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PARTICLE PHYSICS and the COSMIC MICROWAVE BACKGROUND

PARTICLE PHYSICS and the COSMIC MICROWAVE BACKGROUND

and the COSMIC MICROWAVE BACKGROUND

John E. Carlstrom, Thomas M. Crawford, and Lloyd Knox

Temperature and polarization variations across the microwave sky include the fingerprints of fluctuations in the early . They may soon reveal physics at unprecedented energy scales.

ifty years ago Bell Labs Arno Pen- measurements imply that the sum of the zias and Robert Wilson encountered a puz- masses is no more than a few tenths of an eV. zling excess power coming from a horn The CMB data also show the influence of F reflector antenna they had planned to use produced in the early universe and thus constrain for radio astronomical observations. After the primordial helium fraction. Moreover, the painstakingly eliminating all possible instrumental data are nearly impossible to fit without dark en- explanations, they finally concluded that they had ergy and dark —two ingredients missing detected a faint microwave signal coming from all from the of (see the directions in the sky.1 That signal was quickly inter- article by Josh Frieman, PHYSICS TODAY, April 2014, preted as coming from thermal left over page 28). from a much hotter and earlier period in our uni- verse’s history, and the was established as Simple math, difficult observations the dominant cosmological .2 Cooled by The constraining power of CMB observations fol- the expansion of the universe to a temperature just lows in part from the high degree of in the below 3 K, so that its intensity peaks in the mi- CMB and the resulting precision with which theo- crowave region of the spectrum, the radiation de- rists can offer predictions. The coupled, nonlinear tected by Penzias and Wilson is known today as the equations for the evolving distribution are cosmic microwave background (CMB). The two sci- difficult to solve exactly. But because the tempera- entists were awarded the 1978 Nobel Prize in ture of the CMB is the same in every direction to Physics for their discovery. about 1 part in 100 000, the linearized equations, The detection of the CMB and the consensus which are relatively easy to solve, provide an excel- that the universe had a hot and dense early phase lent approximation. Of course, the small level of led to a fertile relationship between and has a downside: It makes measurement particle physics. The hot early universe was a natu- quite challenging. For nearly 30 years after the dis- ral that could reach energies covery of the CMB, observations yielded only in- well beyond what laboratories on will attain creasingly stringent limits on its anisotropy. Then, in the foreseeable future. Precise measurements of in 1992, an instrument aboard the Cosmic Background both the spectrum of the CMB and its tiny variations Explorer (COBE) measured the anisotropy for the in brightness from one point to another on the sky first .3 reflect the influences of high-energy processes in the Since the COBE , observations of the CMB early . with dedicated, specialized telescopes have become For instance, the gravitational effects of neutri- orders of magnitude more sensitive, thanks to re- nos have been detected at high significance; such markable in the development of mi- crowave detectors and measurement techniques. John Carlstrom is a professor of physics and of The 1990s saw experiments across a range of angu- and and deputy director of the Kavli Institute lar scales from the ground and from balloons; mea - for Cosmological Physics (KICP) at the University of Chicago. surements of degree-scale anisotropy in particular Tom Crawford is a senior researcher at the KICP. Lloyd Knox helped establish the current cosmological picture is a professor of physics at the University of California, Davis. of a geometrically flat universe dominated by dark 28 March 2015 Physics Today www.physicstoday.org Physics Today 68(3), 28 (2015) ©American Institute of Physics https://doi.org/10.1063/PT.3.2718 This honeycomb-like array of feedhorns at the 10-m South Pole Telescope directs radiation to superconducting detectors used to measure the polarization of the cosmic microwave background. The seven hexagonal cells in the center, about 5.8 cm across, are sensitive to radiation at frequencies of about 150 GHz. The larger feedhorns surrounding them are used for frequencies near 95 GHz. Progress in detector development is so rapid that within a year arrays should have sensitivities an order of magnitude greater than that of the state-of-the-art detector shown here. (Courtesy of the South Pole Telescope.)

