CMB and physics of the early Universe - 名古屋大学...CMB and physics of the early Universe...

CMB and physics of the early Universe

Kazunori Nakayama(IPNS, KEK)

CMB Workshop (2011/2/17)

2011年2月17日木曜日

Contents

• Inflationary primordial gravitational wave background as a probe of the physics of early Universe

• Gravitational wave detection through B-mode in CMB anisotropy

• Gravitational wave detection through Space laser interferometers


Thermal history

t < 10−35sec?

t ∼ 1sec

t ∼ 1013sec

t ∼ 1017sec

Inflation

Big-bang nucleosynthesis (BBN)

Matter dominationRecombination

Present Universe : dark energy dominate

Radiation dominationReheating


Thermal history

t < 10−35sec?

t ∼ 1sec

t ∼ 1013sec

t ∼ 1017sec

Inflation




well known



Thermal history

t < 10−35sec?

t ∼ 1sec

t ∼ 1013sec

t ∼ 1017sec

Inflation




well known

partly known



Thermal history

t < 10−35sec?

t ∼ 1sec

t ∼ 1013sec

t ∼ 1017sec

Inflation




well known

partly known

poorly knownRadiation dominationReheating


Thermal history

t < 10−35sec?

t ∼ 1sec

t ∼ 1013sec

t ∼ 1017sec

Inflation




well known

partly known

poorly knownRadiation dominationReheating

Gravitational Wave


InflationaryGravitational Background


Solves flatness and horizon problem

Quantum fluctuation of the inflatonSeed of the density perturbationwith nearly scale invariant power spectrum

Accelerated expansiondriven by scalar field

(inflaton)

∆2R ∝ Ask

ns−1 ns scalar spectral index

ns ∼ 1 scale invariant

Power spectrum of the density perturbation

Inflation


14 Komatsu et al.

Fig. 7.— The WMAP 7-year temperature power spectrum (Larson et al. 2010), along with the temperature power spectra from theACBAR (Reichardt et al. 2009) and QUaD (Brown et al. 2009) experiments. We show the ACBAR and QUaD data only at l ! 690, wherethe errors in the WMAP power spectrum are dominated by noise. We do not use the power spectrum at l > 2000 because of a potentialcontribution from the SZ e!ect and point sources. The solid line shows the best-fitting 6-parameter flat "CDM model to the WMAP dataalone (see the 3rd column of Table 1 for the maximum likelihood parameters).

also found that the parameters of the minimal 6-parameter !CDM model derived from two compilationsof Kessler et al. (2009) are di"erent: one compilationuses the light curve fitter called SALT-II (Guy et al. 2007)while the other uses the light curve fitter calledMLCS2K2(Jha et al. 2007). For example, #! derived fromWMAP+BAO+SALT-II and WMAP+BAO+MLCS2K2are di"erent by nearly 2!, despite being derived from thesame data sets (but processed with two di"erent lightcurve fitters). If we allow the dark energy equation ofstate parameter, w, to vary, we find that w derived fromWMAP+BAO+SALT-II and WMAP+BAO+MLCS2K2are di"erent by ! 2.5!.At the moment it is not obvious how to estimate sys-

tematic errors and properly incorporate them in the like-lihood analysis, in order to reconcile di"erent methodsand data sets.In this paper, we shall use one compilation of

the supernova data called the “Constitution” samples(Hicken et al. 2009b). The reason for this choice overthe others, such as the compilation by Kessler et al.(2009) that includes the latest data from the SDSS-IIsupernova survey, is that the Constitution samples arean extension of the “Union” samples (Kowalski et al.2008) that we used for the 5-year analysis (see Sec-tion 2.3 of Komatsu et al. 2009a). More specifically,the Constitution samples are the Union samples plusthe latest samples of nearby Type Ia supernovae opti-cal photometry from the Center for Astrophysics (CfA)supernova group (CfA3 sample; Hicken et al. 2009a).

Therefore, the parameter constraints from a combina-tion of the WMAP 7-year data, the latest BAO datadescribed above (Percival et al. 2009), and the Consti-tution supernova data may be directly compared to the“WMAP+BAO+SN” parameters given in Table 1 and2 of Komatsu et al. (2009a). This is a useful compari-son, as it shows how much the limits on parameters haveimproved by adding two more years of data.However, given the scatter of results among di"erent

compilations of the supernova data, we have decided tochoose the “WMAP+BAO+H0” (see Section 3.2.2) asour best data combination to constrain the cosmologi-cal parameters, except for dark energy parameters. Fordark energy parameters, we compare the results fromWMAP+BAO+H0 and WMAP+BAO+SN in Section 5.Note that we always marginalize over the absolute mag-nitudes of Type Ia supernovae with a uniform prior.

