Observational constraints on the standard cosmological model …physics.iitm.ac.in/~sriram/professional/research/talks/... · 2015. 3. 6. · CO white dwarf star approaching the Chandrasekhar

Observational constraints on thestandard cosmological model and beyond

L. Sriramkumar

Department of Physics, Indian Institute of Technology Madras, Chennai

Workshop on Gravitational Waves

Chennai Mathematical Institute, Chennai

March 2–4, 2015

http://www.physics.iitm.ac.in/~sriram/

Introduction Plan

Plan of the talk

1 Introduction

2 Constraints from the supernovae data

3 Constraints from Planck

4 Constraints from the BAO data

5 Beyond the standard model

6 Summary

L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 2 / 57

Introduction

Ben Wandelt’s cosmic cone

A schematic representation of the past light cone1. On the left are the cos-mological observables, already observed or predicted. On the right are thephysical phenomena they relate to, in the standard cosmological model.

1F. Leclercq, A. Pisani, B. D. Wandelt, arXiv:1403.1260 [astro-ph.CO].L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 3 / 57

Constraints from the supernovae data

Supernovae (SNe) and dark energy2

SNe Ia remain, at present, the most direct and mature method of probingthe dark energy due to several decades of intensive study and use incosmology.Thought to be the result of the thermonuclear destruction of an accretingCO white dwarf star approaching the Chandrasekhar mass limit, they arestandardizable candles which explode with nearly the same brightnesseverywhere in the universe due to the uniformity of the triggering massand hence the available nuclear fuel.Their cosmological use exploits simple empirical relations between theirluminosity and other parameters.

2M. Sullivan et al., Astrophys. J. 737, 102 (2011).L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 4 / 57


The Supernova Legacy Survey (SNLS)3

The Canada-France-Hawaii Telescope (CFHT) Legacy Survey Super-nova Program (SNLS) primary goal was to measure the equation of stateof dark energy. It was designed to precisely measure several hundredType Ia supernovae at redshifts between about 0.3 and unity.

The SNLS survey consisted of:A large imaging survey at CFHT: Between 2003 and 2008, the CFHTLegacy Survey detected and monitored about 1000 SNe.A large spectroscopic survey: About 500 high-redshift Type Ia SNe wereobserved on 8 m class telescopes (Gemini, VLT, Keck). The primarygoal was to obtain supernova identification and redshift. Detailed spec-troscopy of a subsample of distant SNe was also done to validate the useof Type Ia SNe as cosmological candles.

3See http://cfht.hawaii.edu/SNLS/.L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 5 / 57


A supernova explosion in a distant galaxy

A supernova at z = 0.28 discovered by SNLS4. The supernova appears in theleft image at maximum light and on the right is an image after the supernovahas faded.

4C. J. Pritchet et al., arXiv:astro-ph/0406242.L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 6 / 57


SNLS3 and other data sets5

The SNe Ia samples are divided into two categories: those discoveredand confirmed by SNLS, and those taken from the literature which sampledifferent redshift ranges to SNLS.The complete data set consists of 242 well-sampled SNe Ia over 0.08 <z < 1.06 from the SNLS together with a large literature sample: 123 SNeIa at low-redshift, 14 SNe Ia at z & 0.8 from the Hubble Space Telescope,and 93 SNe Ia at intermediate redshift from the first year of the SDSS-IISN search.The advantages of the enlarged SNLS data set are multiple. Most obvi-ously, this represents a threefold increase in the SNLS sample size com-pared to the first year SNLS cosmological analysis, and as such providesa significant improvement in the statistical precision of the cosmologicalconstraints.Moreover, the enlarged data set allows sources of potential astrophysicalsystematics to be examined by dividing our SN Ia sample according toproperties of either the SN or its environment.



Constraints on the background parameters6

All the results from SNLS3 are consistent with a spatially flat, w = −1 uni-verse.

The results for a flat universe with a constant dark energy equation of stateare

Ωm = 0.269± 0.015,

w = −1.061+0.069−0.068,

and, relaxing the assumption of spatial flatness,

Ωm = 0.271± 0.015,

Ωk = −0.002± 0.006,

w = −1.069+0.091−0.092,

including external constraints from WMAP7 and SDSS DR7 and a prior onH0.



