E. Sefusatti, Tests of the Initial Conditions of the Universe after Planck

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Balkan Workshop BW2013
Beyond the Standard Models
25 – 29 April, 2013, Vrnjačka Banja, Serbia

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E. Sefusatti, Tests of the Initial Conditions of the Universe after Planck

  1. 1. Emiliano SefusattiTests of the Initial Conditions of the Universe after PlanckBW2013,Vrnjačka BanjaApril 27th, 2013
  2. 2. Outline• Initial Conditions from Inflation• CMB Constraints• Implications of Planckʼs results (a sample)• Beyond fNL• Prospects for Large-Scale Structure Observations• Conclusions
  3. 3. Predictions of Inflation• A flat, homogeneous UniversePLANCK (2013)Planck Collaboration: The Planck missionFig. 14. The SMICA CMB map (with 3 % of the sky replaced by a constrained Gaussian realization).
  4. 4. Predictions of InflationPlanck Collaboration: Cosmological parameters• A flat, homogeneous Universe• A (nearly) scale invariant power spectrum for (highly Gaussian) initial fluctuationsPLANCK (2013)
  5. 5. Predictions of Inflation• A flat, homogeneous Universe• A (nearly) scale invariant power spectrum for (highly Gaussian) initial fluctuationsΦk1Φk2 = δD(k1 +k2)PΦ(k1)Φk1Φk2Φk3Φk4 = δD(k1 + ... +k4) TΦ(k1,k2,k3,k4) = 0Φk1Φk2Φk3 = δD(k1 +k2 +k3) BΦ(k1, k2, k3) = 0
  6. 6. Assumptions for a simple inflation model• A single, weakly coupled scalar field• with canonical kinetic term• slow rolling down a smooth potential• initially in a Bunch-Davies vacuum
  7. 7. Assumptions for a simple inflation model• A single, weakly coupled scalar field• with canonical kinetic term• slow rolling down a smooth potential• initially in a Bunch-Davies vacuum
  8. 8. Assumptions for a simple inflation model• A single, weakly coupled scalar field• with canonical kinetic term• slow rolling down a smooth potential• initially in a Bunch-Davies vacuum
  9. 9. Assumptions for a simple inflation model• A single, weakly coupled scalar field• with canonical kinetic term• slow rolling down a smooth potential• initially in a Bunch-Davies vacuum
  10. 10. Assumptions for a simple inflation model• A single, weakly coupled scalar field• with canonical kinetic term• slow rolling down a smooth potential• initially in a Bunch-Davies vacuumBΦ(k1, k2, k3) = 0TΦ(k1,k2,k3,k4) = 0Non-Gaussian Initial Conditions
  11. 11. The shape of non-GaussianityMost models predict a scale-invariant curvature bispectrumBΦ(k, k, k) ∼ P2Φ(k) ∼1k6What distinguish them is the shape“shape” = the dependence of the curvature bispectrum predictedby a given model of inflation on the shape of the triangularconfiguration k1, k2, k3BΦ(k1, k2, k3) = fNL1k21k22k23Fr2 =k2k1, r3 =k3k1
  12. 12. Models of primordial non-GaussianityMultiple fieldsModified vacuumModified vacuumNon-CanonicalKinetic term
  13. 13. Text!#$%(%)*+,)-).)!#$%(%)*+,)-)/...)Polarization *+,)-).)012%34516)*+,)-)/...)!Liguori et al. (2007)The CMB Bispectrum
  14. 14. The CMB BispectrumThe Bispectrum of the CMB is the mostdirect probe of the initial bispectrumBl1l2l3∼BΦ(k1, k2, k3)∆l1(k1)∆l2(k2)∆l3(k3)jl1(k1r)jl2(k2r)jl3(k3r)curvaturebispectrumtransferfunctionsCMB angularbispectrumWMAP 7 years:Local -10 fNL 74Equilateral -214 fNL 266Orthogonal -410 fNL 6@ 95% CL Komatsu et al. (2009)• The CMB provides a snapshot of density perturbations at early times• Power spectrum measurements (Clʼs) are matched by linear predictions• The CMB bispectrum is equally sensitive to any model of non-Gaussianity
  15. 15. The CMB BispectrumThe Bispectrum of the CMB is the mostdirect probe of the initial bispectrumBl1l2l3∼BΦ(k1, k2, k3)∆l1(k1)∆l2(k2)∆l3(k3)jl1(k1r)jl2(k2r)jl3(k3r)curvaturebispectrumtransferfunctionsCMB angularbispectrumWMAP 7 years:Local -10 fNL 74Equilateral -214 fNL 266Orthogonal -410 fNL 6@ 95% CL Komatsu et al. (2009)• The CMB provides a snapshot of density perturbations at early times• Power spectrum measurements (Clʼs) are matched by linear predictions• The CMB bispectrum is equally sensitive to any model of non-GaussianityPlanck (T only):Local -8.9 fNL 14.3Equilateral -192 fNL 108Orthogonal -103 fNL 53@ 95% CL Ade et al. (2013)
