In reality, the Hubble constant changes over time (it is generally believed to be decreasing) and so is more correctly called the Hubble parameter H(t). The Hubble constant is the value of the Hubble parameter today. However, the current rate of change of the Hubble constant is very small. It will take hundreds of millions of years to fall by 1% from its current value.

Assuming that Hubble’s law is valid at all distances, at a separation from us of more than 4,300 Mpc (or 14 billion light years) a galaxy will be receding at a velocity greater than 300 000 km/s which is the speed of light. In which case any light it emitted today could never reach us. The Hubble sphere is an imaginary sphere centred on the Earth of radius 4,300 Mpc. If the Hubble parameter didn’t change over time, we could only see objects which emitted light today located inside the Hubble sphere.

The event horizon is the largest proper distance from us from which light emitted now will reach us at some point in the future.

• If an object lies closer than the event horizon then its light will reach us.
• If an object lies further away than the event horizon then it so far away that light emitted now will never reach us.

If the Hubble parameter didn’t vary over time, then the event horizon would simply be the radius of the Hubble sphere (14 billion light years). In most cosmological models, even though the Universe is expanding, the value of the Hubble constant is falling over time. The net effect of this is that the event horizon is larger than the radius of the Hubble sphere and gradually changes over time.

The graph below shows how the event horizon changes over time. In the current model of the Universe the event horizon will gradually increase with time but at a slower and slower rate reaching a maximum value of around 18 billion light years.

## THE REDSHIFT OF THE CMB AND THE TEMPERATURE OF THE UNIVERSE

Observations of the CMB tell us that it formed at a redshift of z = 1100. The observed temperature of the CMB today is 2.73 K.

By what factor has the Universe stretched since light from the CMB was emitted?

This means the Universe has stretched by a factor of 1101 since light from the CMB was emitted.

How much hotter was the temperature of the Universe when light from the CMB was emitted?

What was the temperature of the Universe when light from the CMB was emitted?

Now compare these temperatures and stretch factors to those for some of the objects you learned about previously.

## 3 Cross-Correlation Estimators: CAPS, CCF and CSMHW

As is well known (e.g. Peebles & Ratra 2003) for a flat universe where the dynamics are dominated by dark energy, we expect a positive correlation between the CMB and the galaxy distribution of the nearby Universe (z≲ 1 see, for instance, Afshordi 2004).

In this paper we apply three different techniques to study such a correlation and to compare the performance of each of them for the detection of the ISW effect. The three studied techniques are the CAPS, the CCF and the CSMHW, covering the harmonic, real and wavelet spaces. The CAPS has been already used, for instance, in Afshordi et al. (2004) to estimate the Sunyaev-Zel'dovich effect, the point sources and the ISW signals by cross-correlating the 2MASS infrared source catalogue and the WMAP. The CCF has been more extensively used, for instance in Boughn & Crittenden (2004) and Nolta et al. (2004). We have proposed a new technique based in wavelet space: the CSMHW.

## Planck reveals link between active galaxies and their dark matter environment

Gravitational deflection by quasar-hosting dark matter halos. Credit: David Tree, Professor Peter Richardson, Games and Visual Effects Research Lab, University of Hertfordshire

Scientists have used the tiny distortions imprinted on the cosmic microwave background by the gravity of matter throughout the universe, recorded by ESA's Planck satellite, to uncover the connection between the luminosity of quasars – the bright cores of active galaxies – and the mass of the much larger 'halos' of dark matter in which they sit. The result is an important confirmation for our understanding of how galaxies evolve across cosmic history.

Most galaxies in the universe are known to host supermassive black holes, with masses of millions to billions of times the Sun's mass, at their cores. The majority of these cosmic monsters are 'dormant', with little or no activity going on near them, but about one percent are classified as 'active', accreting matter from their surroundings at very intense rates. This accretion process causes material in the black hole's vicinity to shine brightly across the electromagnetic spectrum, making these active galaxies, or quasars, some of the brightest sources in the cosmos.

While it is still unclear what activates these black holes, switching on and off their phase of intense accretion, it is likely that quasars play an important role in regulating the evolution of galaxies across cosmic history. For this reason, it is crucial to understand the relationship between quasars, their host galaxies, and their environment on even larger scales.

In a recent study led by James Geach of the University of Hertfordshire, UK, scientists have combined data from ESA's Planck mission with the largest survey of quasars available to date to shed light on this fascinating topic.

