View source for Cosmic microwave background spectral distortions

{{short description|Fluctuations in the energy spectrum of the microwave background}}
'''CMB spectral distortions''' are tiny departures of the average [[Cosmic microwave background|cosmic microwave background (CMB)]] [[Spectral energy distribution|frequency spectrum]] from the predictions given by a perfect [[black body]]. They can be produced by a number of standard and non-standard processes occurring at the early stages of [[cosmic history]], and therefore allow us to probe the standard picture of cosmology. Importantly, the CMB frequency spectrum and its distortions should not be confused with the CMB anisotropy power spectrum, which relates to spatial fluctuations of the CMB temperature in different directions of the sky.<ref> {{cite magazine |last= McKee|first= Maggie|date= 30 June 2015|title= Why the Big Bang's Light May Have a Tilt |url= https://www.quantamagazine.org/the-case-for-spectral-distortions-in-the-cosmic-microwave-background-20150630/ |magazine= Quanta|publisher= Simons Foundation |access-date=7 July 2021}} </ref>
 
[[File:SD-epochs.pdf|thumb|right|upright=2.5|alt=Image to show how the distortions transition from a temperature redistribution to the mu distortion to the y distortion as time carries on, with the recombination radiation appearing around 280,000 years after the Big Bang. |Spectral distortions at different cosmological epochs. At very early times, with redshift <math>z>2\times10^6</math>, any injection of energy emerges as a ''temperature shift'' in the black body. As the age of the Universe increases, the processes that lead to thermalization of CMB distortions to a blackbody become less efficient (bremsstrahlung and double Compton scattering when <math>z<10^6</math>, Compton scattering when <math>z<10^4</math>). The spectral distortions also interplay with distinguished epochs of cosmic history such as [[reionization]], [[Recombination (cosmology)|recombination]] and [[Big Bang nucleosynthesis]] as shown. Specifically, during the recombination epoch (<math>\sim300,000</math> years after the Big Bang), the cosmological recombination lines are imprinted on the CMB as a result of non-equilibrium atomic processes during that era <ref name="Voyage2050"/>]]

== Overview == 
The energy spectrum of the CMB is extremely close to that of a perfect blackbody with a temperature of <math>2.7255 K</math>.<ref> {{cite journal|last=Mather|first= J.C.|display-authors=etal|date=1994|title= Measurement of the Cosmic Microwave Background Spectrum by the COBE FIRAS Instrument|journal=[[The Astrophysical Journal]]|volume=420|page=439|doi=10.1086/173574|bibcode= 1994ApJ...420..439M|doi-access=free}} </ref><ref> {{cite journal |last=Fixsen|first=D.J.|display-authors=etal|date=1996|title= The Cosmic Microwave Background Spectrum from the Full COBE FIRAS Data Set|journal=[[The Astrophysical Journal]]|volume=473|issue=2|page=576|doi=10.1086/178173|arxiv=astro-ph/9605054|bibcode=1996ApJ...473..576F|s2cid=18615251}} </ref> This is expected because in the early Universe matter and radiation are in [[thermal equilibrium]]. However, at [[redshift]]s <math>z<2\times10^6</math>, several mechanisms, both standard and non-standard, can modify the CMB spectrum and introduce departures from a blackbody spectrum. These departures are commonly referred to as CMB spectral distortions and mostly concern the average CMB spectrum across the full sky (i.e., the CMB monopole spectrum).

Spectral distortions are created by processes that drive matter and radiation out of equilibrium. One important scenario relates to spectral distortions from early energy injection, for instance, by decaying particles, primordial black hole evaporation or the dissipation of acoustic waves set up by inflation. In this process, the baryons heat up and transfer some of their excess energy to the ambient CMB photon bath via [[Compton scattering]]. Depending on the moment of injection, this causes a distortion, which can be characterized using so-called <math>\mu</math>- and <math>y</math>-type distortion spectra. The dimensionless <math>\mu</math> and <math>y</math>-parameters are a measure for the total amount of energy that was injected into the CMB. CMB spectral distortions therefore provide a powerful probe of early-universe physics and even deliver crude estimates for the epoch at which the injection occurred.<ref> {{cite journal|last1=Sunyaev|first1=R. A.|last2=Zeldovich|first2=Ya. B.|date=1969|title=Distortions of the Background Radiation Spectrum|journal=[[Nature (journal)|Nature]]|volume=223|issue=5207|page=721|doi=10.1038/223721a0|bibcode=1969Natur.223..721S|s2cid=4279379}} </ref> 