  16. 16. The CMB Bispectrum: Planck• Planck temperature data improve WMAPresults by a factors of 2 to 4 (depending onthe shape!)• Planck is very close to theideal CMB experiment (ΔfNLlocal ~ 1)ΔfNL, local ΔfNL, equil. ΔfNL, orth.WMAP 21 140 104Planck 5.8 75 39
  17. 17. The CMB Bispectrum: Planckdvances in Astronomy 2123451020∆fNL200 300 500 700 1000 1500 2000 3000Local modelImaxWMAP (T/T+P)Planck (T/T+P)CMBPol (T/T+P)(a)20304050100∆fNL200 300 500 700 1000 1500 2000 3000Equilateral modelImaxWMAP (T/T+P)Planck (T/T+P)CMBPol (T/T+P)(b)• Planck temperature data improve WMAPresults by a factors of 2 to 4 (depending onthe shape!)• Planck is very close to theideal CMB experiment (ΔfNLlocal ~ 1)Liguori et al. (2010)ΔfNL, local ΔfNL, equil. ΔfNL, orth.WMAP 21 140 104Planck 5.8 75 39Forecastedtemperature polarizationconstraints
  18. 18. Implications of Planck’s results: an exampleDBI inflation (IR)Having characterised single-field inflation bispectra using com-binations of the separable equilateral and orthogonal ans¨atzewe note that the actual leading-order non-separable contribu-tions (Eqs. (6, 7)) exhibit significant differences in the collinear(flattened) limit. For this reason we provide constraints on DBIinflation (Eq. (7)) and the two effective field theory shapes(Eqs. (5, 6)), as well as the ghost inflation bispectrum, whichis an exemplar of higher-order derivative theories (specificallyEq. (3.8) in Arkani-Hamed et al. 2004). Using the primordiamodal estimator, with the SMICA foreground-cleaned data, wefind:fDBINL = 11 ± 69 (FDBI−eqNL = 10 ± 77) ,fEFT1NL = 8 ± 73 (FEFT1−eqNL = 8 ± 77) ,fEFT2NL = 19 ± 57 (FEFT2−eqNL = 27 ± 79) ,fGhostNL = −23 ± 88 (FGhost−eqNL = −20 ± 75) . (86)where we have normalized with the usual primordial f con-where ds24 g dx dx is the metric of the four-dimensional space-time and is a dimensionless parame-ter. The inflaton and the parameter are related to thenotations of Refs. [3,4] by r T3pand T3R4 N.The has the same order of magnitude as the effectivebackground charge N of the warped space and character-izes the strength of the background. The low-energy dy-namics is described by the DBI–Chern-Simons actionSM2Pl2Zd4x gpRZd4x gp 41 4g @ @s4V : (2.3)In the nonrelativistic limit, this action reduces to the usualminimal form.We start the inflaton near 0 through a phase tran-sition.1Without the warped space, the scalar will quicklyroll down the steep potential ( * 1) and make the infla-t comes from backreactions of the[1,4,9] and the de Sitter (dS) spacespace. These effects will smooth out thof a certain IR region of the warped spif we start the inflaton from that regperiod cannot be further increased in tmagnitude. For the case that we consigest lower bound is the closed string cbackground. This gives t pH 1number of e-foldings in this model ilatest e-fold Ne is given byNepH= :It has an interesting relation to thefactor of the inflaton,Ne=3:Since the sound speed cs1, durin1This initial condition can be naturally obtained without tun-ing in e.g. a scenario of Refs. [3,4].2This corresponds to the case of a singlethroat in Refs. [3,4].3So we cannot use the results of Ref. [1tion has been made that cs departs from unless than one.notations of Refs. [3,4] by r T3pand T3R4 N.The has the same order of magnitude as the effectivebackground charge N of the warped space and character-izes the strength of the background. The low-energy dy-namics is described by the DBI–Chern-Simons actionSM2Pl2Zd4x gpRZd4x gp 41 4g @ @s4V : (2.3)In the nonrelativistic