According to the leading scenario of structure formation in the universe, galaxies take shape out of ordinary matter in the densest knots of the cosmic web – a filamentary network, made up primarily of the invisible dark matter, that pervades the cosmos. In turn, the complex distribution of both ordinary and dark matter originates from tiny fluctuations in the primordial universe, which leave an imprint in the cosmic microwave background (CMB), the most ancient light in the history of the universe.

The Planck satellite has been scanning the sky between 2009 and 2013 to create the most precise all-sky map of the CMB, enabling scientists to refine our knowledge of the age, expansion, history, and contents of the universe to unprecedented levels of accuracy.

Gravitational lensing of the cosmic microwave background. Credit: ESA and the Planck Collaboration

And there is more: as predicted by Albert Einstein's general theory of relativity, massive objects bend the fabric of spacetime around them, distorting the path of everything – even light – that passes nearby. This phenomenon, known as gravitational lensing, affects also Planck's measurements of the CMB, which carry an imprint of the large-scale distribution of matter that the most ancient cosmic light encountered along its way to the satellite.

"We know that galaxies form and evolve within an invisible 'scaffolding' of dark matter that we cannot directly observe, but we can exploit the gravitational lensing distortions imprinted on the cosmic microwave background to learn about the dark matter structures around galaxies," says James Geach.

Gravitational lensing distortions of the CMB are small, rearranging the CMB sky picture on scales of about 10 minutes of arc – equivalent to just one third the diameter of the full Moon. But many tiny deflections from across the sky can be combined, with the help of statistical methods, to obtain a stronger signal, piling up the data gathered around many quasars.

In their research, Geach and colleagues analysed the latest gravitational lensing map obtained by the Planck team, made public as part of the Planck Legacy Release in 2018, in combination with 200 000 quasars drawn from the largest sample ever compiled, the more than half-a-million quasars that comprise Data Release 14 of the Sloan Digital Sky Survey quasar catalogue.

"By combining the Planck data with such a large sample of quasars, we could measure the mass of the dark matter halos in which the quasar host galaxies are embedded, and investigate how this varies for quasars of different luminosity," says Geach.

The analysis hints that that the more luminous a quasar is, the more massive its halo of dark matter.

Gravitational deflection by quasar-hosting dark matter halos. Credit: David Tree, Professor Peter Richardson, Games and Visual Effects Research Lab, University of Hertfordshire

"This is compelling evidence that a correlation exists between the luminosity of a quasar, energy that is released in the immediate vicinity of a supermassive black hole – a region spanning perhaps a few light days – and the mass of the encompassing halo of dark matter and surrounding environment, which extends for tens of millions of light years around the quasar," Geach explains.

"We're using the cosmic microwave background as a kind of 'backlight' to the universe. That backlight has been gravitationally lensed by foreground matter, and so by correlating galaxies with the Planck lensing map, we have a new way to study galaxies and their evolution."

The finding supports theoretical models of quasar formation, which predict a correlation between quasar luminosity and halo mass, in particular for the most luminous quasars, where the black holes are accreting matter at close to the maximum rate.

The study focused on distant quasars that are observed as they were when the universe was about four billion years old – about one third of its current age of nearly 14 billion years. This is close to the peak era of supermassive black hole growth. In combination with deeper quasar surveys in the future, the Planck data could enable scientists to push these investigations to even earlier times in cosmic history, up to the epoch when the first quasars formed.

"This result shows the power of Planck's gravitational lensing measurements, which make it possible for us to measure the invisible structures of dark matter in which galaxies form and evolve," says Jan Tauber, Planck project scientist at ESA.

"The legacy of Planck is quite astonishing, with data that are being used for a much wider range of scientific applications than originally conceived for."

"The halo mass of optically-luminous quasars at z

1–2 measured via gravitational deflection of the cosmic microwave background" by J. E. Geach et al. is published in The Astrophysical Journal, Volume 874, Number 1.

## What is the Cosmic Microwave Background?

The early Universe was made of an opaque plasma, a hot sea of ionised gas. It cooled sufficiently for atoms to form about 380,000 years after the Big Bang and the light was free to travel through the Universe almost unimpeded. That light is what we measure today as the cosmic microwave background (CMB).

The Cosmic Microwave Background tells us about the state of the matter it last interacted with all that time ago. It’s essentially a baby picture of the Universe.

Our understanding of the CMB leapt forwards in the 1990s, with the Cosmic Background Explorer satellite discovering tiny fluctuations in an otherwise almost-uniform afterglow, followed by higher-resolution images from balloon-borne experiments.