3.2.5. Time-delay Distance

Can we measure angular diameter distances out tohigher redshifts? Measurements of gravitational lensingtime delays o"er a way to determine absolute distancescales (Refsdal 1964). When a foreground galaxy lenses abackground variable source (e.g., quasars) and producesmultiple images of the source, changes of the source lu-minosity due to variability appear on multiple images atdi"erent times.The time delay at a given image position ! for a given

source position ", t(!,"), depends on the angular diam-eter distances as (see, e.g., Schneider et al. 2006, for a

E.Komatsu et al., arXiv:1001.4538

WMAP result

ns = 0.968± 0.012 (68%CL)


GWs from inflation

ds2 = −dt2 + a2(t)(δij + hij)dxidxj

Tensor perturbation of the metric = GW

Quantum fluctuation of the metric during inflationLong wavelength gravity waves

r = 0.14

Hinf

1014GeV

2

Amplitude is proportional to inflation energy scale

Hinf : Hubble parameterduring inflation

Tensor-scalar ratio : r =∆2

h

∆2R


Smith,Kamionkowski,Cooray(06)

GW energy spectrum

Inflationary GW2011年2月17日木曜日


CMBanisotropy

GW energy spectrum



CMBanisotropy

Space-laserinterferometer

GW energy spectrum


Detection of GWB

CMB anisotropy

Direct detection

f H−10

f ∼ L−1

GWB affects large-scale CMB anisotropy

Temperature anisotropy

Polarization anisotropy (B-mode)

GroundSpace

WMAP, Planck

Planck, QUIET, PolarBeaR, LiteBIRD, ...

LCGT , LIGO (L~1km)

LISA (L~10^5 km) , DECIGO (L~10^3km)

Laser interferometer experiments


CMB Polarization


Pattern of polarization

E-mode

B-mode

Generated by Thomsonscattering at the

last scattering surfacefrom scalar perturbation

Generated by tensor mode

Secondary generationby gravitational lens effect

probe of inflation !


gray:r=10, red:r=1.2, blue:r=0.20

Effect on CMB polarization E.Komatsu et al., arXiv:0803.4547


42 Komatsu et al.

(We found a = 0.67±0.09 and 0.43±0.12 for rout = 6r500.See Table 13.) These results are somewhat puzzling -the X-ray observations directly measure gas out to r500,and thus we would expect to find a ! 1 at least out tor500. This result may suggest that, as we have shown inSection 7.3, the problem is not with the outskirts of thecluster, but with the inner parts where the cooling flowhas the largest e!ect.The relative amplitudes between high and low LX clus-

ters suggest that a significant amount of pressure is miss-ing in low mass (M500 ! 4"1014 h!1 M") clusters, evenif we scale all the results such that high-mass clustersare forced to have a = 1. A similar trend is also seenin Figure 3 of Melin et al. (2010). This interpretation isconsistent with the SZ power spectrum being lower thantheoretically expected. The SPT measures the SZ powerspectrum at l " 3000. At such high multipoles, the con-tributions to the SZ power spectrum are dominated byrelatively low-mass clusters, M500 ! 4 " 1014 h!1 M"

(see Figure 6 of Komatsu & Seljak 2002). Therefore,a plausible explanation for the lower-than-expected SZpower spectrum is a missing pressure (relative to theory)in lower mass clusters.Scaling relations, gas pressure, and entropy of low-

mass clusters and groups have been studied in theliterature.41 Leauthaud et al. (2010) obtained a rela-tion between LX of 206 X-ray-selected galaxy groupsand the mass (M200) derived from the stacking anal-ysis of weak lensing measurements. Converting theirbest-fitting relation to r200–LX relation, we find r200 =1.26 h!1 Mpc

E0.89(z) [LX/(1044 h!2 erg s!1)]0.22. (Note thatthe pivot luminosity of the original scaling relation is2.6 " 1042 h!2 erg s!1.) As r500 ! 0.65r200, their rela-tion is ! 1! higher than the fiducial scaling relation thatwe adopted (equation (81)). Had we used their scalingrelation, we would find even lower normalizations.The next generation of simulations or analytical cal-

culations of the SZ e!ect should be focused more on un-derstanding the gas pressure profiles, both the amplitudeand the shape, especially in low-mass clusters. New mea-surements of the SZ e!ect toward many individual clus-ters with unprecedented sensitivity are now becomingavailable (Staniszewski et al. 2009; Hincks et al. 2009;Plagge et al. 2010). These new measurements would beimportant for understanding the gas pressure in low-massclusters.