limit, this action reduces to the usualminimal form.We start the inflaton near 0 through a phase tran-sition.1Without the warped space, the scalar will quicklyroll down the steep potential ( * 1) and make the infla-space. These effectof a certain IR regioif we start the inflperiod cannot be fumagnitude. For thegest lower bound isbackground. Thisnumber of e-foldinlatest e-fold Ne is gIt has an interestinfactor of the inflatoSince the sound spe1This initial condition can be naturally obtained without tun-ing in e.g. a scenario of Refs. [3,4].2This correspondsthroat in Refs. [3,4].3So we cannot usetion has been made thless than one.123518-2background charge N of the warped spizes the strength of the background. Tnamics is described by the DBI–ChernSM2Pl2Zd4x gpRZd4x gp 41 4gs4V :In the nonrelativistic limit, this action rminimal form.We start the inflaton near 0 thrsition.1Without the warped space, theroll down the steep potential ( * 1) a1This initial condition can be naturally oing in e.g. a scenario of Refs. [3,4].s improvements, may come at least in two occasions—where the redshifted string scale is too low so thatgy effects become significant or where the relativisticating is happening in a relatively deep warped space socosmological rescaling [9] takes effect. We discuss thein Sec. IV.II. THE IR MODELthis section, we study the non-Gaussianity in theplest IR DBI inflation model. We begin with a briefew on the model. Details can be found in Refs. [3,4].he inflaton potential is parametrized asV V012m2 2V012 H2 2; (2.1)re the Hubble parameter H is approximately a con-t. In many inflationary models, there is always natu-a contribution to the potential with j j 1. In theseels, such a potential is too steep to support a longod of slow-roll inflation. This is the well-knownlem which plagues slow-roll inflation [10].owever, it is shown [4] that, with warped space, theinflation can happen for both small and large t generates a scale-invariant spectrum for the densityurbations with a tilt independent of the parameter . Incase, the steepness of the potential does not play suchmportant role. The inflaton stays on the potential due toarping in the internal spacetion impossible. To obtain inflation, it is natural to ethat the speed limit should be nearly saturated. Insolving the equations of motion, we findpt9p2 2H21t3; t H 1;where the time t is chosen to run from 1. The intravels ultrarelativistically with a Lorentz contractiotor1 _ 2= 4 1=2:Nonetheless, the coordinate speed of light is very smato the large warping near 0, and in such a wainflaton achieves ‘‘slow rolling.’’ The potential stays nconstant during the inflation, and we have a periexponential expansion with the Hubble constant_a=a V0p= 3pMPl. There is no lower bound on thetionary scale, and the approximations that H is coand dominated by the potential energy during inflrequire an upper bound on V [4],VM4Pl1Ne:Generally speaking, this bound is not significant, singet enough e-foldings, we need only * 104. Howfor some specific models, such as the simplest one thfocus on in this paper, is determined by density pAs shown in Table 21ndard deviation showsasets. That means thatant, as they do not biast increase the varianceMB primordial signal.l− fcleanNL on a map-by-ion. This is used as anrealization due to theed from the negligiblewo samples, the vari-o very small: Table 216 for any given shape,for that shape. As aned values of flocalNL forILC samples, compar-evident also from thisincluding residuals isween the two compo-ice.m the comparison be-hods in Sect. 7, we caneground-cleaned mapsn this work provide asThe DBI class contains two possibilities based on string con-structions. In ultraviolet (UV) DBI models, the inflaton fieldmoves under a quadratic potential from the UV side of a warpedbackground to the infrared side. It is known