These density variations have now been mapped over the whole sky, first by NASA’s Wilkinson Microwave Anisotrophy Probe and more recently, at higher resolution, by ESA’s Planck satellite.

Launched in 2009, Planck scanned the sky in nine wavelengths, or colours, of microwave light. It operated for over 4 years and, following its decommissioning in 2013, is now permanently switched off and in orbit around the Sun.

The wealth of data it collected has been pored over by the Planck team and released to the world for other astronomers and cosmologists to study.

It’s allowing insight into what cosmologists call the standard cosmological model, the picture of the composition and evolution of the Universe, starting with a primordial soup of matter and ending with the massive structures we see in the Universe today.

It’s thanks to gravity that the tiny temperature and density variations as small as 0.001% in the early Universe – pictured as a seemingly random hodge-podge of hot and cold spots in all-sky maps of the CMB (see at the very top of this article) – expanded and cooled over time to become enormous groups of galaxies arranged in a cosmic web.

### What is the Universe made of?

In a nutshell, the Universe comprises three main constituents:

• Only around 20% of the matter in the Universe is made of the same stuff we are – atoms, molecules and so on.
• The rest is dark matter, which only feels the force of gravity. But even all this matter only accounts for less than a third of the energy content of the Universe.
• The rest – about 68% – is dark energy, which acts as an anti-gravity force pushing everything apart. However, it has only dominated the Universe in the past few billion years.

One of the most counter-intuitive features of the standard model of cosmology is ‘inflation’: the Universe’s first tiny fraction of a second (about one thousand million billion trillionth), in which it expanded by a factor of around 100 thousand billion trillion.

This smoothed out the visible Universe, making it almost the same everywhere, but it also blew up tiny quantum fluctuations to a macroscopic scale. It’s these fluctuations that led to the density variations in the CMB.

While inflation seems like a theory of convenience, with little or no physical motivation, it does explain many of the observed properties of the Universe.

It’s the best theory we have at the moment, but without firm evidence we could simply be barking up the wrong tree, cosmologically speaking.

While there have been refinements to some of the numbers, the basic model of cosmology hasn’t really changed.

By combining Planck’s precise measurements of the CMB with other large-scale studies of the Universe, cosmologists have narrowed down the half-dozen or so basic parameters to the level of a few per cent, sometimes even less.

For instance, using the latest results from Planck the age of the Universe, calculated as 13.8 billion years, can be determined to an accuracy of less than 0.2%, equivalent to 30 million years.

### Cosmic interference

Unfortunately, for cosmologists at least, Earth is not completely isolated in the Universe, and the early Universe is not the only source of microwave light.

Material in our own Galaxy, within the Solar System, and even in different galaxies emits light and confuses the picture.

In fact, most of the sky is dominated by emissions from the Milky Way, so separating these ‘foregrounds’ is critical if we are to get a better view of the early Universe.

While the Cosmic Microwave Background looks the same at every wavelength, these other components have a specific range of colours, and so a multicolour view of the Universe can be split up into its constituent parts.

Planck’s most powerful tool is its nine-colour vision, which allows it to separate the cosmic afterglow from the galactic foregrounds with much greater reliability than previous missions, and refine our cosmological parameters more accurately than ever before.

We think of a beam of light as having a wavelength (or colour) and an intensity (or brightness). But in some situations light can also have a preferred orientation, called its polarisation.

### What is polarisation?

Light is a wave of oscillating electric and magnetic fields travelling through space. The properties of light we see tell us about the source that emitted it.

In astronomy, for example, the colour, or wavelength, of light tells us about the source’s temperature and the intensity of light tells us the density of the gas or dust that’s emitting it.

If the source has a preferred orientation, then there can also be a preferred direction to the electric and magnetic fields we see, and so a preferred orientation of the light. We call this a polarisation.

The effect can also be created when light is scattered off an object. For example, light reflected of a road is slightly polarised, which is why polarised sunglasses can block out some of the reflected glare.

Light in the early Universe was scattered off electrons and the electric field of the light caused the electrons to oscillate.

If the light had been the same everywhere the electrons would have oscillated in random directions, but the distribution of hot and cold regions in the Universe (which we see as hot and cold spots in the CMB) gave the electrons a preferred direction of oscillation, polarising the scattered light.

The particular structures and patterns in the CMB mean that the observed polarisation has a particular structure – a swirly pattern around hot spots, referred to as an ‘E-mode’.