Constraints in the spatially flat case

0.1 0.2 0.3 0.4 0.5Ωm

1.4

1.2

1.0

0.8

0.6

0.4

w

H0

SNLS3

SDSS DR7 LRGs

WMAP7 + ...

Confidence contours on the cosmological parameters Ωm and w assuming a flat uni-verse, produced using the CosmoMC program7. The SNLS3 contours are in blue, theSDSS DR7 LRG contours in green, and the H0 prior in red. WMAP7 constraints areincluded in all contours. The combined constraints are shown in grey.



Constraints in the non-flat case

0.1 0.2 0.3 0.4 0.5Ωm

2.00

1.75

1.50

1.25

1.00

0.75

0.50

0.25

w

H0

SNLS3

SDSS DR7 LRGs

0.1 0.2 0.3 0.4 0.5Ωm

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

ΩD

E

H0

SNLS3

SDSS DR7 LRGs

0.1 0.2 0.3 0.4 0.5Ωm

0.04

0.02

0.00

0.02

0.04

Ωk

H0SNLS3

SDSS DR7 LRGs

WMAP7 + ...

Confidence contours on the cosmological parameters Ωm, ΩDE

, Ωk, and w,with the same choice of colors to represent the different data sets as in theprevious figure8.



Parameterizing the variation in dark energyThe variation in the dark energy is usually parametrized as9

w(a) = w0 + wa (1− a),

with the cosmological constant being equivalent to w0 = 1 and wa = 0.

Upon assuming a spatially flat universe, the best fit values and the 1-σ devia-tions of the parameters (Ωm, w0, wa) prove to be10

Ωm = 0.271+0.015−0.015,

w0 = −0.905+0.196−0.196,

wa = −0.984+1.094−1.097.

In other words, there is no evidence for a deviation from the cosmologicalconstant.

9M. Chevallier and D. Polarski, Int. J. Mod. Phys. D, 10, 213 (2001);E. V. Linder, E. V. 2003, Phys. Rev. Lett. 90, 091301 (2003).



Constraints on the variation in dark energy

0.20 0.25 0.30 0.35Ωm

1.50

1.25

1.00

0.75

0.50

0.25

w0

1.5 1.0 0.5w0

4

3

2

1

0

1

2

wa

SNLS3+SDSS DR7 LRGs+WMAP7+H0 (Flat)

Combined confidence contours in Ωm, w0 and wa using SNLS3, WMAP7,SDSS DR7 LRGs, and a prior on H0. A flat universe is assumed, and a priorof w0 + wa ≤ 0 has been enforced—any apparent discrepancy with this prioris a result of smoothening the CosmoMC output11.



The dark energy survey

Expected constraints from the dark energy survey12.12From https://www.darkenergysurvey.org/reports/proposal-standalone.pdf.


Constraints from Planck The observed angular power spectra

The Planck missionPlanck’s scientific payload contained an array of 74 detectors in nine fre-quency bands sensitive to frequencies between 25 and 1000 GHz, whichscanned the sky with angular resolution between 33′ and 5′.Planck had carried a Low Frequency Instrument (LFI) and a High Fre-quency Instrument (HFI). The detectors of the LFI were pseudo-correlationradiometers, covering bands centered at 30, 44, and 70 GHz. The detec-tors of the HFI were bolometers, covering bands centered at 100, 143,217, 353, 545, and 857 GHz.Planck imaged the whole sky twice in one year, with a combination of sen-sitivity, angular resolution, and frequency coverage never before achieved.



CMB anisotropies as seen by Planck

CMB intensity map at 5′ resolution derived from the joint analysis of Planck,WMAP, and 408 MHz observations13.

13P. A. R. Ade et al., arXiv:1502.01582 [astro-ph.CO].L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 15 / 57


CMB TT angular power spectrum from Planck14

0

1000

2000

3000

4000

5000

6000

DT

T`

[µK

2]

30 500 1000 1500 2000 2500`

-60-3003060

D

TT

`

2 10-600-300

0300600

The CMB TT angular power spectrum from the Planck 2015 data (the bluedots with error bars) and the theoretical, best fit ΛCDM model with a powerlaw primordial spectrum (the solid red curve).