that this case is al-ready at odds with observations, if theoretical internal consis-tency of the model and constraints on power spectra and primor-dial NG are taken into account (Baumann McAllister 2007;Lidsey Huston 2007; Bean et al. 2007; Peiris et al. 2007). Ourresults strongly limit the relativistic r´egime of these models evenwithout applying the theoretical consistency constraints.It is therefore interesting to look at infrared (IR) DBI mod-els (Chen 2005b,a) where the inflaton field moves from the IR tothe UV side, and the inflaton potential is V(φ) = V0 − 12 βH2φ2,with a wide range 0.1 β 109allowed in principle. Inprevious work (Bean et al. 2008) a 95% CL limit of β 3.7was obtained using WMAP. In a minimal version of IR DBI,where stringy effects are neglected and the usual field the-ory computation of the primordial curvature perturbation holds,one finds (Chen 2005c; Chen et al. 2007b) cs (βN/3)−1,ns − 1 = −4/N, where N is the number of e-folds; further,primordial NG of the equilateral type is generated with anamplitude fDBINL = −(35/108) [(β2N2/9) − 1]. For this model,the range N ≥ 60 is compatible with Planck’s 3σ limits onns (Planck Collaboration XXII 2013). Marginalizing over 60 ≤43Planck Collaboration: PlN ≤ 90, we findβ ≤ 0.7 95% CL ,dramatically restricting the allowed parameter smodel.Power-law k-inflation: These models (Armendariz1999; Chen et al. 2007b) predict fequilNL = −170/((non-canonical kinetic term)Constraints on the amplitudeof the predicted bispectrumConstraints on the model parameters
  19. 19. Effective Field Theory of InflationCheung et al. 2008) provides a general way to scan the NG pa-rameter space of inflationary perturbations. For example, onecan expand the Lagrangian of the dynamically relevant degreesof freedom into the dominant operators satisfying some under-lying symmetries. We will focus on general single-field modelsparametrized by the following operators (up to cubic order)S =d4x√−g−M2Pl˙Hc2s˙π2− c2s(∂iπ)2a2(97)− M2Pl˙H(1 − c−2s )˙π(∂iπ)2a2+M2Pl˙H(1 − c−2s ) −43M43˙π3where π is the scalar degree of freedom (ζ = −Hπ). The mea-surements on fequilNL and forthoNL can be used to constrain the mag-nitude of the inflaton interaction terms ˙π(∂iπ)2and (˙π)3whichgive respectively fEFT1NL = −(85/324)(c−2s − 1) and fEFT2NL =−(10/243)(c−2s − 1)˜c3 + (3/2)c2s(Senatore et al. 2010, see alsoChen et al. 2007b; Chen 2010b). These two operators give riseto shapes that peak in the equilateral configuration that are,nevertheless, slightly different, so that the total NG signal willbe a linear combination of the two, possibly leading also toan orthogonal shape. There are two relevant NG parameters,cs, the sound speed of the the inflaton fluctuations, and M3which characterizes the amplitude of the other operator ˙π3.10−2−2000Fig. 23. 68%, 95field inflation pathe change of vaFollowing Senatless parameter ˜cinflationary modnon-interacting mM3 = 0 (or ˜c3(c−sThe mean vaonal NG amplitufequilNL =1 − c2sc2s(forthoNL =1 − c2sc2s(eld Theory of Inflationch to inflation (Weinberg 2008;eneral way to scan the NG pa-erturbations. For example, onee dynamically relevant degreesperators satisfying some under-on general single-field modelsperators (up to cubic order)c2s(∂iπ)2a2(97)M2Pl˙H(1 − c−2s ) −43M43˙π3reedom (ζ = −Hπ). The mea-n be used to constrain the mag-terms ˙π(∂iπ)2and (˙π)3which5/324)(c−2s − 1) and fEFT2NL =(Senatore et al. 2010, see alsoThese two operators give riseilateral configuration that are,o that the total NG signal willtwo, possibly leading also totwo relevant NG parameters,inflaton fluctuations, and M3310−2 10−1 100cs−20000−Fig. 23. 