Dark Energy: is it `just' Einstein's Cosmological Constant Lambda?
DDark Energy: is it ‘just’ Einstein’s Cosmological Constant Λ?
Ofer Lahav a a Department of Physics & Astronomy, University College London, Gower Street, LondonWC1E 6BT, UK
ARTICLE HISTORY
Compiled September 23, 2020
ABSTRACT
The Cosmological Constant Λ, a concept introduced by Einstein in 1917, has beenwith us ever since in different variants and incarnations, including the broader con-cept of ‘Dark Energy’. Current observations are consistent with a value of Λ corre-sponding to about present-epoch 70% of the critical density of the Universe. This iscausing the speeding up (acceleration) of the expansion of the Universe over the past6 billion years, a discovery recognised by the 2011 Nobel Prize in Physics. Coupledwith the flatness of the Universe and the amount of 30% matter (5% baryonic and25% ‘Cold Dark Matter’), this forms the so-called ‘ΛCDM standard model’, whichhas survived many observational tests over about 30 years. However, there are cur-rently indications of inconsistencies (‘tensions’ ) within ΛCDM on different valuesof the Hubble Constant and the clumpiness factor. Also, time variation of DarkEnergy and slight deviations from General Relativity are not ruled out yet. Severalgrand projects are underway to test ΛCDM further and to estimate the cosmologicalparameters to sub-percent level. If ΛCDM will remain the standard model, then theball is back in the theoreticians’ court, to explain the physical meaning of Λ. Is Λ analteration to the geometry of the Universe, or the energy of the vacuum? Or maybeit is something different, that manifests a yet unknown higher-level theory?
KEYWORDS
Cosmology, Dark Matter, Cosmological Constant, Dark Energy, galaxy surveys
1. Introduction
It is well established that the Universe started in a Big Bang about 13.8 billion yearsago. The expansion of the Universe is a natural outcome of Einstein’s theory GeneralRelativity, for particular the mass/energy contents of the Universe, but it is still amystery what the Universe is actually made of. The expansion can be described bya single function of time, the cosmic scale factor, a ( t ), which determines how thedistances between galaxies change in time. It can also be expressed as a = 1 / (1 + z ),where z is the cosmological redshift. The rate of expansion is defined as H ( t ) =˙ a/a (dot indicates derivative with respect to time), where the present-epoch value isthe Hubble Constant H . Recent observations indicate that the universe is not onlyexpanding - it is also accelerating at the present epoch, ¨ a >
0. But what is acceleratingthe Universe? The composition of the Universe, agreed by most astronomers, is a ratherbizarre mixture: baryonic (ordinary) matter, Cold Dark Matter, massive neutrinos and
CONTACT Ofer Lahav. Email: [email protected] a r X i v : . [ phy s i c s . pop - ph ] S e p ark Energy. Dark Energy is a broad term, which includes the Cosmological ConstantΛ, a concept born in 1917, in Einstein’s famous article [1]. It is accepted that about70% of the present-epoch Universe is made of ‘Dark Energy’, a mysterious substancewhich causes the cosmic acceleration. A further 25% of the Universe is made frominvisible ‘Cold Dark Matter’ that can only be detected through its gravitational effects,with the ordinary atomic matter making up the remaining 5%, and an additionaltiny contribution from massive neutrinos, with its exact value still unknown Thiscomposition is illustrated in Figure 1, based on the Planck Collaboration results [2].This “Λ + Cold Dark Matter”(ΛCDM) paradigm and its extensions pose fundamentalquestions about the origins of the Universe. If Dark Matter and Dark Energy trulyexist, we must understand their nature. Alternatively, General Relativity and relatedassumptions may need radical modifications. These topics have been flagged as keyproblems by researchers and by advisory panels around the world, and significantfunding has been allocated towards large surveys of Dark Energy. Commonly, DarkEnergy is quantified by an equation of state parameter w (the ratio of pressure todensity, see below). The case where w = − w may vary with cosmic time. Essentially, w affects boththe geometry of the Universe and the growth rate of structures. These effects can beobserved via a range of cosmological probes, including the CMB, Supernovae TypeIa, galaxy clustering, clusters of galaxies, and weak gravitational lensing. The Type IaSupernova surveys [3,4] revealed that our Universe is not only expanding but is alsoaccelerating in its expansion. The 2011 Nobel Prize in Physics was awarded for thisremarkable discovery. Evidence for cosmic acceleration was actually noted even earlierin the 1990s, when galaxy clustering measurements [5] indicated a low matter densityparameter. This suggested the possibility of a Cosmological Constant when combinedwith the assumption that space is ‘flat’ (e.g. two light beams would travel in parallellines). Flatness (zero curvature) is predicted by Inflation, a theory of exponentialexpansion in the early Universe, in a tiny fraction of a second just after the Big Bang.The flatness of the universe was later confirmed by CMB anisotropy measurements.We start this review by providing some background and history on Λ in GeneralRelativity and on the concept of Dark Energy and a Newtonian version for the Λ term(Section 2). Then we summarise the modern probes of Dark Energy (Section 3) andthe landscape of galaxy surveys (Section 4), before presenting results from the DarkEnergy Survey (Section 5) and discussing tension in the Hubble Constant (Section 6).We close by considering the outlook for Dark Energy research (Section 7).