8. CONCLUSION

With the WMAP 7-year temperature and polariza-tion data, new measurements of H0 (Riess et al. 2009),and improved large-scale structure data (Percival et al.2009), we have been able to rigorously test the stan-dard cosmological model. The model continues to bean exquisite fit to the existing data. Depending onthe parameters, we also use the other data sets suchas the small-scale CMB temperature power spectra(Brown et al. 2009; Reichardt et al. 2009, for the primor-dial helium abundance), the power spectrum of LRGsderived from SDSS (Reid et al. 2010a, for neutrino prop-erties), the Type Ia supernova data (Hicken et al. 2009b,

41 A systematic study of the thermodynamic properties of low-mass clusters and groups is given in Finoguenov et al. (2007) (alsosee Finoguenov et al. 2005a,b).

Fig. 20.— Two-dimensional joint marginalized constraint (68%and 95% CL) on the primordial tilt, ns, and the tensor-to-scalarratio, r, derived from the data combination of WMAP+BAO+H0.The symbols show the predictions from “chaotic” inflation mod-els whose potential is given by V (!) ! !! (Linde 1983), with" = 4 (solid) and " = 2 (dashed) for single-field models, and" = 2 for multi-axion field models with # = 1/2 (dotted;Easther & McAllister 2006).

for dark energy), and the time-delay distance to thelens system B1608+656 (Suyu et al. 2010, for dark en-ergy and spatial curvature). The combined data setsenable improved constraints over the WMAP-only con-straints on the cosmological parameters presented inLarson et al. (2010) on physically-motivated extensionsof the standard model.We summarize the most significant findings from our

analysis (also see Table 2, 3, and 4):

1. Gravitational waves and primordial powerspectrum. Our best estimate of the spectral indexof a power-law primordial power spectrum of curva-ture perturbations is ns = 0.968±0.012 (68% CL).We find no evidence for tensor modes: the 95% CLlimit is r < 0.24.42 There is no evidence forthe running spectral index, dns/d ln k = #0.022±0.020 (68% CL). Given that the improvementson ns, r, and dns/d lnk from the 5-year resultsare modest, their implications for models of infla-tion are similar to those discussed in Section 3.3of Komatsu et al. (2009a). Also see Kinney et al.(2008), Peiris & Easther (2008) and Finelli et al.(2010) for more recent surveys of implications forinflation. In Figure 20, we compare the 7-yearWMAP+BAO+H0 limits on ns and r to the pre-dictions from inflation models with monomial po-tential, V (") $ "!.

2. Neutrino properties. Better determinations ofthe amplitude of the third acoustic peak of thetemperature power spectrum and H0 have led toimproved limits on the total mass of neutrinos,!

m" < 0.58 eV (95% CL), and the e!ective num-ber of neutrino species, Ne! = 4.34+0.86

!0.88 (68% CL),both of which are derived from WMAP+BAO+H0without any information on the growth of struc-ture. When BAO is replaced by the LRG power

42 This is the 7-year WMAP+BAO+H0 limit. The 5-yearWMAP+BAO+SN limit was r < 0.22 (95% CL). For comparison,the 7-year WMAP+BAO+SN limit is r < 0.20 (95% CL). Theselimits do not include systematic errors in the supernova data.

WMAP 7-year resultE.Komatsu et al. (2010)

Inflation modelsbegin to be

constrained fromobservations


B-mode from inflation

- 3 -

Fig. 1.1.1. The sensitivity of EPIC-LC, WMAP and Planck to CMB polarization anisotropy. E-mode polarization anisotropy from scalar perturbations are shown in red; B-mode from tensor perturbations are shown in blue for r = 0.3 and r = 0.01 Inflationary Gravitational Waves (IGWs); and B-mode polarization produced by lensing of the E-mode polarization is shown in green. The science goal of EPIC is to reach the level of r = 0.01 for the entire < 100 multipole range after foreground subtraction. Expected B-mode foreground power spectra for polarized dust (orange dash-dotted) and synchrotron (orange dotted) at 70 GHz are determined by power-law models fits to the foreground power in a combination of WMAP 23 GHz polarization maps [29], low frequency radio maps [30], and 100 micron dust map for |b| > 20˚ [31] for a 65% sky cut. The sensitivity of EPIC-LC is given over a range from the required baseline sensitivity (top of the cyan band) and a 1-year mission to the design TES-option sensitivity and a 2-year mission (bottom of the cyan band). The sensitivity for EPIC-CS is taken from required mission parameters. WMAP assumes an 8-year mission life; Planck assumes 1.2 years at goal sensitivities for HFI. Note the sensitivity curves show band-combined sensitivities to C is broad / = 0.3 bins in order to compare the full raw statistical power of the three experiments in the same manner. Final sensitivity to r after foregrounds removal will naturally be reduced.