68%, 95%, and 99.7% confidence regions in the single-field inflation parameter space (cs, ˜c3), obtained from Fig. 22 viathe change of variables in Eq. (98).Following Senatore et al. (2010) we will focus on the dimension-less parameter ˜c3(c−2s − 1) = 2M43c2s /( ˙HM2Pl). For example, DBIinflationary models corresponds to ˜c3 = 3(1 − c2s )/2, while thenon-interacting model (vanishing NG) correspond to cs = 1 andM3 = 0 (or ˜c3(c−2s − 1) = 0).The mean values of the estimators for equilateral and orthog-onal NG amplitudes are given in terms of cs and ˜c3 byfequilNL =1 − c2sc2s(−0.275 + 0.0780A)forthoNL =1 − c2s(0.0159 − 0.0167A) (98)one scalar DFe Field Theory of Inflationproach to inflation (Weinberg 2008;a general way to scan the NG pa-y perturbations. For example, oneof the dynamically relevant degreesnt operators satisfying some under-ocus on general single-field modelsg operators (up to cubic order)π2− c2s(∂iπ)2a2(97)+M2Pl˙H(1 − c−2s ) −43M43˙π3of freedom (ζ = −Hπ). The mea-can be used to constrain the mag-ction terms ˙π(∂iπ)2and (˙π)3which−(85/324)(c−2s − 1) and fEFT2NL =2)c2s(Senatore et al. 2010, see also0b). These two operators give riseequilateral configuration that are,nt, so that the total NG signal will10−2 10−1cs−20000−10˜c3Fig. 23. 68%, 95%, and 99.7% confidence regions in thfield inflation parameter space (cs, ˜c3), obtained from Fithe change of variables in Eq. (98).Following Senatore et al. (2010) we will focus on the dimless parameter ˜c3(c−2s − 1) = 2M43c2s /( ˙HM2Pl). For examinflationary models corresponds to ˜c3 = 3(1 − c2s )/2, wnon-interacting model (vanishing NG) correspond to csM3 = 0 (or ˜c3(c−2s − 1) = 0).The mean values of the estimators for equilateral anonal NG amplitudes are given in terms of cs and ˜c3 byequil 1 − c2sEquilateral -192 fNL 108Orthogonal -103 fNL 53S = d4x√−g−M2Pl˙Hc2s˙π2− c2s(∂iπ)2a2− M2Pl˙H(1 − c−2s )˙π(∂iπ)2a2+M2Pl˙H(1 − cwhere π is the scalar degree of freedom (ζsurements on fequilNL and forthoNL can be used tnitude of the inflaton interaction terms ˙π(∂give respectively fEFT1NL = −(85/324)(c−2s−(10/243)(c−2s − 1)˜c3 + (3/2)c2s(SenatoreChen et al. 2007b; Chen 2010b). These twoto shapes that peak in the equilateral conevertheless, slightly different, so that thebe a linear combination of the two, possan orthogonal shape. There are two relevcs, the sound speed of the the inflaton flwhich characterizes the amplitude of the44Implications of Planck’s results: an example
  20. 20. Implications of Planck’s results: an exampleSenatore et al. (2010)
  21. 21. 10−2 10−1 100cs−20000−10000010000˜c3(c−2s−1)Implications of Planck’s results: an exampleSenatore et al. (2010), PLANCK (2013)
  22. 22. Beyond fNLRunning non-GaussianityA scale-dependent fNL2 parameters:amplitude (fNL) and running (nNG)fNL(k) = fNLkkPnNGThe level of non-Gaussianity couldbe different at different scalesshaonuswprmlacoantaLo Verder et al. (2008), ES, Liguori, Yadav, Jackson, Pajer (2009)Becker Huterer (2009) from WMAP data
  23. 23. Beyond fNLThe PLANCK analysis considered several models• Feature and resonant models• Non Bunch-Davies vacuum• Quasi-single field inflation• et al.• + some preliminary tests of the initial trispectrumNo evidence so far!However ...!#$#% #% ##% #% ##% #% (##%)*+,%0345,6%Fig. 8. Modal bispectrum coefficients βRn for the mode expansion(Eq. (63)) obtained from Planck foreground-cleaned maps usinghybrid Fourier modes. The different component separation meth-ods, SMICA, NILC and SEVEM exhibit remarkable agreement. Thevariance from 200 simulated noise maps was nearly constant foreach of the 300 modes, with the average ±1σ variation shown inred.!!#$!!#%!!#!!#!!#!# (!!# $!!# )!!# %!!# *!!# !!#+,-./01,#234$#567,#89:;,#!!3=4#?@A@5#?5=B(orthonormal basis for the primordial bispectrum)
  24. 24. From the CMB to the Large-Scale Structure
  25. 25. From the CMB to the Large-Scale StructureNo direct access tomatter perturbations ...... but a large volumeto explore, with severalobservables:1. galaxies2. weak lensing3. clusters4. Ly-alpha forest5. 21 cm (?)Predictions arechallenging!