2. Background: a brief history of Dark Energy
Over a century ago Einstein added the Cosmological Constant Λ to his equations [1](see Figure 2). It is a complicated equation, but we can think of it in a symbolic wayas: G + Λ = T, (1)where G represents the gravity in space-time, and T (called the ‘energy-momentumtensor’) describes the contents of the Universe. One way to interpret this equation isin the words of John Archibald Wheeler: ‘Matter tells spacetime how to curve; curvedspacetime tells matter how to move.’ Einstein added Λ primarily as a way of gener-ating a static universe, which neither expands nor contracts. With Edwin Hubble’s2 ark Energy 68.9% Dark Matter26.2%Baryons4.9% Figure 1.
The relative amounts of the different constituents of the Universe: Baryonic (ordinary) matter,Dark Matter and Dark Energy. The plot is based on the results from the Planck collaboration [2]. observations of the expansion of the universe a few years later it seemed to Einsteinthat the Λ term was not needed anymore, and he blamed himself that inventing Λwas the ‘blunder of his life’ . One may argue that Einstein ‘missed opportunities’in a number of ways: to predict the expansion/contraction of the Universe withoutΛ, to notice that his static solution is unstable, so a Universe with Λ would also ex-pand/contract, and to view Λ as a free parameter, which could also lead for exampleto an accelerating Universe. But this 1917 study was probably the first paper on rela-tivistic cosmology, and the first time the cosmological constant Λ was proposed. DarkEnergy, an extension of the Λ, is now the focus of projects worth billions of dollars,with hundreds of scientists spending significant parts of their careers on this problem.While Einstein abandoned Λ, his friend Arthur Stanley Eddington (Plumian Profes-sor at Cambridge; see Figure 3 ) was actually very keen on the Cosmological Constant,considering it as the possible source of expansion. In his popular book ‘The ExpandingUniverse’ [7] he stated: “I am a detective in search of a criminal - the CosmologicalConstant. I know he exists, but I do not know his appearance, for instance I do notknow if he is a little man or a tall man....”.The big conceptual question is if Λ should be on the left hand side of equation(1), as part of the curvature (as originally introduced by Einstein), or on the righthand side, as part of the energy-momentum tensor T , for example associated with thevacuum energy Λ = 8 πGρ vac /c . In fact, oddly, Quantum field theory predicts forthe amount of vacuum energy 10 times the observed value; that is a challenging For a historical review of Einstein’s 1917 paper see [6]. It seems non-intuitive that the vacuum contains energy. But recall in Quantum Mechanics even the groundstate of a simple harmonic oscillator has energy, E = hν . Summing up the contributions from many harmonicsoscillators (up to a certain energy cutoff) gives rise to vacuum energy. Vacuum energy can also be viewed interms of ‘virtual particles’ (also known as ‘vacuum fluctuations’), which are created and destroyed out of thevacuum. Vacuum energy has been verified experimentally in the lab by the Casimir effect. Figure 2.
The first page of Einstein’s 1917 paper [1] on “Cosmological considerations in the General Theoryof Relativity” (in German). igure 3. Arthur Eddington (right) and Albert Einstein at the Cambridge Observatory (now part of theInstitute of Astronomy), in 1930. Einstein introduced the Cosmological Constant Λ in 1917, but then deserted it,while Eddington favoured keeping Λ as part of General Relativity. Credit: Royal Astronomical Society/SciencePhoto Library w of Dark Energy, defined as the ratio of its pressure p to its energydensity ρ , w = p/ρc . (2)The Dark Energy density varies with the scale factor a ( t ) as ρ ∝ a − w ) . (3)For vacuum energy, the equation of state parameter is w = − ρ m ∝ a − , so the matterand Λ densities were equal at z eq = (Ω Λ / Ω m ) / − ≈ . , (4)where the density parameter for Λ is normalised by the Hubble Constant H , Ω Λ ≡ Λ / (3 H ) = 0 .
7, and the matter density ρ m is scaled by the critical density Ω m ≡ ρ m /ρ c = 0 .
3. The acceleration actually started earlier, at z acc = (2Ω Λ / Ω m ) / − ≈ . . (5)We note that (1 + z acc ) / (1 + z eq ) = 2 / ≈ .