energy and . The next decade saw the questions about remain, the predictions of launch of two successor satellites to COBE, the the simplest versions of the have been so suc- Wilkinson Microwave Anisotropy Probe (WMAP) in cessful that most cosmologists accept that some 2001 and in 2009. form of inflation truly did occur in the very early These days the temperature of the CMB has universe. The 2014 in Astrophysics was been exquisitely mapped out by the satellite exper- recently awarded to , , and iments and by large-aperture, ground-based tele- for their pioneering contribu- scopes such as the South Pole Telescope and the tions to the theory of cosmic inflation. Several others Atacama Cosmology Telescope. The new observa- made critical contributions as well. For a first-hand tional frontier is CMB polarization, first detected account of the discovery and early development of in 2002 by the DASI (Degree Angular Scale Interfer- the theory see reference 6. ometer) experiment at the South Pole4 and soon Inflation is, by definition, a period of accel- thereafter by WMAP.5 Since those initial measure- erating expansion. As explained in figure 1, an ments, the polarization signature of density fluctu- accelerating cosmos has a causal structure very ations in the primordial has been mapped different from that of a decelerating cosmos. In a with high signal to noise, and the effects of gravi - decelerating universe, a pair of separated points tational lensing on the polarization have been evolves from being causally disconnected—in detected. which case the , unable to influence each The anisotropy in the CMB is of crucial physical other, are said to be superhorizon, or separated importance because those tiny temperature fluctua- by a horizon—to being causally connected, or sub- tions reflect the small density inhomogeneities that, horizon. In an accelerating universe, the opposite under the influence of gravity, grew over time to be- occurs. In the inflationary scenario, the universe come all the structures we see in the universe. With- undergoes an accelerating stage, which is followed out an anisotropic CMB, we would not exist. But by a long period of deceleration. what was the origin of the small fluctuations? A In view of the early period of accelerating ex- compelling answer comes from the next great syn- pansion, two separated regions in the universe that ergy between the CMB and particle physics: the the- are now causally disconnected could have been able ory of inflation. to interact with each other during the inflationary . Causally connected perturbations in those In and out of causal contact two regions—for example, an underdensity in one Once a highly speculative idea, inflation is now a and an overdensity in the other—could thus have part of the standard cosmology. Although deep been created at very early . As we will see, www.physicstoday.org March 2015 Physics Today 29 Cosmic microwaves

Figure 1. In an expanding universe, the distance between two A B separated points increases over time, simply due to the expansion of the between them. The two panels here show the trajectories of two points, A and B. For the decelerating expansion illustrated in the top panel, the separation rate is greater in the past and even exceeds the speed of at sufficiently early time. Thus A and B go from being out of causal contact—unable to influence Subluminal each other—to being in causal contact. In an accelerating cosmos, the separation rate is smaller in the past; the two points go from being in causal contact to being out of causal contact. In the inflationary universe scenario, an early epoch of acceleration—the inflationary era—smoothly maps onto a long period of deceleration. Thus two points can go from being in causal contact to out of causal contact and, much later, back into causal contact. (Courtesy of Marius Millea.) Time Superluminal Space Singularity DECELERATION provides a for Superluminal generating such perturbations. Quantum mechani- A B cal fluctuations initially created with subnuclear wavelengths are stretched by the cosmic expansion to milli meter length scales within a tiny fraction of Subluminal a second; at present they are astrophysically large. Thus observations of cosmic structure give physi- cists an opportunity to probe physics on extremely small length scales. A recipe for accelerated expansion Accelerating expansion requires the universe to have an that dilutes relatively slowly