  26. 26. The Matter Power Spectrummatter overdensity: δm ≡ρm(x) − ¯ρm¯ρmδk1δk2 ≡ δD(k1 + k2) Pm(k1)0.01 0.1 1 100.011100k h Mpc1k4ΠPkk3Nbodynonlinearlinearmatter power spectrum
  27. 27. 0.01 0.1 1 100.011100k h Mpc1k4ΠPkk3NbodynonlinearlinearTextLarge scales:initial conditions, inflationmatter overdensity: δm ≡ρm(x) − ¯ρm¯ρmδk1δk2 ≡ δD(k1 + k2) Pm(k1)matter power spectrumThe Matter Galaxy Power SpectrumPg(k) b2Pm(k)galaxy power spectrum
  28. 28. fNL = - 5000fNL = - 500fNL = + 500fNL = + 5000Ωm 0.271+0.005−0.004 0.271+0.001−0.001σ8 0.808+0.005−0.005 0.808+0.003−0.003h 0.703+0.004−0.004 0.703+0.001−0.0010.96 0.965 0.97 0.975!0.0100.01nssPlanck + EUCLIDPlanck0.26 0.270.790.80.810.82#m$8PlanPlanFigure 3.1: The marginalized likelihood contours (68.3% and 95.4% CL) for PlaThe Galaxy Power SpectrumForecasted constraints onspectral index and its runningfor EUCLIDAmendola et al. (2012)Constraints on the initial power spectrum:
  29. 29. The Galaxy Power Spectrumusing the halo auto spectra to computeresults as the cross spectra; i.e. westochasticity. Examples of the variouresulting bias factors are plotted in FAs can be seen, we numerically copredicted scale dependence. Becaustatistics of rare objects, the errors onsimulations plotted in Fig. 8 are lartempt to improve the statistics on thebining the bias measurements fromFigure 8 plots the average ratio betwein our simulations and our analyticusing c ¼ 1:686 as predicted from tmodel [78]. In computing the averagewe used a uniform weighting acrossIMPRINTS OF PRIMORDIAL NON-GAUSSIANITIES ON . . . PHYSICAL REVIEWThe bias of galaxies receives asignificant scale-dependentcorrection for NG initialconditions of the local typeDalal et al. (2008)“Gaussian”biasScale-dependent correctiondue to local non-GaussianityLarge effect on large scales!Pg(k) = [b1 + ∆b1(fNL, k)]2P(k)∆b1,NG(fNL, k) ∼fNLD(z) k2Constraints on the initial bispectrum:
  30. 30. CMB WMAP (95% CL): -10 fNL 74[WMAP7, Komatsu et al. (2009)]QSOs (95% CL): -31 fNL 70[SDSS, Slosar et al. (2008)]AGNs (95% CL): 25 fNL 117[NVSS, Xia et al. (2010)]Limits from LSS are competitive with the CMB!(at least for the local model ...)The Galaxy Power SpectrumPg(k) = [b1 + ∆b1(fNL, k)]2P(k)The bias of galaxies receives asignificant scale-dependentcorrection for NG initialconditions of the local typeConstraints on the initial bispectrum:
  31. 31. CMB WMAP (95% CL): -10 fNL 74[WMAP7, Komatsu et al. (2009)]QSOs (95% CL): -31 fNL 70[SDSS, Slosar et al. (2008)]AGNs (95% CL): 25 fNL 117[NVSS, Xia et al. (2010)]Limits from LSS are competitive with the CMB!(at least for the local model ...)The Galaxy Power SpectrumPg(k) = [b1 + ∆b1(fNL, k)]2P(k)CMB PLANCK (95% CL): -8.9 fNL 14.3[PLANCK (2013)]?EUCLID/LSST (95% CL): ΔfNL 5 (~1?), expected![Carbone et al. (2010), Giannantonio et al. (2012)]The bias of galaxies receives asignificant scale-dependentcorrection for NG initialconditions of the local typeConstraints on the initial bispectrum:
  32. 32. The Galaxy BispectrumFuture, large volume surveyscould provide:ΔfNLlocal ~ 5 and ΔfNLeq ~ 10i.e. competitive constraintsfor all types of non-GaussianityES Komatsu (2007), ES, Crocce Desjacques (2012)The galaxy 3-point function is thenatural equivalent of the CMBbispectrumBgal b31 [Binitial + Bgravity] + b21 b2 P2m