The distortion of space by gravitational waves would manifest itself as a subtle distortion to the polarisation pattern, adding in a different pattern of swirls, called a ‘B-mode’.

Unfortunately, the signature of gravitational waves is much weaker than the normal CMB polarisation pattern. It’s also masked by other sources, such as gravitational lensing and polarised light from our Galaxy.

### What causes light to be polarised?

Light can become polarised if its source has a preferred direction. For example, the galactic magnetic field causes dust particles to be aligned in the same direction, and the light they emit also has this preferred orientation.

Similarly, electrons spiral around the magnetic field lines and emit light with orientations that also correspond to the magnetic field.

While these might be a nuisance to cosmologists, to astrophysicists they’re a fascinating insight into the structure of the Galaxy and the formation of stars.

Light from the early Universe is also slightly polarised, and the pattern of polarisation provides clues as to what happened at the beginning of time, as well as more recently in cosmic history.

There’s little benefit looking at one spot in the CMB, as we don’t know anything about the initial conditions at each point in the Universe. But by averaging them together, and looking at patterns over the sky, we can build up a statistical picture.

The polarisation, or orientation, of the Cosmic Microwave Background has a very particular pattern – it looks swirly. This isn’t that surprising, as the pattern of hot and cold regions on the sky leads to this swirliness.

### Multi-coloured Milky Way

Planck’s ability to observe at nine wavelengths makes its data particularly rich. Below are just four of its views of our Galaxy

Interstellar dust grains in our Galaxy glow at submillimetre wavelengths and can be aligned to the magnetic field to give this polarised view.

### Spinning dust

Dust particles can be set spinning in the galactic magnetic field at a rate of billions of rotations per second, emitting millimetre-wave light.

Electrons from within our Galaxy and beyond spiral round the magnetic field lines. As they do, they emit radio waves detected by Planck.

### Carbon monoxide

The coldest gas in our Galaxy can form molecules such as carbon monoxide. This shows the regions where cold gas is collapsing to form stars.

### Looking for patterns in the CMB

Cosmologists are hunting for a much fainter pattern in the orientation, hiding among the swirls.

These so-called ‘B-modes’, if seen in the early Universe, would provide evidence of gravitational waves propagating through the cosmos, originating from the massive expansion of space during inflation.

It is one of the only testable predictions that inflation makes, and finding them would be a huge discovery.

Unfortunately, the expected signal is incredibly weak and is easily masked by a huge number of other effects.

As well as polarised light coming from our Galaxy, the polarisation patterns are also distorted by gravitational lensing, which twists the orientation around and mixes up the patterns.

In March 2014 a team of cosmologists running telescopes at the South Pole reported that they may have found this B-mode signature in their maps of the sky.

The cosmological community, and the rest of astronomy, was buzzing with speculation.

The findings were made by an experiment called Background Imaging of Cosmic Extragalactic Polarization (BICEP2).

It focused on one patch of sky and while it had to compete with the obscuring effects of the Earth’s atmosphere it did so with a large number of detectors – in some ways making it more sensitive than Planck.

Its Achilles’ heel, however, was that BICEP2 only saw one colour of light, and so wasn’t able to confidently separate out the foreground interference.

The assumptions made were too optimistic, and a subsequent collaboration with Planck showed that much of what had been seen was due to dust in our Galaxy, not a signature of inflation.

That’s not the end of the story, though, as the same team are running more telescopes from Antarctica with a greater range of colours.

Combined with Planck’s maps of the galactic emissions, we may yet discover the cosmological B-modes.

There is a huge breadth in the scientific results possible with Planck’s data. Not only from our Galaxy and the early Universe, but also much of the stuff in-between.

When the first stars lit up, their intense light started stripping atoms of their electrons, re-ionising the Universe.

This ionised gas scattered light travelling through the Universe, altering its preferred orientation and subtly distorting our measurements of the CMB.

Planck’s latest results have established that this probably happened about 500 million years after the Big Bang. This is good news for astronomers, as the stars and galaxies that caused the effect should be visible to the James Webb Space Telescope when it is launched.

There is still much to learn from Planck’s observations. While almost all the data from the mission is now available, there is a lot left to understand.

As well as cosmological discoveries, we are just at the beginning of exploring the polarised images of the sky, and astronomers will undoubtedly make many new discoveries about our local neighbourhood.