CMB TE and EE angular power spectra from Planck15

-140

-70

0

70

140

DT

E`

[µK

2]

30 500 1000 1500 2000

`

-100

10

D

TE

`

0

20

40

60

80

100

CEE

`[1

05µK

2]

30 500 1000 1500 2000

`

-404

CE

E`

The CMB TE (on the left) and EE (on the right) angular power spectra fromthe Planck 2015 data (the blue dots with error bars) and the theoretical, bestfit ΛCDM model with a power law primordial spectrum (the solid red curves).



Best fit values of the cosmological parameters16

Parameter TT+lowP TT+lowP+lensing TT+lowP+BAO TT,TE,EE+lowP

Ωbh2 0.02222± 0.00023 0.02226± 0.00023 0.02226± 0.00020 0.02225± 0.00016

Ωch2 0.1197± 0.0022 0.1186± 0.0020 0.1190± 0.0013 0.1198± 0.0015

100θMC 1.04085± 0.00047 1.04103± 0.00046 1.04095± 0.00041 1.04077± 0.00032τ 0.078± 0.019 0.066± 0.016 0.080± 0.017 0.079± 0.017

ln(1010As) 3.089± 0.036 3.062± 0.029 3.093± 0.034 3.094± 0.034ns 0.9655± 0.0062 0.9677± 0.0060 0.9673± 0.0045 0.9645± 0.0049

H0 67.31± 0.96 67.81± 0.92 67.63± 0.57 67.27± 0.66Ωm 0.315± 0.013 0.308± 0.012 0.3104± 0.0076 0.3156± 0.0091

Confidence limits on the parameters of the base ΛCDM model, for variouscombinations of the Planck 2015 data, at the 68% confidence level.


Constraints from Planck Constraints on the background cosmological parameters

Tension regarding H0

Comparison of the H0 measurements, with estimates of ±1-σ errors, from anumber of techniques17. These are compared with the spatially flat ΛCDMmodel constraints from Planck and WMAP9.


Constraints from Planck Constraints on dark energy

Why is the CMB relevant for dark energy?18

1 Change the expansion history and hence distance to the last scattering surface,with a shift in the peaks, sometimes referred to as a geometrical projection effect

2 Cause the decay of gravitational potentials at late times, affecting the low-multipoleCMB anisotropies through the integrated Sachs-Wolfe (ISW) effect

3 Enhance the cross-correlation between the CMB and large-scale structure, throughthe ISW effect

4 Change the lensing potential, through additional DE perturbations or modifica-tions of GR

5 Modify the lensing B-mode contribution, through changes in the lensing potential6 Modify the primordial B-mode amplitude and scale dependence, by changing the

sound speed of gravitational waves



Constraints on the dark energy parameters

−2 −1 0 1

w0

−3

−2

−1

0

1

2

wa

Planck+BSH

Planck+WL

Planck+BAO/RSD

Planck+WL+BAO/RSD

Marginalized posterior distributions of the (w0,wa) parameterization for variousdata combinations19.



Evolution of the equation of state20

0 1 2 3 4 5

z

−1.5

−1.0

−0.5

0.0

w(z

)

Planck+BSH

Planck+WL+BAO/RSD

Reconstructed equation of state w(z) as a function of redshift, when assuminga Taylor expansion of w(z) to first order, for different combinations of the datasets. The colored areas show the regions which contain 95 % of the models.


Constraints from Planck Constraints on inflation

The scalar spectral index and running21

For the base ΛCDM model with a power law power spectrum of curvatureperturbations, the constraint on the scalar spectral index, ns, with the Planckfull mission temperature data is

ns = 0.9655± 0.0062 (68 % CL, Planck TT + low P).

The running of the scalar spectral index is constrained by the Planck 2015 fullmission temperature data to

dns

d ln k= −0.0084± 0.0082 (68 % CL, Planck TT + low P).

The combined constraint including high-` polarization is

dns

d ln k= −0.0057± 0.0071 (68 % CL, Planck TT, TE, EE + low P).

Adding the Planck CMB lensing data to the temperature data further reducesthe central value for the running, i.e. dns/d ln k = −0.0033± 0.0074 (68 % CL,Planck TT + low P+ lensing).