with expansion. In inflationary models, such an Time energy density is usually obtained via the introduc- Space ACCELERATION tion of a new ϕ, called the field. Just as the dynamics of ordinary particles are governed by a , so the dynamics of the inflaton field are governed by what particle call a truly constant in time, the grows expo- potential V(ϕ). (It’s really a potential energy density.) nentially, proportional to eHt. In that limit, the hori- The potential V(ϕ) is only one of two contribu- zon length is exactly c/H, with c being the speed of tions to the energy density of the inflaton field. The light. In other words, points separated by more than second contribution, a four-dimensional kinetic en- c/H are out of causal contact. ergy, arises from temporal and spatial derivatives. As inflation proceeds, the gradients of the in- The total energy density of ϕ is thus flaton field are stretched out by the expansion and the field becomes very smooth. If the inflationary 1 dϕ 2 c2 epoch lasts long enough for the scale factor to in- ρϕ=+·V() + ∇∇ϕϕ. 2 ( dt ( 2 crease by about e60, then any initial irregularities will be stretched out to length scales that today are un- A generic inflaton field will not lead to infla- observably large; the result is a smooth observable tion. But if the gradients in the field are small universe with negligible spatial curvature. In one enough over a large enough patch of space and if simple model of inflation, the potential satisfies 1 2 2 the value of ϕ is sufficiently far away from the value V(ϕ)∝ ⁄2 m ϕ , where m is the mass of the inflaton. that minimizes the potential, then ϕ will rapidly In that realization, the entire evolve to satisfy something called the slow-roll con- once existed in a patch with a diameter of less than 1 2 −29 −14 dition, ⁄2 (dϕ/dt) ≪ V(ϕ). When both the spatial and 10 m, or 10 of a proton radius. The total mass temporal derivatives of the inflaton field are small, energy in that patch was about 104 J, the caloric con- V(ϕ) is nearly constant in time and makes the dom- tent of two diet Cokes. Today the observable uni- inant contribution to the energy density. Under such verse includes regular Cokes and about 1070 J of conditions, the patch inflates. mass energy from other sources, a result compatible That the inflation results in a patch of essen- with the perhaps surprising fact that energy is not tially constant energy density follows from the gen- conserved in . eral relativistic result that the Hubble parameter H ≡ a−1 da/dt is proportional to ρ1/2; here a is the so- We are quantum fluctuations called scale factor that describes the size of the uni- Quantum mechanics limits how smooth the inflaton verse. Since H is nearly constant, da/dt increases as field can be; fluctuations in the field necessarily per- a does—that is, the cosmic expansion accelerates. In sist at a level dictated by the uncertainty . the limit where the energy density, and thus H, is But as figure 2 shows, those fluctuations, too, will 30 March 2015 Physics Today www.physicstoday.org be stretched to astrophysically large length scales by LcH cosmic expansion; thus quantum fluctuations pro- = = Horizon length = / vide the initial seeds of all structure in the universe. popularized the notion that we are star Trough stuff. The idea that “we are quantum fluctuations” Crest deserves to be in the zeitgeist as well. As ϕ rolls toward the potential minimum, V(ϕ) ħ1/2 1 1 2 = 2 eventually becomes smaller than ⁄2 (dϕ/dt) ; the c1/2 2Lπ slow-roll condition is no longer met, and inflation Superhorizon ends. Decays of the inflaton to other particles— irrelevant during inflation because the decay prod- ucts were quickly diluted by expansion—then be-

come important. The remaining energy in the ϕ field TIME converts to a thermal bath of the particles of the standard model, and perhaps other particles as well. ħ1/2 1 = 2 The small but nonzero spatial fluctuations in ϕ, c1/2 λ stretched from quantum to astrophysical scales by cosmic expansion, cause inflation to end at different Subhorizon times in different locations. In those regions where ħ1/2 1 = 2 inflation ends relatively early, the mass density is c1/2 λ lower due to the extra expansion that the region has undergone since the end of inflation. Thus the slightly different expansion histories of different SPACE locations result in density differences; those small density perturbations eventually grow under the influence of gravity to create all the structures we Figure 2. Fluctuations in the value of the inflaton field, which is observe in the universe today. responsible for the accelerating expansion of the cosmos, evolve Figure 3, of the Hubble Space Telescope’s Ultra differently, depending on whether their wavelength λ is less than or Deep Field, is an iconic representation of that cosmic greater than the horizon length L = c/H. (Here c is the structure. The seen there—and, at smaller and H is the Hubble parameter.) When λ ≪ L, the expansion (red) scales, stars, , and people—demonstrate that smooths out the field, but the quantum uncertainty principle limits today the universe is anything but smooth. Images how smooth the field can be. As a result, the amplitude of the such as the Hubble Ultra Deep Field contain an im- fluctuation is inversely proportional to λ and thus decreases as mense quantity of . Unfortunately, relat- the universe expands. (The influence of the uncertainty principle is ing that information to of the early universe reflected by the appearance of Planck’s constant ħ in the expression is difficult because the of cosmic structure for the amplitude.) As λ becomes larger than the horizon, the crest is complicated and nonlinear. and trough of the wave cease to be in causal contact, so the amplitude The CMB power spectrum stops evolving. For superhorizon evolution, its asymptotic value corresponds to replacing the wavelength in the subhorizon case Most cosmologists take inflation seriously because, with 2πL. Eventually, cosmic expansion stretches the fluctuations as we will discuss in the following section, the the- to astrophysically large length scales. ory has offered numerous successful predictions. Those predictions have been tested primarily via observations of the CMB, whose temperature fluc- tuations are shown in figure 4. That state-of-the art The most informative statistic of the CMB is image was made with data from the Planck satellite. its angular power spectrum, shown in figure 5. The CMB last interacted with matter Roughly speaking, the power spectrum shows the when the universe was just a few hundred thousand anisotropy as a function of angular scale. To actually years old. Up to that time, the universe was dense obtain the fluctuation power displayed in the figure, and hot enough that no neutral could survive. one decomposes the CMB map of the sky into spher-