26, regardless of the values of Ω Λ and Ω m .In the Newtonian limit of General Relativity the equation of motion looks familiar: d rdt = − GMr + c r . (6)In addition to the famous inverse square law, the second term is a linear force, thatsurprisingly was already discussed by Newton in Principia (see e.g. [9] for review).An intuitive Newtonian way to think about the Λ term is as a repulsive linear force,opposing the inverse squared gravitational force. It is interesting that such a forcecan be noticeable on the Mpc scale . For example, the Λ-force affects the accelerationof the Milky Way and Andromeda towards each other (see e.g. [10–12]). For furtherdiscussion on Dark Energy and Cosmological Parameters see reviews in [13–16].
3. Primary probes of Dark Energy
Observational Cosmology provides tests of Einstein’s General Relativity and alter-native theories. The subject has developed in recent decades from ‘metaphysics’ to ahighly quantitative discipline, as recognised by the award of the Nobel Prize in Physics The critical density is defined as ρ c ≡ H / πG . For Hubble constant H = 70 km s − Mpc − it is ρ c ≈ . × − kg m − . This is a very low density, just over five protons per cubic metre of space. Mpc stands for Megaparsec, which is a distance of million parsecs, equivalent to about 3.26 million lightyears, or 3 . × kilometers. .0 0.2 0.4 0.6 0.8 1.0 redshift z n o r m a li z e d d e n s i t i t e s Constant Dark Energy densityDark + Baryonic Matter density
Figure 4.
The variation of densities with cosmic time: matter ρ m ∝ a − and a constant Dark Energy ρ Λ corresponding to w = − z = 0 indicate the present approximately observeddensity parameters, Ω Λ = 0 . m = 0 .
3. As discussed in the text, the crossing of the two curves, when thetwo densities were equal, happened at z eq ≈ .
30 (about 3.5 billion years ago, for Hubble Constant H = 70km s − Mpc), while acceleration started earlier (marked by the rightmost dot), at z acc ≈ .
64 (about 6 billionyears ago). For reference, our Solar System formed about 4.5 billion years ago.
Figure 5.
Supernovae Type Ia as standard candles: Hubble diagram for the Dark Energy Survey (DES)supernova (SN) 3YR sample (red) and other low-redshift data (orange). Top: Distance modulus ( µ ) frombinned data (black bars) and for each SN (red, orange circles). The dashed gray line shows the best-fit model,while the green and blue dotted lines show models with no dark energy and matter densities Ω m = 0 . . Figure 6.
Baryonic Acoustic Oscillations (BAO): Galaxy clustering as a probe of the geometry of the universe.The same acoustic features (BAO) seen in the CMB can be observed in the distribution of galaxies, providinga standard cosmological ruler. Credit: Euclid collaboration.
Exploding stars called Supernovae Type Ia are understood to originate in binary sys-tems in which at least one of the two companion stars is a white dwarf. A Supernovabecomes as bright as an entire galaxy of tens of billions of stars and then begins to fadeaway within a matter of weeks. Supernovae Type Ia are observed to all have nearlythe same absolute luminosity when they reach their peak light (after some calibra-tion corrections), hence the concept of ‘standard candles’. By comparing the apparentbrightnesses of different Supernovae we can determine their relative distances. We canalso measure the redshift to the Supernova (or its host galaxy), and look at the re-lation of distance and redshift (the so-called Hubble diagram). This relation dependson the geometry of the Universe, and hence on the amounts of Dark Matter and DarkEnergy. This method led to the discovery that the Universe is accelerating at present[3,4], which was recognised by the award of the Nobel Prize in Physics 2011. See Figure5 for recent results.
Another major cosmological probe is the spatial clustering of galaxies (deviation froma random uniform spatial distribution). What is useful as a standard ruler is a fea-ture called baryon acoustic oscillations (BAO), first discovered by the 2dF and SDSSteams [18,19]. Until approximately 370,000 years after the Big Bang, the Universe wasa sea of colliding protons, electrons, and photons, forming an opaque, ionized plasma.Gravity pulled the protons and electrons together, while the pressure of the energeticphotons acted to push them apart. This competition between gravity and pressurecreated a series of sound waves, ‘acoustic oscillations’, in the plasma. As the Universeexpanded and cooled, the photons lost energy and became less effective at ionizingatoms, until gradually all the protons and electrons combined to form neutral hydro-gen. Thereafter, the Universe became transparent to photons, which travelled withoutfurther interacting with matter. The distance travelled by the sound waves up to thatpoint became imprinted in the spatial distribution of matter, which means that todaythere is a slight tendency for pairs of galaxies to be separated by about 480 millionlight years. Comparing this scale to how much galaxies appear to be separated on thesky, i.e., their angular separation, allows us to work out how far away they are. Com-paring this distance to the redshift of their light, just as we do for Supernovae, tells usabout the expansion history of the Universe. The same acoustic features (BAO) areseen in the CMB. See an illustration in Figure 6. There is additional useful informa-tion in galaxy clustering, in particular in ‘redshift distortion’ (the deviation of galaxymotions from the smooth Hubble flow) and in the entire statistical fluctuations atdifferent physical scales. There are other important probes of the mass distribution, inparticular ‘Lyman- α clouds’ (inferred from spectra of Quasars) and peculiar velocities(deviations from the smooth Hubble flow).9 igure 7. Gravitational Lensing: A schematic diagram showing the effects of gravitational lensing. Theobserver (on the right hand side) would see distorted images by the intervening clumpy distribution of darkmatter. Credit: Michael Sachs under Creative Commons.