Joint constraints on the spectral index and running22

0.92 0.94 0.96 0.98 1.00ns

−0.0

40.0

00.

04

Ru

nn

ing

spec

tral

ind

exdn

s/d

lnk

Planck 2013

Planck TT+lowP

Planck TT,TE,EE+lowP

Marginalized joint 68 % and 95 % CL for (ns,dns/d ln k) using Planck TT +low P and Planck TT, TE, EE + low P. The thin black stripe shows the predictionfor single field monomial chaotic inflationary models with 50 < N∗ < 60.



Constraints on the tensor-to-scalar ratio r23

The constraints on the tensor-to-scalar ratio inferred from the Planck full mis-sion data for the ΛCDM + r model are:

r0.002 < 0.10 (95 % CL, Planck TT + low P),r0.002 < 0.11 (95 % CL, Planck TT + low P + lensing),r0.002 < 0.11 (95 % CL, Planck TT + low P + BAO),r0.002 < 0.10 (95 % CL, Planck TT, TE, EE + low P).



Spectral index and running with tensors24

0.92 0.94 0.96 0.98 1.00ns

−0.0

40.0

00.

04

Ru

nn

ing

spec

tral

ind

exdn

s/d

lnk

Planck 2013

Planck TT+lowP


Marginalized joint confidence contours for (ns,dns/d ln k), at the 68 % and95 % CL, in the presence of a non-zero tensor contribution, and using PlanckTT + low P or Planck TT, TE, EE + low P.



Joint constraints on r and ns25

0.94 0.96 0.98 1.00

Primordial tilt (ns)

0.0

00.

150.3

0

Ten

sor

tosc

alar

rati

or

Planck 2013

Planck TT+lowP


Marginalized joint confidence contours for (ns, r), at the 68 % and 95 % CL, inthe presence of running of the spectral indices, and for the same combinationsof data as in the previous figure.



Constraints on the slow roll parameters26

0.00 0.02 0.04 0.06 0.08ε2

0.00

00.

008

0.01

6

ε 1

Convex

Concave

Planck 2013 Planck TT+lowP Planck TT,TE,EE+lowP

−0.04 −0.02 0.00 0.02ηV

0.00

00.

008

0.01

6

ε V

ConvexConcave

Joint 68 % and 95 % CL regions for (ε1, ε2) (top panel) and (εV, η

V) (bottom

panel) for Planck TT + low P (red contours), Planck TT, TE, EE + low P (bluecontours), and compared with the Planck 2013 results (grey contours).



Performance of models in the ns-r plane27

Marginalized joint 68 % and 95 % CL regions for ns and r0.002 from Planck incombination with other data sets, compared to the theoretical predictions ofselected inflationary models.



Constraints upon inclusion of BICEP data28

Marginalized joint 68 % and 95 % CL regions for ns and r0.002 from Planckalone and in combination with its cross-correlation with BICEP2/Keck Arrayand/or BAO data compared with the theoretical predictions of selected infla-tionary models.



Power spectra with features29

1

2

3

0.0001 0.001 0.01 0.1

10

9 P

R(k

)

k [Mpc-1] Primordial power spectra with features that lead to an improved fit to the datathan the conventional, nearly scale, invariant spectra.


Constraints from Planck Constraints on non-Gaussianities

Template bispectraFor comparison with the observations, the scalar bispectrum is often expressedin terms of the parameters f loc

NL, f eq

NLand forth

NLas follows:

GRRR(k1,k2,k3) = floc

NLG

locRRR(k1,k2,k3) + f

eq

NLG

eqRRR(k1,k2,k3) + f

orth

NLG

orthRRR(k1,k2,k3).

Illustration of the three template basis bispectra30.30E. Komatsu, Class. Quantum Grav. 27, 124010 (2010).



The theoretical CMB TTT angular bispectrum

Theoretical predictions for the reduced bispectrum of the CMB, with inflation-ary models involving non-Gaussianities of local (left), equilateral (center) andorthogonal (right) type31.

31F. Leclercq, A. Pisani, B. D. Wandelt, arXiv:1403.1260 [astro-ph.CO].L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 33 / 57


The observed CMB TTT angular bispectrum

The CMB TTT angular bispectrum, as observed by Planck32.