The current best observational limits set in the 1990s by [[Cosmic Background Explorer|COBE-satellite/FIRAS-instrument]] (COBE/FIRAS) are <math>|\mu|<9\times 10^{-5}</math> and <math>|y|<1.5\times 10^{-5}</math> at 95% confidence level. Within <math>\Lambda</math>CDM we expect <math>\mu\sim2\times 10^{-8}</math> and <math>y\sim{\rm few}\times10^{-6}</math>, signals that have come into reach of current-day technology (see {{section link||Experimental and observational challenges}}). Richer distortion signals, going beyond the classical <math>\mu</math> and <math>y</math> distortions, can be created by photon injection processes, relativistic electron distributions and during the gradual transition between the <math>\mu</math> and <math>y</math>-distortion eras. The cosmological recombination radiation (CRR) is a prime example within [[Lambda-CDM model|<math>\Lambda</math>CDM]] that is created by photon injection from the recombining hydrogen and helium [[Plasma (physics)|plasma]] around redshifts of <math>z\sim10^3-10^4</math>.

== History == 
The first considerations of spectral distortions to the CMB go back to the early days of CMB cosmology starting with the seminal papers of [[Yakov Zeldovich|Yakov B. Zeldovich]] and [[Rashid Sunyaev]] in 1969 and 1970. These works appeared just a few years after the first detection of the CMB by [[Arno Allan Penzias]] and [[Robert Woodrow Wilson]] and its interpretation as the echo of the [[Big Bang]] by [[Robert H. Dicke]] and his team in 1965.<ref> {{cite journal|last=Dicke|first=R. H.|display-authors=etal|title=Cosmic Black-Body Radiation|journal=[[The Astrophysical Journal]]|year=1965|volume=142|page=414|doi=10.1086/148306|bibcode=1965ApJ...142..414D}}</ref><ref>{{cite journal|last=Penzias|first=A.A.|author2=R. W. Wilson|title=A Measurement Of Excess Antenna Temperature At 4080 Mc/s|journal=Astrophysical Journal Letters|date=July 1965|pages=419–421|doi=10.1086/148307|volume = 142|bibcode=1965ApJ...142..419P|doi-access=free}}</ref> These findings constitute one of the most important pillars of Big Bang cosmology, which predicts the blackbody nature of the CMB. However, as shown by Zeldovich and Sunyaev, energy exchange with moving electrons can cause spectral distortions.

The pioneering analytical studies of Zeldovich and Sunyaev were later complemented by the numerical investigations of Illarionov and Sunyaev in the 1970s. These treated the thermalization problem including Compton scattering and the [[Bremsstrahlung]] process for a single release of energy. In 1982, the importance of [[Double Compton scattering|double Compton emission]] as a source of photons at high redshifts was recognized by Danese and de Zotti. Modern considerations of CMB spectral distortions started with the works of Burigana, Danese and de Zotti and Hu, Silk and Scott in the early 1990s. 

After COBE/FIRAS provided stringent limits on the CMB spectrum, essentially ruling out distortions at the level <math>\tfrac{\Delta I}{I} \sim 10^{-5}-10^{-4}</math>, the interest in CMB spectral distortions decreased. In 2011, PIXIE<ref name="PIXIE"> {{cite journal |last=Kogut|first=A.|display-authors=etal|date=2011|title=The Primordial Inflation Explorer (PIXIE): a nulling polarimeter for cosmic microwave background observations|journal=Journal of Cosmology and Astroparticle Physics|volume=2011|issue=7|page=25|doi=10.1088/1475-7516/2011/07/025|arxiv=1105.2044|bibcode=2011JCAP...07..025K|s2cid=119188059|url=https://iopscience.iop.org/article/10.1088/1475-7516/2011/07/025}}</ref> was proposed to [[NASA]] as a mid-Ex satellite mission, providing first strong motivation to revisit the theory of spectral distortions. Although no successor of COBE/FIRAS has been funded so far, this led to a renaissance of CMB spectral distortions with numerous theoretical studies and the design of novel experimental concepts <ref> {{cite journal |last=Kogut|first=A.|display-authors=etal|date=2020|title=CMB Spectral Distortions: Status and Prospects|journal=Bulletin of the American Astronomical Society|volume=51|issue=7|page=113|url=https://core.ac.uk/download/pdf/227725745.pdf|publisher= Astro 2020 White Paper|arxiv=1907.13195|bibcode=2019BAAS...51g.113K}} </ref>