Galaxy clusters, first catalogued by George Abell and others, are peaks in the ‘cos-mic web’ of the galaxy distribution. Examples of galaxy clusters are shown in twoinsets in Figure 8. As the geometry and growth of structure depend on Dark Energy,counting the number of galaxy clusters of a given mass within a given volume of theUniverse provides another cosmological test. The main challenge when interpretingcluster counts is that the mass of a cluster (which is mostly Dark Matter) is not di-rectly observable, so we have to calibrate mass-observable relations using techniquessuch as the Sunyaev-Zel’dovich effect, X-ray emission, and calibration by weak gravi-tational lensing. Powerful computer simulations play a key role in understanding theformation of structure and in assessing the accuracy of these cluster mass estimates.
Gravitational lensing was predicted by Einstein’s General Theory of Relativity. Theeffect is that light rays are bent when they pass through a gravitational field. Thiswas first proved by the solar eclipse experiment in 1919 by Eddington and Dyson.Bending of light from a distant galaxy by a massive cluster along the line-of-sightgenerates ‘strong lensing’, with the distorted images in the form of apparent ‘arcs’.Milder intervening mass fluctuations produce ‘weak lensing’ (see an illustration inFigure 7). Weak gravitational lensing is sensitive to both the expansion history andthe growth history of density fluctuations, and therefore is sensitive to the amounts ofDark Matter and Dark Energy. The apparent distortions of distant galaxies in a smallpatch of sky will be correlated, since their light has travelled through nearly the same10 igure 8.
The distribution of dark matter projected on the sky (across 139 square degrees). The dark massmap was derived from weak gravitational lensing by the DES collaboration. The colour scale represents thedensity of mass: yellow and red are regions with more dense matter; green and blue are regions with less densematter. As examples of the correspondence of mass to light, two regions (in red) of dark matter over-densitiesare identified with known galaxy clusters, while an under-dense region (in blue) corresponds to a void. Credit:The Dark Energy Survey collaboration (based on [20]).
A somewhat unexpected probe of Dark Energy has emerged from the discovery ofGravitational Waves. The first event, GW150914, a Binary Black Hole merger, wasdetected by LIGO [21] on 14 September 2015, and subsequently was recognised bythe award of the Nobel Prize in Physics 2017. The later he LIGO & Virgo detection[22] of Binary Neutron Star (BNS) merger GW170817 and electromagnetic followupsturned out to be relevant for constraining cosmological models. Several ground andspace telescopes (including the Dark Energy camera [23] in Chile) captured an opticalflash from this Gravitational Wave event. In particular, the Fermi Gamma-ray spacetelescope detected a flash from the BNS system only 1.7 seconds after the GravitationalWave measurement. Given the distance of about 130 Million Light years to the hostgalaxy NGC4993, this implies that the speed of Gravitational Waves is equal to thespeed of light to within one part in 10 . This has ruled out certain models of gravity,which have predicted, at least in their simplest form, differences between the speed ofgravity and light.
4. The landscape of galaxy surveys
The 1998-1999 results of the accelerating Universe from the Supernovae Type Ia ob-servations have stimulated many galaxy surveys designed to verify and characteriseDark Energy. Back in 2006, the U.S. Dark Energy Task Force (DETF) report clas-sified Dark Energy surveys into numbered stages: Stage II projects were on-going atthat time; Stage III were near-future, intermediate-scale projects; and Stage IV werelarger-scale projects in the longer-term future. These projects can be further dividedinto ground-based and space-based surveys. Space-based missions have the advan-tage of not having to observe through the Earth’s atmosphere, which blurs the lightand absorbs infrared light. Further, surveying in Astronomy is divided into spectro-scopic and imaging. Spectroscopic surveys produce accurate redshifts of galaxies, butare demanding in terms of observing time. Multi-band photometric surveys can mea-sure far more galaxies, but the deduced ‘photometric redshifts’ are less accurate thanspectroscopic redshifts. Among the spectroscopic surveys we note: the current SDSSBaryon Oscillation Spectroscopic Survey (BOSS) , eBOSS (‘extended BOSS’) , theDark Energy Spectroscopic Instrument (DESI) and under construction the SubaruPrime Focus Spectrograph (PFS) , 4MOST , HETDEX , Euclid and the Nancy http://desi.lbl.gov/ http://pfs.ipmu.jp/factsheet/ https://hetdex.org/hetdex.html Redshift z A r e a (cid:2) d e g (cid:3) BOSS (gals) eBOSS (gals/QSO)HETDEX (gals)DESI (gals) DESI (Ly α F)PFS (gals) PFS (gals)PFS (Ly α F)Euclid (gals)Roman-WFIRST (gals)
Figure 9.