  33. 33. 0.02 0.04 0.06 0.08 0.105102050100kmax h Mpc1fNLV 10 h3Gpc3, z 1kmin 0.009 h Mpc1b1 2, b2 0.8PBPBFIG. 15: One-σ uncertainty on the fNL parameter, marA Fisher matrix analysis for Galaxy correlatorsThe uncertainty on fNL (local)from Power Spectrum Bispectrum ( both)marginalized (b1, b2)
  34. 34. • Abundance of galaxy clustersOther probesPNG affects the high-mass tailof the cluster mass function2 Williamson, et al.10SZ M500 (1014Msol /h70)110LX/E(z)1.85(1044ergs-1h70-2;0.5-2.0keV)Fig. 4.— The X-ray luminosity and SZ inferred masses500(ρcrit) for our cluster sample. We plot statistical uncertaintiesly, and note that the statistical uncertainty of the SZ mass esti-ate is limited by the assumed scatter in the SZ significance-massation. Clusters from the shallow fields are in blue, and clustersm the deep fields are in red. We also show the best-fit relationsPratt et al. (2009) (dotted), Vikhlinin et al. (2009a) (dash-dot),d Mantz et al. (2010) (dashed).ost massive galaxy clusters in this region of the sky,dependent of the cluster redshift. These exceedinglyFig. 5.— A Mortonson et al. (2010)-style plot showing the massM200(ρmean) and redshift of the clusters presented in this paper.Some of the most extreme objects in the catalog are annotated withthe R.A. portion of their object name. The red solid line showsthe mass above which a cluster at a given redshift is less than5% likely to be found in the 2500 deg2 SPT survey region in 95%of the ΛCDM parameter probability distribution. The black dot-dashed line shows the analogous limit for the full sky. The blueopen data point (redshift slightly offset for clarity) denotes themass estimate for SPT-CL J2106-5844 from combined X-ray andSZ measurements in Foley et al. (2011). That work concludes thatthis cluster is less than 5% likely in 32% of the ΛCDM parameterprobability distribution, and we show the corresponding MortonsonWilliamson et al. (2011)Sample of the mostmassive clusters in theSPT catalog vs the“probability of theirexistence”JCAP04(200Effects of scale-dependent non-Gaussianity on cosmological structuresLoVerde et al. (2008)
  35. 35. • Abundance of galaxy clusters• Weak Lensing• ...• 21cm (?)• μ-distorsions of the CMB spectrum (??)Other probesPNG affects the high-mass tailof the cluster mass functionPNG affects also the nonlinearevolution of the matter powerspectrum at small scalesAll probes present significanttheoretical and numerical challenges!
  36. 36. Conclusions• After the first PLANCK results the simplest model of inflation is aliveand kicking: no indication of any departure from a single-field, slow rollinflation with canonical kinetic term from a Bunch-Davies vacuum• PLACK will further improve its constraints by adding polarizationinformation• Constraints on non-Gaussianity can, in some cases, severely reduce theparameter space of many non-minimal models (without, however, rulingthem out)• Future cosmological observations will focus on the large-scale structure:the large volume available makes them, in principle, an even more powerfulprobe of the initial conditions than the CMB• However, the analysis of its several observables is challenging: wehave to deal with the nonlinear evolution of structures and the complex baryonphysics (to mention two among many problems ...!)