[[File:Spectral distortions in the early universe new.gif|thumb|upright=2|left|alt=Movie showing how a smooth almost-inverse parabolic shape at very early redshifts bigger than 1 million compare to a distortion with a unique bumpy shape known as a mu distortion as redshifts get lower, until a redshift of 10 thousand, where this spline gets much sharper and we call this a y distortion. Over time, this shape becomes more pronounced as the energy injection epoch changes from early times to late times in the Universe's growth| The spectral distortion in the cosmic microwave background (CMB) looks different depending on the moment in the universe's history where this black body was modified. At very early times where <math>z>10^6</math>, any injection of energy emerges as a ''temperature shift'' in the black body. If the energy injection is later (still very early in the Universe's history), we see the shape of the <math>\mu</math>- distortion, whereas we can see a sharper fluctuation at later times, associated with <math>y</math>-distortion. Here some energy is injected into the CMB at time defined by the redshift <math>z_h</math> with the resultant distortion being plotted.]]

== Thermalisation physics  ==
In the cosmological 'thermalization problem', three main eras are distinguished: the thermalization or temperature-era, the <math>\mu</math>-era and the <math>y</math>-era, each with slightly different physical conditions due to the change in the density and temperature of particles caused by the Hubble expansion.

=== Thermalization era ===
In the very early stages of cosmic history (up until a few months after the [[Big Bang]]), photons and baryons<ref> In the language of cosmologists, the term "baryons" includes the electrons even if the latter are leptons in particle physics </ref> are efficiently coupled by scattering processes and, therefore, are in full thermodynamic equilibrium. Energy that is injected into the medium is rapidly redistributed among the photons, mainly by Compton scattering, while the photon [[number density]] is adjusted by photon non-conserving processes, such as double Compton and thermal Bremsstrahlung. This allows the photon field to quickly relax back to a [[Planckian distribution]], even if for a very short phase a spectral distortion appears. Observations today cannot tell the difference in this case, as there is no independent cosmological prediction for the CMB monopole temperature.<ref> One exception is when energy release occurs in a narrow window after the era of Big Bang Nucleosynthesis but before the <math>\mu</math>-era. In this case one can in principle use measurements of the light element abundances to deduce an independent CMB monopole measurement. By combining the two, a constraint on the energy release can be derived </ref> This regime is frequently referred to as the thermalization or temperature era and ends at redshift <math>z\sim2\times10^{6}</math>.

===  {{math|''μ''}}-distortion era === 
At redshifts between <math>5\times10^4</math> and <math>2\times10^6</math>, efficient energy exchange through Compton scattering continues to establish kinetic equilibrium between matter and radiation, but photon number changing processes stop being efficient. Since the photon number density is conserved but the energy density is modified, photons gain an effective non-zero chemical potential, acquiring a [[Bose–Einstein statistics|Bose-Einstein]] distribution. This distinct type of distortion is called <math>\mu</math>-distortion after the chemical potential known from standard thermodynamics.<ref>The <math>\mu</math>-parameter is normalized to the electron temperature, which makes it dimensionless, and it has the opposite sign convention</ref> The value for the chemical potential can be estimated by combining the photon energy density and number density constraints from before and after the energy injection. This yields the well-known expression,<ref> {{cite journal|last1=Sunyaev|first1=R. A.|last2=Zeldovich|first2=Ya. B.|title=Small-Scale Fluctuations of Relic Radiation|journal=[[Astrophysics and Space Science]]|year=1970|volume=7|issue=1|page=3|doi=10.1007/BF00653471|bibcode=1970Ap&SS...7....3S|s2cid=117050217}} </ref> 

<math display="block">\mu \sim 1.4\; \frac{\Delta \rho}{\rho},</math> 
where <math>\tfrac{\Delta \rho}{\rho}</math> determines the total energy that is injected into the CMB photon field. With respect to the equilibrium blackbody spectrum, the <math>\mu</math>-distortion is characterized by a deficit of photons at low frequencies and an increment at high frequencies. The distortion changes sign at a frequency of <math>\nu\sim130 {\rm GHz}</math>, allowing us to distinguish it observationally from the <math>y</math>-type distortion.