Constraints on the scalar non-Gaussianity parametersThe constraints on the primordial values of the non-Gaussianity parametersfrom the Planck data are as follows33:

f locNL

= 0.8± 5.0,

f eqNL

= −4± 43,

forthNL

= −26± 21.

These constraints imply that slowly rolling single field models involving thecanonical scalar field which are favored by the data at the level of power spec-tra are also consistent with the data at the level of non-Gaussianities.


Constraints from Planck Constraints on relativistic species

Constraints on the neutrino massesThe constraints on the sum of the neutrino masses, assuming three speciesof degenerate massive neutrinos, are as follows34:∑

mν < 0.72 eV (95 % CL, Planck TT + low P),∑mν < 0.21 eV (95 % CL, Planck TT + low P + BAO),∑mν < 0.49 eV (95 % CL, Planck TT, TE, EE + low P),∑mν < 0.17 eV (95 % CL, Planck TT, TE, EE + low P + BAO).


Constraints from Planck Constraints on relativistic species

Constraints on the number of relativistic speciesThe constraints on the sum of the number of relativistic species are as fol-lows35:

Neff = 3.13± 0.32 (68 % CL, Planck TT + low P),Neff = 3.15± 0.23 (68 % CL, Planck TT + low P + BAO),Neff = 2.99± 0.20 (68 % CL, Planck TT, TE, EE + low P),Neff = 3.04± 0.18 (68 % CL, Planck TT, TE, EE + low P + BAO).

A significant density of additional radiation still seems to be allowed.


Constraints from the BAO data

Baryon Acoustic Oscillations (BAO)

Snapshots of an evolving spherical density perturbation before and after de-coupling36.

36D. J. Eisenstein, H.-J. Seo and M. White, Astrophys. J. 664, 660 (2007),B. A. Bassett and R. Hlozek, arXiv:0910.5224 [astro-ph.CO].



The scale of BAOThe BAO are frozen relics left over from the pre-decoupling universe.

The scale of BAO is set by the comoving size of the sound horizon at decou-pling, which is given by

rs =c√3

tdec∫0

dt

a(t).

For zdec ' 1100, one finds that rs ' 150 Mpc.

One finds that the sound horizon can be approximated, around the WMAP5best-fit location as37

rs(zd) = 153.5

(Ωb h

2

0.02273

)−0.134 (Ωm h2

0.1326

)−0.255

Mpc.

37E. Komatsu et al., Astrophys. J. Suppl. 180, 330 (2009).L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 39 / 57


BAO in real space38

The Baryon Acoustic Peak (BAP) in the correlation function—the BAP is visible in theclustering of the SDSS LRG galaxy sample, and is sensitive to the matter density[shown are models with Ωm h

2 = 0.12 (top), 0.13 (second) and 0.14 (third), all withΩb h

2 = 0.024]. The bottom line without a BAP is the correlation function in the pureCDM model, with Ωb = 0.

38D. J. Eisenstein et al., Astrophys. J. 633, 560 (2005).L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 40 / 57


BAO in the WiggleZ survey

0 50 100 150 200

s [h−1 Mpc]

−60

−40

−20

0

20

40

60

80

s2ξ 0

[h−2

Mpc2

]

0.2<z<0.6

no reconstructionreconstructed

0 50 100 150 200

s [h−1 Mpc]

−60

−40

−20

0

20

40

60

80

s2ξ 0

[h−2

Mpc2

]

0.4<z<0.8


0 50 100 150 200

s [h−1 Mpc]

−60

−40

−20

0

20

40

60

80

s2ξ 0

[h−2

Mpc2

]

0.6<z<1.0


0 50 100 150 200

s [h−1 Mpc]

−60

−40

−20

0

20

40

60

80

s2ξ 0

[h−2

Mpc2

]

0.2<z<1


The WiggleZ two-point correlation functions (red squares) for three redshifts bins andthe full z range. These are plotted as ξ s2 to emphasize the feature39.