  37. 37. New Light in Cosmologyfrom the CMBSCHOOL WORKSHOP22 - 26 July 2013 29 July - 2 August 2013Miramare, Trieste, ItalyTOPICS of the School:• EARLY UNIVERSE• CMB THEORY• CMB EXPERIMENTS• PLANCK PRODUCTS• LENSING ISW• BIG SCIENCE FROM SMALL SCALESThe purpose of the School is to provide the theoretical and computational tools to study the implications ofthe recent results from CMB experiments. It is intended for graduate students, as well as more senior non-expert researchers that are interested in these fields. The Workshop is devoted to the discussion of theexperimental CMB results in all their aspects, their relation with other probes and the future prospects.PARTICIPATIONScientists and students from all countries which are members of the United Nations, UNESCO or IAEA mayattend the School and Workshop. As it will be conducted in English, participants should have an adequateworking knowledge of this language. Although the main purpose of the Centre is to help research workersfrom developing countries, through a programme of training activities within a framework of internationalcooperation, students and post-doctoral scientists from advanced countries are also welcome to attend.As a rule, travel and subsistence expenses of the participants should be borne by the home institution.Every effort should be made by candidates to secure support for their fare (or at least half-fare). However,limited funds are available for some participants who are nationals of, and working in, a developing country,and who are not more than 45 years old. Such support is available only for those who attend the entireactivity. There is no registration fee to be paid.HOW TO APPLY FOR PARTICIPATION:The application forms can be accessed at the School Workshop website: http://agenda.ictp.it/smr.php?2474Once in the website, comprehensive instructions will guide you step-by-step, on how to fill out and submitthe application forms.SCHOOL WORKSHOP SECRETARIAT:Telephone: +39 040 2240 363 - Telefax: +39 040 2240 7363 - E-mail: smr2474@ictp.itICTP Home Page: http://www.ictp.it/IN COLLABORATION WITHTHE ITALIAN INSTITUTE FORNUCLEAR PHYSICSORGANIZERS:C. Baccigalupi (SISSA)P. Creminelli (ICTP)R. Sheth (ICTP UPenn)A. Zacchei (INAF - OATS)LECTURERS:C. Baccigalupi (SISSA)A. Jaffe (Imperial College)J. Lesgourgues (CERN EPFL)A. Lewis (Sussex University)L. Senatore (CERN Stanford)R. Stompor (APC, Paris)A. Zacchei (INAF - OATS)SCIENTIFIC SECRETARY:D. Lopez Nacir (ICTP)DEADLINEfor requesting participation15 April 2013extended to28 April 2013January 2013Deadline in 2 days!
  38. 38. 2000 2002 2004 2006 2008 2010 2012020406080100120140PNG in the last 10 years?# of articles with“Non-Gaussian”in the titleon the ADS data base
  39. 39. PNG in the last 10 years?# of articles with“Non-Gaussian”in the titleon the ADS data base2000 2002 2004 2006 2008 2010 2012020406080100120140non-primordial NG
  40. 40. 2000 2002 2004 2006 2008 2010 2012020406080100120140PNG in the last 10 yearsCOBE(≪1σ)WMAP1(0.8 σ)WMAP3(0.7 σ)WMAP7(1.5 σ)?non-primordial NG# of articles with“Non-Gaussian”in the titleon the ADS data baseWMAP5(1.7 σ)Yadav Wandelt (2.8σ ?)
  41. 41. 2000 2002 2004 2006 2008 2010 2012020406080100120140PNG in the last 10 yearsInflation / Theorynon-primordial NG# of articles with“Non-Gaussian”in the titleon the ADS data baseCOBE(≪1σ)WMAP1(0.8 σ)WMAP3(0.7 σ)WMAP7(1.5 σ)?WMAP5(1.7 σ)Yadav Wandelt (2.8σ ?)
  42. 42. 2000 2002 2004 2006 2008 2010 2012020406080100120140PNG in the last 10 yearsInflation / Theorynon-primordial NG# of articles with“Non-Gaussian”in the titleon the ADS data baseCMB COBE(≪1σ)WMAP1(0.8 σ)WMAP3(0.7 σ)WMAP7(1.5 σ)?WMAP5(1.7 σ)Yadav Wandelt (2.8σ ?)
  43. 43. 2000 2002 2004 2006 2008 2010 2012020406080100120140PNG in the last 10 yearsInflation / Theorynon-primordial NG# of articles with“Non-Gaussian”in the titleon the ADS data baseLarge-Scale StructureCMB COBE(≪1σ)WMAP1(0.8 σ)WMAP3(0.7 σ)WMAP7(1.5 σ)?WMAP5(1.7 σ)Yadav Wandelt (2.8σ ?)Dalal et al.
  44. 44. 2000 2002 2004 2006 2008 2010 2012020406080100120140PNG in the last 10 yearsInflation / Theorynon-primordial NG# of articles with“Non-Gaussian”in the titleon the ADS data baseLarge-Scale StructureCMB COBE(≪1σ)WMAP1(0.8 σ)WMAP3(0.7 σ)WMAP7(1.5 σ)?WMAP5(1.7 σ)Yadav Wandelt (2.8σ ?)PlanckfNL = 0?Dalal et al.

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