Instead, the cosmos was filled with a foggy plasma ical harmonic modes Yℓm with complex coefficients of photons, electrons, and protons strongly coupled aℓm. The fluctuation power Cℓ for a specified value of through photon–electron scattering and Coulomb ℓ is then given by interactions. The tight coupling also meant that ℓ matter beginning to compress under the influence Ca1 2 ℓℓ=∣∣.∑ m of gravity would bounce back due to the pressure 2+ℓ 1 mℓ=− support of the photons, a process that resulted in acoustic oscillations in the plasma. The spherical harmonic Yℓm executes ℓ cycles in 360°, When the universe cooled sufficiently, the pro- so hot and cold spots separated by a degree corre- tons and electrons combined into hydrogen atoms. spond to modes with ℓ ≈ 180. At that “” time, the universe became transparent. The CMB photons we see today thus Predictions of inflation provide us with an image of a spherical shell, called Inflation is not merely a theory that was constructed the last scattering surface, sufficiently distant from to be consistent with preexisting facts. It has made us that photons headed in our direction from it are several falsifiable predictions. In this section we de- just arriving here today, 13.8 later. scribe some of the most important ones. www.physicstoday.org March 2015 Physics Today 31 Cosmic microwaves

Figure 3. The Hubble Ultra Deep Field image looks back as much as 13 billion years. This image, from the Hubble Space Telescope, is approximately 3 arcminutes on each side. (Courtesy of NASA and the Space Telescope Institute.)

‣ Small spatial curvature. Any curvature of space present as infla- tion begins is rapidly expanded away, just as the curvature of a bal- loon decreases as the balloon is inflated. Thus the radius of curva- ture, the distance over which effects of nonzero curvature become sig- nificant, should be very large. Cur- rent CMB measurements show that the curvature radius is at least four times the radius of the observable universe. ‣ A nearly scale-invariant spec- trum of density perturbations. To the extent that the energy density during inflation remains constant, an inflating patch of the cosmos looks the same at ‣ Acoustic peaks in the CMB angular power spec- all times and the horizon length L = c/H is fixed. As trum. According to inflation theory, acoustic oscil- illustrated in figure 2, all mode amplitudes take on lations in the primordial plasma will result in a nearly the same value once the wavelength has series of peaks in the CMB angular power spectrum. stretched out enough to be significantly larger than As figure 5 shows, those peaks have now been well L. The primary difference between modes that be- measured. came superhorizon earlier is that they have under- The period of superhorizon evolution in the gone more expansion since horizon crossing and inflationary scenario provides special initial con - thus have longer wavelengths. ditions for the acoustic oscillations—namely, all Inflation cannot be completely time-translation modes with the same wavelength begin to oscillate invariant because it has to end. If the terminating at the same time with zero initial momentum. As a transition is smooth, we should see evidence that result of those special conditions, the primordial the average value of the mode amplitudes should plasma includes a of standing waves for which vary slightly with wavelength. Strong evidence for all modes of a given wavelength have the same ini- such a departure from has indeed tial phase. Because modes of a given wavelength all been found through analysis of the CMB angular oscillate at a specific rate governed by the sound power spectrum. speed in the plasma, they remain phase synchro-