The survey area vs. redshift ranges for a selection of current and spectroscopic surveys. ‘gals’ and‘QSO’ indicate surveyed galaxies and quasars. ’Ly α F’ stands for Lyman- α Forest, a technique that providesthe distribution of gas clouds along the line-of-sight to distant quasars. Credit: Krishna Naidoo’s PhD thesis(UCL), based on a Table given in [13]. magnitude m AB (5 σ ) A r e a (cid:2) d e g (cid:3) DESDESDESDESDESSuMIRESuMIRESuMIRESuMIRESuMIRERubin-LSSTRubin-LSSTRubin-LSSTRubin-LSSTRubin-LSSTRubin-LSSTEuclidEuclidEuclidEuclidEuclidEuclidRoman-WFIRSTRoman-WFIRSTRoman-WFIRSTRoman-WFIRST ugrizyjhf184
Figure 10.
The survey area vs. limiting apparent magnitudes (per filter) for a selection of imaging surveys.The larger the magnitude, the fainter the object. The (monochromatic) AB magnitude system is defined as m AB = − . ( f ν ) + 8 .
90, where the spectral flux density f ν is in Janskys. The 5 σ indicates the level ofsignal-to-noise. Credit: as in Figure 9. igure 11. From left to right: the Dark Energy Camera (DECam) on the Blanco 4m telescope in Chile, theCCD array in the focal plane, and the galaxy NGC1365, a barred spiral galaxy 56 million light-years away,observed with DECam at ‘first light’ in 2012. Credit: the DES collaboration
Roman Wide-Field Infrared Survey Telescope (WFIRST) . The sky area vs. redshiftrange are shown for some of these surveys in Figure 9.Current imaging surveys include the Dark Energy Survey (DES) , the HyperSuprime Cam (HSC) , the Kilo-Degree Survey (KiDS) , PAU , and under con-struction the Vera Rubin Observatory of Legacy Survey of Space and Time (LSST) ,and the above-mentioned Euclid and Roman-WFIRST. Figure 10 shows the sky areavs. magnitudes (per filter) for some of these imaging surveys.
5. The Dark Energy Survey
As discussed in the previous Section, many ongoing and planned imaging and spec-troscopic surveys aim at measuring Dark Energy and other cosmological parameters.As a showcase we focus here on DES . For an overview of DES see the article ‘DES:more than Dark Energy’ [24] and the DES book [25], which tells the story of thisexperiment, from construction to science.In short, DES is an imaging survey of 5000 square degrees of the Southern sky,utilising a 570 mega-pixel camera (called DECam) on the 4m Blanco telescope in Chile(see Figure 11). Photometric redshifts (approximate distances) to the galaxies wereobtained from the multi-band photometry to produce a three dimensional map of 300million galaxies. The main goal of DES is to determine the Dark Energy equation ofstate w and other key cosmological parameters to high precision. DES has measured w using four complementary techniques (described in Section 3) in a single survey:galaxy clustering, counts of galaxy clusters, weak gravitational lensing and thousandsof Type Ia Supernovae in a ‘time domain’ survey over 27 square degrees. DES isan international collaboration, with more than 400 scientists from 26 institutions inthe US, the UK, Spain, Brazil, Germany, Switzerland and Australia involved. Thesurvey had its first light in September 2012 and started observations in August 2013.Observations were completed in 2019, over 758 nights spread over 6 years.DES imaged about an eighth of the sky to a depth of approximately 24th magnitude(about 15.8 million times fainter than the dimmest star that can be seen with the naked http://kids.strw.leidenuniv.nl/ I have chosen DES as a showcase as its observations are already complete. Also, I happen to have an ’insider’sview’, as I have been involved in the project since its early days back in 2004, in particular as co-chair of itsScience Committee until 2016, and later as chair of its Advisory Board. a) Constraints on cosmological pa-rameters determined by DES Year1 galaxy clustering and weak lens-ing (blue), Planck CMB measurements(green), and the combination of thetwo (red), assuming the ΛCDM model.Within the measurements’ accuracy,the Planck and DES constraints areconsistent with each other. Here, Ω m is the matter density parameter, and S is a parameter related to the ampli-tude of density fluctuations (see text).For each colour, the contour plots rep-resent 68% and 95% confidence levels.Credit: [26]. The KiDS collaboration: KiDS + VIKING-450: Cosmic shear tomography with optical + infrared data Fig. 4.