39E. A. Kazin et al., Mon. Not. Roy. Astron. Soc. 441, 3524 (2014).L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 41 / 57


Fourier pairs ξ(r) and P (k)

100 150 200 2500

0.2

0.4

0.6

0.8

1

r

ξ(r)

0 0.1 0.2 0.3 0.4−1.5

−1

−0.5

0

0.5

1

1.5

k

P(k)

Schematic illustration of the Fourier pairs ξ(r) and P (k). A sharp peak in thecorrelation function (left panel) corresponds to a series of oscillations in thepower spectrum (right panel). The BAP in the correlation function will inducecharacteristic BAO in the power spectrum40.

40B. A. Bassett and R. Hlozek, arXiv:0910.5224 [astro-ph.CO].L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 42 / 57


BAO in Fourier space41

BAO in the SDSS power spectra—the BAP of the previous figure now becomes aseries of oscillations in the matter power spectrum of the SDSS sample. The solidlines show the ΛCDM fits to the WMAP3 data, while the dashed lines include nonlinearcorrections.

41M. Tegmark et al., Phys. Rev. D 74, 123507 (2006).L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 43 / 57


BAO in the SDSS power spectra42

BAO recovered from the SDSS Data (release 7galaxy sample) for each of the redshifts slices (solidcircles with 1-σ error bars). These are comparedwith BAO in the default ΛCDM model (solid lines).

42W. Percival et al., arXiv:0907.1660 [astro-ph.CO].L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 44 / 57


BAO as a standard ruler

The radial length of an object is given by cdz/H(z) where dz is the difference inredshift between the front and back of the object, while the transverse size of theobject is dA(z) θ and θ is its angular size. If one knows that the object is spherical (butdoes not know the actual diameter), then one can determine the product dA(z)H(z)

from measuring dz/θ. If, as in the case of BAO, one can theoretically determine thediameter, one has the bonus of finding dA(z) and H(z) separately43.

43B. A. Bassett and R. Hlozek, arXiv:0910.5224 [astro-ph.CO].L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 45 / 57


BAO surveysBAO surveys measure the distance ratio

dz =rs(zdrag)

DV

(z),

where rs(zdrag) is the comoving sound horizon at the baryon drag epoch(when baryons became dynamically decoupled from the photons) and DV(z)is a combination of the angular diameter distance, dA(z), and the Hubble pa-rameter, H(z), appropriate for the analysis of spherically-averaged two-pointstatistics:

DV(z) =

[(1 + z)2 d2

A(z) c z

H(z)

]1/3

.



Constraints from WiggleZ

64.5 66.0 67.5 69.0 70.5H0

0.28

0.30

0.32

0.34

0.36

Ωm

ΛCDM

60 63 66 69 72H0

−0.024

−0.016

−0.008

0.000

0.008

ΩK

oΛCDM

50 60 70 80 90 100H0

−2.0

−1.6

−1.2

−0.8

−0.4

w

wCDM

−3.0 −2.5 −2.0 −1.5 −1.0 −0.5w

−0.045

−0.030

−0.015

0.000

0.015

ΩK

owCDM

CMB

CMB, 6dF

CMB, WiggleZ pre-recon

CMB, WiggleZ post-recon

CMB, WiggleZ, 6dFGS

Marginalized joint confidence regions of cosmological parameter pairs from the Wig-gleZ survey and the CMB (Planck 2013 + WMAP9 polarization) data44.

44E. A. Kazin et al., Mon. Not. Roy. Astron. Soc. 441, 3524 (2014).L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 47 / 57


Constraints from BAO surveys and Planck

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

z

0.90

0.95

1.00

1.05

1.10

(DV/

r dra

g)/

(DV/

r dra

g) P

lan

ck

6DFGS

SDSS MGS

BOSS LOWZBOSS CMASS

WiggleZ

Acoustic scale distance ratio rs/DV(z) divided by the distance ratio of the

Planck base ΛCDM model45. The grey bands shows the approximate 68%and 95% ranges allowed by Planck.


Beyond the standard model Low ` anamolies in the CMB data

Hemispherical asymmetry: Prior to PlanckWith the first year WMAP data, it was discovered that the angular powerspectrum, when estimated locally at different positions on the sphere,appears not to be isotropic46.In particular, the power spectrum calculated for a hemisphere centeredat (θ, φ) = (110, 237) (in galactic co-latitude and longitude) was largerthan when calculated in the opposite hemisphere over the multipole range` = 2–40.