Figure 4. The temperature fluctuations in the cosmic microwave background are only a few parts per million of the 3-K mean value. The data yielding this image of the entire sky were obtained with instruments aboard the Planck satellite. A single pixel on this map covers more of the sky than the Hubble Ultra Deep Field shown in figure 3. (Courtesy of the Planck collaboration.)

32 March 2015 Physics Today www.physicstoday.org nized for all time. The result is a series of acoustic peaks in the CMB WAVELENGTH (megaparsecs) power spectrum, in which the nth 397 162 107 77 61 50 42 36 32 peak corresponds to modes that arrived at their nth extremum at the decoupling time. WMAP ‣ Gaussian perturbations. The SPT expectation that energy density 2 ACT perturbations are Gaussian follows Planck from the wavefunction of a har- 1000 monic oscillator in its ground state being Gaussian. To the extent that density fluctuations δρ depend linearly on δϕ, the density pertur- bations will be Gaussian as well. For an essentially constant inflaton field, the energy density is de - termined solely by the potential 100 V(ϕ). The Taylor-series expansion POWERFLUCTUATION (μK) 1 2 2 2 δρ =(dV/dϕ) δϕ + ⁄2 (d V/dϕ) δϕ indicates that a nonzero second derivative causes a non-Gaussian δρ. However, a large second- 0500 1000 1500 2000 2500 3000 derivative term for the potential ℓ would also ruin the slow-roll MULTIPOLE VALUE ( ) behavior of the inflaton field; such considerations greatly restrict the amount of non- Gaussianity allowed in the simplest models. The Figure 5. The angular power spectrum of the cosmic microwave Planck data have dramatically improved the sensi- background (CMB) displays a series of acoustic peaks, as predicted tivity of searches for non-Gaussianity. Quadratic by inflation theory. A peak at a multipole value of ℓ means that the corrections are limited to be less than about 10−4 fluctuations in the CMB include a significant component of hot spots times the linear, Gaussian term.7 and cold spots separated by 180/ℓ degrees. The first peak corresponds to acoustic oscillations (defined in the text, which also gives a precise The hunt for gravitational waves definition of the fluctuation power) that reached their first extremum One key prediction of inflation that remains uncon- about 370 000 years after the Big Bang, when the universe decoupled, firmed is the existence of a nearly scale-invariant or became transparent to photons. As indicated on the upper axis, spectrum of gravitational waves—degrees of free- those modes now have a wavelength of about 400 megaparsecs dom in the spacetime that can be excited (1.3 × 109 light-years). Modes with a current wavelength of 162 Mpc without any corresponding excitation of matter oscillated faster and achieved their second extremum at decoupling. fields. Just as with fluctuations of the inflaton field, Between those two wavelengths are modes with ℓ ≈ 400 that hit a they obey an uncertainty principle and, in the null in their oscillations at decoupling; those modes are responsible course of superluminal expansion, have their ampli- for the trough at 213 Mpc. The data shown here were obtained by the tude set to a value proportional to the Hubble pa- Wilkinson Microwave Anisotropy Probe (WMAP), the South Pole rameter H during inflation. Detecting the influence Telescope (SPT), the Atacama Cosmology Telescope (ACT), and of that gravitational-wave background on the CMB the Planck satellite. The curve is the prediction of a representative would allow cosmologists to infer H and hence the inflationary model. (Courtesy of Zhen Hou.) energy scale of the inflationary potential; observa- tions of density perturbations, by contrast, provide a relatively indirect look at the inflationary era. Attempts to measure the effect of gravitational BICEP2 collaboration announced it had detected waves on the CMB’s temperature fluctuations have B modes whose power spectrum had an angular produced upper limits only. However, as the elec- dependence consistent with inflation.9 Subsequent trons and protons in the primordial plasma combine data from the Planck collaboration10 and, most re- into hydrogen, any gravitational waves that are cently, a collaborative cross-correlation of BICEP2 around will produce unique signatures in the - and Planck data sets11 have demonstrated that the ization of the CMB—divergence-free patterns, signal originally reported by BICEP2 is consistent called B modes, that, to linear order, cannot be cre- with having arisen entirely from dust emission ated by density perturbations.8 To better constrain in our own . (For more, see PHYSICS TODAY, the , scientists will need to mea- May 2014, page 11, and the Commentary by Mario sure the CMB polarization and tease out the signa- Livio and , December 2014, ture of gravitational waves. page 8.) Several ground- and balloon-based experi- The excitement surrounding searches for infla- ments currently under way are attempting to do just tionary gravitational waves has not abated. After all, that. The instruments the researchers are using are a detection of gravitational waves from inflation so sensitive that the studies are limited by system- would open a window to physics at energy scales atic effects. For example, in March of last year, the a trillion times larger than those accessible at www.physicstoday.org March 2015 Physics Today 33 Cosmic microwaves