Marginalised posterior contours (inner 68% confidence level, outer 95% confidence level) in the ⌦ m - plane ( left ) and the ⌦ m - S plane( right ) for the fiducial KV450 setup (blue), the optical-only KiDS-450 analysis from H17 (green), DESy1 using cosmic shear only (purple;Troxel et al. 2018b), HSC-DR1 cosmic shear (orange; Hikage et al. 2018), and the Planck-Legacy analysis (red; Planck Collaboration et al. 2018,TT + TE + EE + lowE). ues, respectively. All other setups no. 1-9 lie in between thoseextremes. The two extremes with the highest and lowest S val-ues are discrepant with Planck at the 1 . and 2 . level, re-spectively, in terms of their marginal errors on S . Compared tothe fiducial KV450 setup the OQE-shift setup no. 9 yields an S that is 0 . lower whereas the DIR-C15 setup no. 6 is 0 . highcompared to the fiducial value of S .Figure 6 shows that all redshift distributions tested here yield S values that are consistent within ⇠ . However, it shouldbe noted that these data points are correlated because a largefraction of the spec- z calibration sample is the same for mostsetups, the clustering- z setups no. 7–9 and the COSMOS-2015setup no. 6 being exceptions. The highest S values (and cor-respondingly the lowest mean redshifts) are obtained with theDIR method when using the COSMOS-2015 photo- z catalogueinstead of the spec- z catalogue or when excluding DEEP2 (thehighest-redshift spec- z catalogue) from the spec- z calibrationsample. The lowest S values are measured for the DIR n ( z )when COSMOS and VVDS are excluded from the spec- z cal-ibration sample and the two setups that are based on shiftingthe fiducial DIR n ( z ) to best fit the CC and OQE measurements.The range spanned by these di ↵ erent choices for the n ( z ) can beregarded as a very conservative estimate of the systematic uncer-tainty introduced by the redshift distributions. As reported in Table 5 we carry out a number of further tests tocheck the influence of the systematic e ↵ ects that we model withnuisance parameters, their priors, the selection of the data vector,and the fixed mass of the neutrinos.In setup no. 10 we test the influence of the z i nuisance pa-rameters. When the redshift uncertainties are not marginalisedover we find almost identical results to the fiducial setup thatincludes their marginalisation. The total uncertainty on S is re-duced by merely ⇠ n ( z ) here as our uncertainties are esti-mated from a spatial bootstrap analysis of the calibration sam-ple. So also this sampling variance is subdominant for KV450.This e ↵ ect can be compared to the range of results shown inSect. 7.2 suggesting that systematic errors in the redshift cali-bration dominate over sample variance and shot noise but arehard to quantify.The choice of the prior for the intrinsic alignment amplitude A IA does not have a large e ↵ ect on the results either. Using aninformative Gaussian prior (setup no. 11) again yields almostidentical results to the fiducial setup, with a very similar con-straint on the intrinsic alignment amplitude A IA = . + . . withtighter error compared to A IA = . + . . for the fiducial setup.Switching from the non-linear to the linear power spectrum tomodel the GI and II terms in Eq. 9 (setup no. 12) does not havean appreciable e ↵ ect on the results either. Also allowing for red-shift evolution in the IA model (setup no. 13) does not changethe results in a significant way, meaning that IA modelling andprior choices are currently subdominant in the systematic errorbudget.A somewhat larger e ↵ ect can be seen when baryon feed-back is left unaccounted for (setup no. 14). In that case themean posterior value of S is lowered by ⇠ . . This is due tothe fact that baryon feedback dilutes structures on small scales( k ⇡ h Mpc ) and hence lowers the amplitude of the powerspectrum. When this is not modelled the power spectrum am-plitude increases for a given S . Thus, a smaller value of S issu cient to describe the observed amplitude of the correlationfunctions. Allowing for extremely wide priors on the HMCodebaryon feedback parameters (setup no. 15) gives consistent re-sults with the fiducial setup. This can be understood in the waythat already our slightly informative fiducial prior erases mostsmall-scale information so that even a more conservative priordoes not lead to a further loss of statistical power. Alternatively,one could just disregard the smallest scales for ⇠ + and not modelthe baryon feedback at all as it was done by Troxel et al. (2018b) The enhancement of the power spectrum by stellar feedback on verysmall scales ( k h Mpc ) is unimportant for the ✓ range probed byKV450. Article number, page 15 of 31 (b) Marginalised posterior contours inthe Ω m - S plane. The three WeakLensing experiments (KiDS, DESY1,HSC) tend to give a clumpiness S lower than that from the CMB Planckdata. Credit: [27]. Figure 12.