46H. K. Eriksen, F. K. Hansen, A. J. Banday, K. M. Gorski and P.B. Lilje, Astrophys. J. 605, 14 (2004);F. K. Hansen, A. J. Banday and K. M. Gorski, Mon. Not. Roy. Astron. Soc. 354, 641 (2004).


Beyond the standard model Low ` anamolies in the CMB data

Hemispherical asymmetry: Planck 2013

The two-point (upper left), pseudo-collapsed (upper right), equilateral three-point (lowerleft), and rhombic four-point (lower right) correlation functions (Nside = 64). Correlationfunctions are shown for the analysis performed on northern (blue) and southern (red)hemispheres determined in the ecliptic coordinate frame47.


Beyond the standard model Distance duality relation

The distance-duality relationIn any metric theory of gravity, the luminosity distance dL(z) and the angulardiameter distance d

A(z) are related as follows48:

dL(z) = (1 + z)2 dA(z).

While this relation is impervious to gravitational lensing, it depends cruciallyon photon conservation. The distance-duality relation can become a powerfultest of a wide range of both exotic and fairly mundane physics49.

48J. M. H. Etherington, Phil. Mag. 15, 761 (1933).49B. A. Bassett and M. Kunz, Phys. Rev. D 69, 101305 (2014).


Beyond the standard model Distance duality relation

Constraints on the distance-duality relation

0.0 0.5 1.0 1.5 2.0

0.0

0.5

1.0

1.5

2.0

2.5

z

Η

ΗVI

ΗV

0.0 0.5 1.0 1.5 2.00.0

0.5

1.0

1.5

2.0

z

Η

ΗVI

ΗV

Constraints on the ratio η(z) = dL/[d

A(1 + z)2] from the supernovae and the

BAO data50.

50R. Nair, S. Jhingan and D. Jain, JCAP 1105, 023 (2011).L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 52 / 57

Beyond the standard model The growth rate

The growth rateThe growth rate f(z) is defined through the relation51

f(z) =d ln δ

d ln a,

where δ(a) denotes the perturbation in the dark matter.

Recall that, in the matter dominated epoch, δ ∝ a.

51See, for instance, M. J. Mortonson, D. H. Weinberg and M. White, arXiv:1401.0046 [astro-ph.CO].L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 53 / 57


The growth indexThe so-called growth index γ is defined through the relation52

g(a) = exp

∫d ln a [Ωγm(a)− 1] ,

where g = δ(a)/a, with δ denoting the perturbation in the dark matter. Withingeneral relativity and in the standard ΛCDM model, it is found that γ ' 0.55.

The growth rate is known to be different when there is variation in the darkenergy and in different models of gravity.

52E. V. Linder, Phys. Rev. D 72, 043529 (2005).L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 54 / 57


Constraints from Euclid on the growth rate

0.0 0.5 1.0 1.5 2.0

0.3

0.4

0.5

0.6

0.7

z

fHzLΣ

8HzL

Forecasts of the errors expected on the growth rate (dark-blue error bars), expressedthrough the bias-free combination f(z)σ8(z), obtainable from the Euclid redshift sur-vey53. The solid black line represents the fiducial f(z)σ8(z), computed for the standardcosmology, while the dashed green line shows the growth in a DGP model. The ma-genta and pink error bars are measurements from past and the recent WiggleZ survey.

53E. Majerotto et al., arXiv:1205.6215 [astro-ph.CO].L. Sriramkumar (IIT Madras, Chennai) Constraints on the standard cosmological model March 3, 2015 55 / 57

Summary

Summary

The six parameter base ΛCDM model continues to provide a very goodmatch to the more extensive 2015 Planck data, including polarization.The 2015 Planck TT, TE, EE, and lensing spectra are consistent witheach other under the assumption of the base ΛCDM cosmology.All of the BAO measurements are compatible with the base ΛCDM pa-rameters from Planck54.


Thank you for your attention

Documents

Observational constraints on the standard cosmological model …physics.iitm.ac.in/~sriram/professional/research/talks/... · 2015. 3. 6. · CO white dwarf star approaching the Chandrasekhar