The next step is to determine the new ultra-high-energy physics responsible for inflation. Inflation predicts a cosmological background of stochastic gravitational waves, produced during inflation through quantum-mechanical excitations of the gravitational field [14-15]. Since the production process is purely gravitational, the theory predicts that the amplitude of the gravitational-wave background depends only on the universal expansion rate -- or equivalently on the cosmological energy density, the age of the Universe, or the height of the inflaton potential -- during inflation. Since the cosmological energy density during inflation varies from one model of inflation to another, the amplitude of gravitational wave background cannot be

Inflation GWs

Gravitational lens effect

r = 0.3r = 0.01

arXiv:0805.4207

Ground telescope (QUIET-II, PolarBeaR,...) :Space telescope (LiteBIRD, EPIC) : r 0.003

r 0.03


What’s next?Inflationary GWs gives us information about

the inflation energy scale.

Still we do not know thermal history of the Universe between inflation and BBN.

Direct detection of GWs will help us understand complete thermal history of the

Universe.

DECIGO, BBO

Reheating temperature TR


Direct detection of GWs

Figure 1: (Top) Spectra of the gravitational wave background for inflationary scale Hinf =1014 GeV and 1013 GeV. Here we have taken TR = 107 GeV. Also shown are sensitivitiesof planned space-based gravitational wave detectors, DECIGO with a correlation analysis(blue dashed line), ultimate-DECIGO (purple dotted line), and correlation of analysis ofultimate-DECIGO (red dot-dashed line). (Bottom) Same as the top panel for the dilutionfactor F = 10 for T!=10 GeV and TR = 107 GeV.

5

KN, J.Yokoyama, 0910.0715

CMBanisotropy

Space-laserinterferometer


H−1Hubble horizon

radius

Inflation Radiation

Different modes (frequency) of GWs experienced different thermal history.

GW spectrum reflects thermal history of the Universe

t

Reheating matter

CMB scale

Directdetection

scale

TR

t0


H−1Hubble horizon

radius

GW wavelength

Inflation Radiation

Different modes (frequency) of GWs experienced different thermal history.

GW spectrum reflects thermal history of the Universe

t

Reheating matter

CMB scale

Directdetection

scale

TR

t0


R.D.M.D. reheatingHorizon entry

during

DECIGOcorrelated

ultimate-DECIGO

ul-DECIGOcorrelated

DECIGO

Gravitational Wave Spectrum



during

DECIGOcorrelated

ultimate-DECIGO

ul-DECIGOcorrelated

DECIGO

Normalizationis determined

by r




during

DECIGOcorrelated

ultimate-DECIGO

ul-DECIGOcorrelated

DECIGO

Normalizationis determined

by r


Bending point isdetermined by TR


Direct detection of GWsInflationary GWs contains informationabout thermal history after inflation

as well as inflation itself.

Detecting GWs is an only way to probe theearly Universe much before BBN.

We can understand all the history of theUniverse after inflation by GWs !

When did the radiation dominatedUniverse begin?

What did happen after inflation?

TR


Future observationscan determineor constrain TR

DECIGO-correlated ultimate-DECIGO

ultimate-DECIGO (corr)

TR can be determinedGW can be detected

KN, S.Saito,Y.Suwa, J.Yokoyama (2008)


Future observationscan determineor constrain TR

DECIGO-correlated ultimate-DECIGO

ultimate-DECIGO (corr)

TR can be determinedGW can be detected

CMB CMB

KN, S.Saito,Y.Suwa, J.Yokoyama (2008)


SummaryInflationary GWs contains informationabout thermal history after inflation

as well as inflation itself.

B-mode will tell us about the inflation energy scale

Direct detection will tell us about thermalhistory between inflation and BBN.

We can understand all the history of theUniverse after inflation by GWs !


Back-up Slides


ρGW(k) ∼ 1G

h2k(k/a)2 k/a ∼ H

ρtot ∼1G

H2

at horizon entry

ΩGW(k) =ρGW(k)

ρtot∼ const. at horizon entry

After horizon entry,

ΩGW(k) ∝ const. in RD

ΩGW(k) ∝ a−1 in MD

∝ k0

∝ k−2

ΩGW(k)

k

∝ k−2

At the horizon entry,

∝ a(k)/a0 ∝ k−2


10 6 10 5 10 4 10 3 10 2 10 1 100

10 16

10 14

10 12

10 10

10 8

10 6

fr / Hz

gw

Extrapolated

Extragalactic‘Average’

Astrophysical foreground(1) White Dwarf binary

Farmer and Phinney (03)

Completely stochastic

Cannot be removed.

Merger of WD binary

Gravitational Waves


(2) Population III Stars

Suwa, Takiwaki, Kotake, Sato (06)

Collapse of first stars Gravitational Waves

May hide inflationary GW

But SFR at earlyepoch is uncertain

Duty cycle maynot be so large

Can be removed.


CMB and physics of the early Universe - 名古屋大学...CMB and physics of the early Universe...

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