Examples of ‘tension’ in the standard ΛCDM model. eye). The quality of the data is excellent – the typical blurring of the images due to thecamera, the telescope optics, and the atmosphere is about 0.9 arcseconds. On a typicalobserving night, the camera took about 200 images; since each DECam digital image isa gigabyte in size, DES typically collected about 200 gigabytes of data on clear nights,‘big data’ for an astronomy experiment. In addition to serving the scientific interestsof the collaboration, the DES data processed by DESDM are being made publiclyavailable on a regular basis and can be downloaded from the internet by anyone inthe world. DES scientists are working closely with data sets and scientists from othersurveys and observatories. Comparing DES data with complementary data from othersurveys allows us to obtain new information and make new discoveries.
The first major DES cosmology results were announced in August 2017, and publishedthe following year ([26]). This analysis combined galaxy clustering and weak gravita-tional lensing data from the first year of DES survey data that covered about 1300square degrees, utilising measurements of three two-point correlation functions (hencereferred to as ‘3 times 2pt’): (i) the cosmic shear correlation function of 26 millionsource galaxy shapes in four redshift bins, (ii) the galaxy angular auto-correlation func-tion of 650,000 luminous red galaxy positions in five redshift bins, and (iii) the galaxy-shear cross-correlation of luminous red galaxy positions and source galaxy shears. Theheadline results strongly support the ΛCDM cosmological model. Combining the DESYear 1 data with Planck CMB measurements, baryonic acoustic oscillation measure-16ents from the SDSS, 6dF, and BOSS galaxy redshift surveys, and Type Ia Super-nova distances from the Joint Light-curve Analysis, this analysis finds the Dark Energyequation of state parameter to be w = − . +0 . − . (68% CL) , in spectacular agreementwith the cosmological constant model, for which w = − m = 0 . ± . S = σ (Ω m / . . = 0 . ± .
012 ( σ is the rms fluc-tuation in spheres of radius of 8( H / − Mpc). The future analysis of the full DESdata (Years 1-3 and then Years 1-6), which covers a larger area of sky and goes deeperthan the Year 1 data, will provide stronger constraints on these parameters as wellas on the time variation of the equation of state parameter of Dark Energy, modifiedgravity and neutrino mass.
The first DES Supernova Ia (SNe Ia) cosmology results were announced in January2018 and published a year later [28]. The analysis used a sample of 207 spectro-scopically confirmed SNe Ia from the first three years of DES-SN, combined witha low-redshift sample of 122 SNe from the literature, thus 329 SNe Ia in total (seeFigure 5). The ΛCDM model, combining DES-SN with Planck, yields a matter den-sity Ω m = 0 . ± . w CDM model (with constant w ), the analysis finds w = − . ± . m = 0 . ± .
6. Tension in clumpiness and in the Hubble constant: systematics or newphysics?
The ΛCDM model has survived detailed observational tests over 30 years. However,it is still undergoing ‘health checks’ from time to time. ΛCDM is the winning model,as demonstrated e.g. in Planck [2], DES [26] and recently by the CMB Atacama Cos-mology Telescope (ACT) [29] and eBOSS [30] results. But we have already indicatedin the previous chapter some inconsistency in the clumpiness parameter S : the onederived from weak lensing is about 3- σ smaller than the value deduced from Planck(see e.g. the recent KiDS results [31]).An even larger tension, of about 4.4- σ , exists between the Hubble Constant measure-ments from the cosmic ladder in the nearby universe and from the CMB experimentsthat probe the early universe. Edwin Hubble discovered the law of expansion of theUniverse by measuring distances to nearby galaxies. The Hubble Constant is derived17 igure 13. Four methods for measuring the Hubble Constant: from the cosmic ladder SH0ES [33], from theCMB Planck [34], from the Gravitational Wave event GW170817 associated with the galaxy NGC4993 as aBright Siren [38] and from GW170814 as Dark Siren [39], where the Hubble constant posterior distributionwas obtained by marginalizing over 77,000 possible host galaxies catalogues by DES. Credit: [39] from the ratio of the recession velocity v and the distance d : H = v/d. (7)Note H has units of inverse time, although the units are written as km s − Mpc − toreflect the way it is being measured. Astronomers have argued for decades about thesystematic uncertainties in various methods and derived values over the wide range50 km s − Mpc − < ∼ H < ∼