Dr Chris North is Odgen Science Lecturer and STFC Public Engagement Fellow at Cardiff University. This article originally appeared in the May 2015 issue of BBC Sky at Night Magazine.

## Cosmic Microwave Background Anisotropies

AbstractCosmic microwave background (CMB) temperature anisotropies have and will continue to revolutionize our understanding of cosmology. 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. Future observations should test this model and measure its key cosmological parameters with unprecedented precision. The phenomenology and cosmological implications of the acoustic peaks are developed in detail. Beyond the peaks, the yet to be detected secondary anisotropies and polarization present opportunities to study the physics of inflation and the dark energy. The analysis techniques devised to extract cosmological information from voluminous CMB data sets are outlined, given their increasing importance in experimental cosmology as a whole.

## 2 WMAP And NVSS Data Sets

The two data sets that have been used in order to perform the CMB-nearby Universe cross-correlation are the WMAP ( Bennett et al. 2003a, and references therein) first-year data and the NVSS ( Condon et al. 1998).

### 2.1 WMAP data

The WMAP radiometers observe at five frequencies: 22.8, 33.0, 40.7, 60.8 and 93.5 GHz, having 1, 1, 2, 2 and 4 receivers per frequency band, respectively. All the papers, data and products generated by the WMAP team can be found at the Legacy Archive for Microwave Background Data Analysis (LAMBDA) website. 2 The WMAP maps are presented in the healpix scheme ( Górski et al. 2005) at the Nside= 512 resolution parameter. The WMAP team and other groups have proposed different CMB maps obtained from the WMAP data. In this work, we have used the map proposed by the WMAP team and already used by other groups ( Komatsu et al. 2003 Eriksen et al. 2004 Hansen, Banday & Górski 2004 Mukherjee & Wang 2004 Vielva et al. 2004 Cruz et al. 2005) for the study of the non-Gaussianity and the isotropy of the CMB. This map is generated (see Bennett et al. 2003b for details, and Vielva et al. 2004 for a summarized description) as the noise weighted combination of all the maps produced by the receivers in which the CMB is the dominant signal (40.7, 60.8 and 93.5 GHz), after subtraction of the foreground emission and application of the so-called ‘Kp0’ Galactic mask (defined by the WMAP team and where the brightest point sources are also masked). Whereas for the non-Gaussianity studies the resolution Nside= 256 was commonly chosen, in the present work we have degraded the combined, corrected and masked map down to Nside= 64 (pixel size ≈55 arcmin). The reason for this is that, as pointed out by Afshordi (2004), almost all the signal of the ISW effect is expected to be generated by structures with a scale larger than 2°. Hence, a WMAP resolution of around 1° is enough.

### 2.2 NVSS data

The NVSS catalogue covers around 80 per cent of the sky and has flux and polarization measurements for almost two million point sources with a minimum flux ≈2.5 mJy at 1.4 GHz. This catalogue has already been used for performing the correlation with the WMAP data ( Boughn & Crittenden 2002, 2004 Nolta et al. 2004). In this work, we have represented the point-source catalogue in the healpix scheme, also at the Nside= 64 resolution. Only sources above 2.5 mJy have been used, which represents 50 per cent completeness ( Condon et al. 1998). As pointed out by Boughn & Crittenden (2002) and Nolta et al. (2004), the mean density of point sources varies as a function of the declination. This systematic effect was corrected, by imposing that the mean of the galaxy density at each iso-latitude band is the same. The iso-latitude bands are defined taking into account the change in the rms noise levels in the NVSS (see fig. 10 of Condon et al. 1998). Alternative strategies (such as that proposed by Nolta et al. 2004) were also considered, proving that results are not sensitive to the particular correction procedure.

As said before, the NVSS catalogue covers around 80 per cent of the sky: for an equatorial declination lower than −50° there are no observations and, within the range −37° > Δ > −50° the coverage is not good enough. Hence, we only consider sources with an equatorial declination Δ≥ −37°. With all these constraints, we have a galaxy distribution map of ≈1 600 000 radio sources with an average number of 40.4 counts per pixel.

In Fig. 1 we have plotted the two maps to be analysed: WMAP (left) and NVSS (right). Both are in Galactic coordinates and the joint mask (Kp0 +Δ < −37°) has been applied. The residual monopole and dipole outside the mask have been removed.

Analysed WMAP and NVSS data after the application of the joint mask and the subtraction of the residual monopole and dipole. The maps are represented in the healpix scheme, with a resolution parameter Nside= 64 pixel size ≈55 arcmin).