<math>\mu</math>-distortion signals can be created by decaying particles, evaporating primordial black holes, primordial magnetic fields and other non-standard physics examples. Within <math>\Lambda</math>CDM cosmology, the adiabatic cooling of matter and dissipation of acoustic waves set up by inflation cause a <math>\mu</math>-distortion with <math>\mu\sim2\times10^{-8}</math>. This signal can be used as a powerful test for inflation, as it is sensitive to the amplitude of density fluctuations at scales corresponding to physical scales of <math>\lambda\sim0.6 \,{\rm kpc}</math> (i.e., dwarf galaxies). By combining COBE’s measurements of the large-scale CMB anisotropies with the <math>\mu</math>-distortion constraint, the first limits on the small-scale power spectrum could be obtained well-before direct measurements became possible <ref> {{cite journal|last=Hu|first=Wayne|display-authors=etal|title=Power spectrum constraints from spectral distortions in the cosmic microwave background|journal=[[The Astrophysical Journal]]|volume=430|page=L5|year=1994|doi=10.1086/187424|arxiv=astro-ph/9402045|bibcode=1994ApJ...430L...5H|s2cid=16628087}} </ref>

=== {{math|''y''}}-distortion era ===	 	 	
At redshifts <math>z\lesssim5\times10^4</math>, also Compton scattering becomes inefficient. The plasma has a temperature of <math>T<10^5 {\rm K}</math>, such that CMB photons are boosted via non-relativistic Compton scattering, giving rise to a <math>y</math>-distortion. Again, by considering the total energetics of the problem and using photon number conservation, one can obtain the estimate<ref name="ZS69"> {{cite journal|last1=Zeldovich|first1=Ya. B.|last2=Sunyaev|first2=R. A.|date=1969|title=The Interaction of Matter and Radiation in a Hot-Model Universe|journal=[[Astrophysics and Space Science]]|volume=4|issue=3|page=301|doi=10.1007/BF00661821|bibcode=1969Ap&SS...4..301Z|s2cid=118207102}} </ref>

<math display="block">y \sim \frac{1}{4}\; \frac{\Delta \rho}{\rho}.</math>
The name for the <math>y</math>-distortion simply stems from the choice of dimensionless variables in the seminal paper of Zeldovich and Sunyaev, 1969.<ref name="ZS69"/> There, the energy injection caused by the hot electrons residing inside clusters of galaxies was considered and the associated effect is more commonly referred to as the thermal [[Sunyaev-Zeldovich effect|Sunyaev-Zeldovich (SZ) effect]]. 
Like for the <math>\mu</math>-distortion, in principle many non-standard physics examples can cause <math>y</math>-type distortions. However, the largest contribution to the all-sky <math>y</math>-distortion stems from the cumulative cluster SZ signal, which provides a way to constrain the amount of hot gas in the Universe. While at <math>z<10^4</math>, the cosmic plasma on average has a low temperature, electrons inside galaxy clusters can reach temperatures of a few keV. In this case, the scattering electrons can have speeds of <math>v\sim0.1 c</math>, such that relativistic corrections to the Compton process become relevant. These relativistic corrections carry information of electron temperatures which can be used as a measure for the cluster energetics.<ref> {{cite journal|last=Hill|first=J. C.|title=The Sunyaev-Zel'dovich Effect and Large-Scale Structure|year=2015|arxiv=1510.06237}}</ref>

=== Beyond {{math|''μ''}} and {{math|''y''}} distortions ===
The classical studies mainly considered [[Kerma (physics)|energy release]] (i.e., heating) as a source of distortions. However, recent work has shown that richer signals can be created by direct photon injection and non-thermal electron populations, both processes that appear in connection with decaying or annihilating particles. Similarly, it was demonstrated that the transition between the <math>\mu</math> and <math>y</math>-eras is more gradual and that the distortion shape is not simply given by a sum of <math>\mu</math>- and <math>y</math>. All these effects could allow us to differentiate observationally between a wide range of scenarios, as additional time-dependent information can be extracted.