100 km s − Mpc − .One of the most reliable results on the Hubble constant came from the Hubble SpaceTelescope (HST) Key Project [32]. This study used the empirical period–luminosityrelation for Cepheid variable stars, and calibrated a number of secondary distance in-dicators, SNe Ia, the Tully–Fisher relation, surface-brightness fluctuations, and TypeII Supernovae. This approach was further extended, based on HST observations of 70long-period Cepheids in the Large Magellanic Cloud combined with Milky Way paral-laxes and masers in NGC4258, to yield H = 74 . ± . − Mpc − [33] (SH0ES).By contrast, the Planck CMB experiment [34] gives a lower value, H = 67 . ± . − Mpc − . The tension of 4.4- σ between H from Planck and the traditionalcosmic distance ladder methods is of great interest and under investigation. A lowvalue, H = 67 . ± . − Mpc − , has also been measured by ACT[29], anotherCMB experiment.Other methods have been used recently, for example by calibrating of the tipof the red-giant branch applied to SNe Ia, finding H = 69 . ± . . ± . . km s − Mpc − [35]. The method of time delay in gravitationally-lensed quasars[36] (H0LiCOW) gives the result H = 73 . +1 . − . km s − Mpc − , but see a revision [37]18o H = 67 . +4 . − . km s − Mpc − .Another method that recently came to fruition is based on Gravitational Waves;the ‘Bright Siren’ applied to the binary neutron star merger GW170817 and the‘Dark Siren’ implemented on the binary black hole merger GW170814 yield H =70 +12 − km s − Mpc − [38] and H = 75 +40 − km s − Mpc − [39] respectively. With manymore gravitational wave events, the future uncertainties on H from standard sirenswill get smaller. Figure 13 summarizes four of the methods discussed above.For further discussion of the Hubble Constant measurements see [40] and [41]. Thereis possibly a trend for higher H at the nearby Universe and a lower H at the earlyUniverse, which leads some researchers to propose a time-variation of the Dark Energycomponent or other exotic scenarios. Ongoing studies are addressing the question ofwhether the Hubble tension is due to systematics in at least one of the probes, or isa signature of new Physics. On the whole, although there are inconsistencies in theHubble Constant and clumpiness factor, they are not at the level of shaking up theΛCDM paradigm.
7. Discussion and Outlook
The accelerated expansion of the Universe and the ΛCDM model have been over-whelmingly supported by a host of cosmological measurements. But we still have noclue as to what is causing the acceleration, and what Dark Matter and Dark En-ergy are. Even if Dark Energy is ‘just’ the enigmatic Cosmological Constant Λ, wedesperately need to understand it.It may well be that the ΛCDM model is indeed the best description of our Universe,with Dark Matter and Dark Energy ingredients that will eventually detected indepen-dently, e.g. in the lab. But there is also a chance that the Dark sector is the ‘modernEther’ and future generations will adopt an entirely different description of the Uni-verse. It is also possible that the community has converged on a single preferred modeldue to ‘over communication’ [42]. Should a discrepancy between data and the existingcosmological theory be resolved by adding new entities such as Dark Matter and DarkEnergy, or by modifying the underlying theory? This reminds us of two cases in thehistory of studies of our own Solar System. Anomalies in the orbit of Uranus wereexplained by hypothesizing a previously unseen (i.e. ‘dark’) planet, Neptune, withinNewtonian gravity, which was subsequently discovered. On the other hand, anomaliesin the perihelion of Mercury were successfully explained by invoking a new theoryof gravitation beyond Newton, Einstein’s General Relativity, instead of by the ‘dark’planet Vulcan (e.g. a discussion in [43] and references therein). Unfortunately, historydoes not provide a definitive guide to choosing between dark stuff or a new theory ofgravity in explaining cosmological observations.Various speculations have been proposed about the origins of Λ: e.g. that we hap-pen to reside in an unusual patch of the universe (e.g., in a large void), mimickingthe appearance of Λ; that the Cosmological Constant Λ is something different to vac-uum energy, as the value predicted by fundamental theory is as much as 10 timeslarger than observations permit; that perhaps the observed Λ is a superposition ofdifferent contributions; that perhaps modifications to General Relativity are required;that a higher-level theory, connecting General Relativity to Quantum Mechanics andThermodynamics, is still to be discovered; or that we should possibly consider Λ inthe context of a Multiverse: anthropic reasoning suggests a large number of universes(‘multiverse’) in which Λ and other cosmological parameters take on all possible values.19e happen to live in one of the universes that is ‘habitable’.It is likely that ultimately the full explanation of Dark Energy of the Universe mayrequire a revolution in our understanding of fundamental Physics. It might even requirethinking beyond the boundaries of Physics. Michael Collins, one of the Astronauts ofthe Apollo 11 mission to the Moon allegedly said “I think a future flight should includea poet, a priest and a philosopher. We might get a much better idea of what we saw.”Likewise, we might need an entirely new perspective on the mystery of Dark Energy.
Acknowledgements
I express thanks to my DES and UCL collaborators for many inspiring discussions onthis topic over the years. In particular I thank Richard Ellis for initiating this article,and to Lucy Calder, Josh Frieman, Andrew Liddle, Michela Massimi, Julian Mayersand David Weinberg with whom I have interacted on related review articles, includingsome chapters in the DES book [25]. Rebecca Martin, Krishna Naidoo and LorneWhiteway have kindly commented on earlier versions of this article. I acknowledgesupport from a European Research Council Advanced Grant TESTDE (FP7/291329)and STFC Consolidated Grants ST/M001334/1 and ST/R000476/1.
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