Analysed WMAP and NVSS data after the application of the joint mask and the subtraction of the residual monopole and dipole. The maps are represented in the healpix scheme, with a resolution parameter Nside= 64 pixel size ≈55 arcmin).

### 2.3 Simulations

We have also performed realistic simulations in order to carry out the analysis. 1000 Gaussian simulations of the WMAP data have been performed, following the concordance cosmological model given by table 1 of Spergel et al. (2003)-Ωλ= 0.71, Ωm= 0.29, Ωb= 0.047, H0= 72, τ= 0.166, n= 0.99− and using the cmbfast code ( Seljak & Zaldarriaga 1996). For each realization, we have simulated all the WMAP data measured by the receivers at 40.7, 60.8 and 93.5 GHz, these have been convolved with the real beams provided at the LAMBDA website, the anisotropic WMAP noise was added, the maps were combined using a noise-weighted average, the combined map was degraded to the Nside= 64 resolution and the joint mask was applied. We have cross-correlated the 1000 CMB simulations with the NVSS data, in order to evaluate the significance level of the cross-correlation obtained from WMAP and NVSS. This is enough to quantify the covariance matrix associated with random cross-correlations, and we have checked that it is almost independent of the cosmological model used to simulate the CMB.

## Studying in more detail

The CMB is useful to scientists because it helps us learn how the early universe was formed. It is at a uniform temperature with only small fluctuations visible with precise telescopes. "By studying these fluctuations, cosmologists can learn about the origin of galaxies and large-scale structures of galaxies and they can measure the basic parameters of the Big Bang theory," NASA wrote.

While portions of the CMB were mapped in the ensuing decades after its discovery, the first space-based full-sky map came from NASA's Cosmic Background Explorer (COBE) mission, which launched in 1989 and ceased science operations in 1993. This &ldquobaby picture&rdquo of the universe, as NASA calls it, confirmed Big Bang theory predictions and also showed hints of cosmic structure that were not seen before. In 2006, the Nobel Prize in physics was awarded to COBE scientists John Mather at the NASA Goddard Space Flight Center, and George Smoot at the University of California, Berkeley.

A more detailed map came in 2003 courtesy of the Wilkinson Microwave Anisotropy Probe (WMAP), which launched in June 2001 and stopped collecting science data in 2010. The first picture pegged the universe's age at 13.7 billion years (a measurement since refined to 13.8 billion years) and also revealed a surprise: the oldest stars started shining about 200 million years after the Big Bang, far earlier than predicted.

Scientists followed up those results by studying the very early inflation stages of the universe (in the trillionth second after formation) and by giving more precise parameters on atom density, the universe's lumpiness and other properties of the universe shortly after it was formed. They also saw a strange asymmetry in average temperatures in both hemispheres of the sky, and a "cold spot" that was bigger than expected. The WMAP team received the 2018 Breakthrough Prize in Fundamental Physics for their work.

In 2013, data from the European Space Agency's Planck space telescope was released, showing the highest precision picture of the CMB yet. Scientists uncovered another mystery with this information: Fluctuations in the CMB at large angular scales did not match predictions. Planck also confirmed what WMAP saw in terms of the asymmetry and the cold spot. Planck's final data release in 2018 (the mission operated between 2009 and 2013) showed more proof that dark matter and dark energy &mdash mysterious forces that are likely behind the acceleration of the universe &mdash do seem to exist.

Other research efforts have attempted to look at different aspects of the CMB. One is determining types of polarization called E-modes (discovered by the Antarctica-based Degree Angular Scale Interferometer in 2002) and B-modes. B-modes can be produced from gravitational lensing of E-modes (this lensing was first seen by the South Pole Telescope in 2013) and gravitational waves (which were first observed in 2016 using the Advanced Laser Interferometer Gravitational Wave Observatory, or LIGO). In 2014, the Antarctic-based BICEP2 instrument was said to have found gravitational wave B-modes, but further observation (including work from Planck) showed these results were due to cosmic dust.

As of mid-2018, scientists are still looking for the signal that showed a brief period of fast universe expansion shortly after the Big Bang. At that time, the universe was getting bigger at a rate faster than the speed of light. If this happened, researchers suspect this should be visible in the CMB through a form of polarization. A study that year suggested that a glow from nanodiamonds creates a faint, but discernible, light that interferes with cosmic observations. Now that this glow is accounted for, future investigations could remove it to better look for the faint polarization in the CMB, study authors said at the time.