== Cosmological recombination radiation (CRR) == 
About 280,000 years after the Big Bang, electrons and protons became bound into electrically neutral atoms as the Universe expanded. In cosmology, this is known as recombination and preludes the [[Decoupling (cosmology)|decoupling of the CMB photons]] from matter before they free stream throughout the Universe around 380,000 years after the Big Bang. Within the energy levels of hydrogen and helium atoms, various interactions take place, both collisional and radiative. The line emission arising from these processes is injected into the CMB, showing as small distortions to the CMB blackbody commonly referred to as the cosmological recombination radiation (CRR). The specific spectral shape of this distortion is directly related to the redshift at which this emission takes place, freezing the distortion in time over the microwave frequency bands. Since the distortion signal arises from the hydrogen and two helium recombination eras, this gives us a unique probe of the pre-recombination Universe that allows us to peek behind the last scattering surface that we observe using the CMB anisotropies.<ref name="Voyage2050"> {{cite journal|last=Chluba|first=J.|display-authors=etal|title=New Horizons in Cosmology with Spectral Distortions of the Cosmic Microwave Background|journal=Voyage 2050 Proposals|year=2021|volume=51|issue=3|pages=1515–1554|doi=10.1007/s10686-021-09729-5|arxiv=1909.01593|bibcode=2021ExA....51.1515C|s2cid=202539910|url=https://www.cosmos.esa.int/documents/1866264/3219248/ChlubaJ_Voyage-2050-SDWP-main.pdf/b91871ad-75c4-5b75-3300-049682255629?t=1565184628801}} </ref> It gives us a unique way to constrain the primordial amount of helium in the early Universe, before recombination, and measure the early expansion rate.

== Experimental and observational challenges ==
The expected [[Lambda-CDM model|Lambda-CDM]] (LCDM) distortion signals are small – The largest distortion, arising from the cumulative flux of all hot gas in the Universe, has an amplitude that is about one order of magnitude below the limits of COBE/FIRAS. While this is considered to be an ‘easy’ target, the cosmological recombination radiation (CRR), as the smallest expected signal, has an amplitude that is another factor of <math>10^3</math> smaller. All LCDM distortions are furthermore obscured by large Galactic and extragalactic foreground emissions (e.g., dust, synchrotron and free-free emission, cosmic infrared background), and for observations from the ground or balloons, atmospheric emission poses another hurdle to overcome. 

A detection of the LCDM distortions therefore requires novel experimental approaches that provide unprecedented sensitivity, spectral coverage, control of systematics and the capabilities to accurately remove foregrounds. Building on the design of FIRAS and experience with [[ARCADE]], this has led to several spectrometer concepts to observe from space (PIXIE, PRISM, PRISTINE, SuperPIXIE and Voyage2050),<ref name="PIXIE"/><ref name="Voyage2050"/> balloon (BISOU) and the ground (APSERa and Cosmo at Dome-C, TMS at [[Teide Observatory]]). These are all designed to reach important milestones towards a detection of CMB distortions. As an ultimate frontier, a full characterization and exploitation of the cosmological recombination signal could be achieved by using a coordinated international experimental campaign, potentially including an observatory on the moon <ref> {{cite journal|last=Silk|first=J.|title=The limits of cosmology: role of the Moon|year=2020|doi=10.1098/rsta.2019.0561|journal=Phil. Trans. R. Soc. A.|volume=379|issue=2188|pmid=33222642|arxiv=2011.04671|s2cid=226289839|url=https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2019.0561}} </ref>

In June 2021, the [[European Space Agency]] unveiled its plans for the future L-class missions as part of ''Voyage 2050'' with a chance for ''`high precision spectroscopy`'' for the new ''early universe'' part of their strategy, opening the door for spectral distortions telescopes for the future.<ref>{{cite press release
| author       = ESA
| date         = 11 June 2021
| title        = Voyage 2050 sets sail: ESA chooses future science mission themes
| url          = https://www.esa.int/Science_Exploration/Space_Science/Voyage_2050_sets_sail_ESA_chooses_future_science_mission_themes
| access-date  = 7 July 2021
}}</ref>

==See also==
{{cmn|
* [[Bremsstrahlung]]
* [[Compton scattering]]
* [[Cosmic Background Explorer]]
* [[Cosmic Background Imager]]
* [[Cosmic microwave background]]
* {{annotated link|Cosmological perturbation theory}}
* [[Degree Angular Scale Interferometer]]
* [[European Space Agency Science Programme]]
* {{annotated link|Gravitational wave background}}
* [[List of cosmic microwave background experiments]]
* {{annotated link|Observational cosmology}}
* [[Primordial fluctuations]]
* [[Recombination (cosmology)]]
* [[Sachs–Wolfe effect]]
* [[Sunyaev–Zeldovich effect]]
* [[Redshift-space distortions]]
}}

== References ==

{{reflist}}

{{Portal bar|Physics|Astronomy|Stars|Spaceflight|Outer space|Solar System|Science}}

[[Category:Cosmic background radiation]]<!-- cat. has  leftside : for draft -->