the Large Hadron Collider and provide the first the CMB. If discovered, that gravitational imprint observational evidence that the gravitational field is would open up an observational window onto a quantum field. Even as current experiments run quantum gravitational effects, extremely early and others are being built, physicists in the US times, and extremely high energies. are planning an ambitious next-generation ex - periment that will use telescopes at the South Pole, We thank Brent Follin, Daniel Green, Zhen Hou, Ryan the high Atacama plateau in Chile, and possibly Keisler, Marius Millea, Rajiv Singh, and Gergely Zimanyi Northern Hemisphere sites to image the polari - for their comments. zation over most of the sky with unprecedented sensitivity and in multiple frequency channels. In References addition, the international CMB community is 1. A. A. Penzias, R. W. Wilson, Astrophys. J. 142, 419 (1965). working on satellite mission concepts. All of those 2. R. H. Dicke et al., Astrophys J. 142, 414 (1965). efforts are aiming for a sensitivity to the inflationary 3. G. F. Smoot et al., Astrophys. J. Lett. 396, 1 (1992). B-mode signals at a level of 1% of the current upper 4. J. M. Kovac et al., 420, 772 (2002). limits. Success in those endeavors would yield ad- 5. A. Kogut et al., Astrophys. J. Suppl. Ser. 148, 161 (2003). ditional science dividends, including a determina- 6. A. H. Guth, The Inflationary Universe: The Quest for a tion of the absolute masses of and an ex- New Theory of Cosmic Origins, Addison-Wesley (1997). quisitely sensitive profile of the contents of the 7. For an overview of the Planck mission and the cosmol- primordial plasma.12 ogy results from its February 2015 data release, see Thirty years ago inflation was a highly specu- R. Adam et al. (Planck collaboration), http://xxx.lanl .gov/abs/1502.01582. lative idea about the origin of the Big Bang, born 8. U. Seljak, M. Zaldarriaga, Phys. Rev. Lett. 78, 2054 from the application of modern ideas about parti- (1997); M. Kamionkowski, A. Kosowsky, A. Stebbins, cles and fields to questions about the early evolution Phys. Rev. Lett. 78, 2058 (1997). of the universe. With its empirical successes, infla- 9. P. A. R. Ade et al. (BICEP2 collaboration), Phys. Rev. tion is by consensus the best paradigm—notwith- Lett. 112, 241101 (2014). standing some notable dissenting views—for the 10. R. Adam et al. (Planck collaboration), http://arxiv.org mechanism that generated the primordial density /abs/1409.5738. fluctuations that led to all structure in the universe. 11. P. A. R. Ade et al. (BICEP2–Keck and Planck collabora- Its success has motivated physicists to search for tions), Phys. Rev. Lett. (in press). the siblings of those fluctuations, the gravitational 12. K. N. Abazajian et al., Astropart. Phys. 63, 55 (2015); waves, via their signature in the polarization of K. N. Abazajian et al., Astropart. Phys. 63, 66 (2015). ■

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