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

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

  1. 1. Emiliano Sefusatti Tests of the Initial Conditions of the Universe after Planck BW2013,Vrnjačka Banja April 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 Universe PLANCK (2013) Planck Collaboration: The Planck mission Fig. 14. The SMICA CMB map (with 3 % of the sky replaced by a constrained Gaussian realization).
  4. 4. Predictions of Inflation Planck Collaboration: Cosmological parameters • A flat, homogeneous Universe • A (nearly) scale invariant power spectrum for (highly Gaussian) initial fluctuations PLANCK (2013)
  5. 5. Predictions of Inflation • A flat, homogeneous Universe • A (nearly) scale invariant power spectrum for (highly Gaussian) initial fluctuations Φk1 Φk2 = δD(k1 +k2)PΦ(k1) Φk1 Φk2 Φk3 Φk4 = δD(k1 + ... +k4) TΦ(k1,k2,k3,k4) = 0 Φk1 Φk2 Φk3 = 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 vacuum BΦ(k1, k2, k3) = 0 TΦ(k1,k2,k3,k4) = 0 Non-Gaussian Initial Conditions
  11. 11. The shape of non-Gaussianity Most models predict a scale-invariant curvature bispectrum BΦ(k, k, k) ∼ P2 Φ(k) ∼ 1 k6 What distinguish them is the shape “shape” = the dependence of the curvature bispectrum predicted by a given model of inflation on the shape of the triangular configuration k1, k2, k3 BΦ(k1, k2, k3) = fNL 1 k2 1k2 2k2 3 F r2 = k2 k1 , r3 = k3 k1
  12. 12. Models of primordial non-Gaussianity Multiple fields Modified vacuum Modified vacuum Non-Canonical Kinetic term
  13. 13. Text !#$%'(%)*+,)-).) !#$%'(%)*+,)-)/...) Polarization *+,)-).) 012%34516)*+,)-)/...) ! Liguori et al. (2007) The CMB Bispectrum
  14. 14. The CMB Bispectrum The Bispectrum of the CMB is the most direct probe of the initial bispectrum Bl1l2l3 ∼ BΦ(k1, k2, k3)∆l1 (k1)∆l2 (k2)∆l3 (k3)jl1 (k1r)jl2 (k2r)jl3 (k3r) curvature bispectrum transfer functions CMB angular bispectrum WMAP 7 years: Local -10 fNL 74 Equilateral -214 fNL 266 Orthogonal -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 Bispectrum The Bispectrum of the CMB is the most direct probe of the initial bispectrum Bl1l2l3 ∼ BΦ(k1, k2, k3)∆l1 (k1)∆l2 (k2)∆l3 (k3)jl1 (k1r)jl2 (k2r)jl3 (k3r) curvature bispectrum transfer functions CMB angular bispectrum WMAP 7 years: Local -10 fNL 74 Equilateral -214 fNL 266 Orthogonal -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 Planck (T only): Local -8.9 fNL 14.3 Equilateral -192 fNL 108 Orthogonal -103 fNL 53 @ 95% CL Ade et al. (2013)
  16. 16. The CMB Bispectrum: Planck • Planck temperature data improve WMAP results by a factors of 2 to 4 (depending on the shape!) • Planck is very close to the ideal CMB experiment (ΔfNLlocal ~ 1) ΔfNL, local ΔfNL, equil. ΔfNL, orth. WMAP 21 140 104 Planck 5.8 75 39
  17. 17. The CMB Bispectrum: Planck dvances in Astronomy 2 1 2 3 4 5 10 20 ∆fNL 200 300 500 700 1000 1500 2000 3000 Local model Imax WMAP (T/T+P) Planck (T/T+P) CMBPol (T/T+P) (a) 20 30 40 50 100 ∆fNL 200 300 500 700 1000 1500 2000 3000 Equilateral model Imax WMAP (T/T+P) Planck (T/T+P) CMBPol (T/T+P) (b) • Planck temperature data improve WMAP results by a factors of 2 to 4 (depending on the shape!) • Planck is very close to the ideal CMB experiment (ΔfNLlocal ~ 1) Liguori et al. (2010) ΔfNL, local ΔfNL, equil. ΔfNL, orth. WMAP 21 140 104 Planck 5.8 75 39 Forecasted temperature polarization constraints
  18. 18. Implications of Planck’s results: an example DBI inflation (IR) Having characterised single-field inflation bispectra using com- binations of the separable equilateral and orthogonal ans¨atze we 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 DBI inflation (Eq. (7)) and the two effective field theory shapes (Eqs. (5, 6)), as well as the ghost inflation bispectrum, which is an exemplar of higher-order derivative theories (specifically Eq. (3.8) in Arkani-Hamed et al. 2004). Using the primordia modal estimator, with the SMICA foreground-cleaned data, we find: fDBI NL = 11 ± 69 (F DBI−eq NL = 10 ± 77) , fEFT1 NL = 8 ± 73 (F EFT1−eq NL = 8 ± 77) , fEFT2 NL = 19 ± 57 (F EFT2−eq NL = 27 ± 79) , fGhost NL = −23 ± 88 (F Ghost−eq NL = −20 ± 75) . (86) where we have normalized with the usual primordial f con- where ds2 4 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 the notations of Refs. [3,4] by r T3 p and T3R4 N. The has the same order of magnitude as the effective background 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 action S M2 Pl 2 Z d4 x g p R Z d4 x g p 4 1 4 g @ @ s 4 V : (2.3) In the nonrelativistic limit, this action reduces to the usual minimal form. We start the inflaton near 0 through a phase tran- sition.1 Without the warped space, the scalar will quickly roll down the steep potential ( * 1) and make the infla- t comes from backreactions of the [1,4,9] and the de Sitter (dS) space space. These effects will smooth out th of a certain IR region of the warped sp if we start the inflaton from that reg period cannot be further increased in t magnitude. For the case that we consi gest lower bound is the closed string c background. This gives t p H 1 number of e-foldings in this model i latest e-fold Ne is given by Ne p H= : It has an interesting relation to the factor of the inflaton, Ne=3: Since the sound speed cs 1, durin 1 This initial condition can be naturally obtained without tun- ing in e.g. a scenario of Refs. [3,4]. 2 This corresponds to the case of a single throat in Refs. [3,4]. 3 So we cannot use the results of Ref. [1 tion has been made that cs departs from un less than one. notations of Refs. [3,4] by r T3 p and T3R4 N. The has the same order of magnitude as the effective background 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 action S M2 Pl 2 Z d4 x g p R Z d4 x g p 4 1 4 g @ @ s 4 V : (2.3) In the nonrelativistic limit, this action reduces to the usual minimal form. We start the inflaton near 0 through a phase tran- sition.1 Without the warped space, the scalar will quickly roll down the steep potential ( * 1) and make the infla- space. These effect of a certain IR regio if we start the infl period cannot be fu magnitude. For the gest lower bound is background. This number of e-foldin latest e-fold Ne is g It has an interestin factor of the inflato Since the sound spe 1 This initial condition can be naturally obtained without tun- ing in e.g. a scenario of Refs. [3,4]. 2 This corresponds throat in Refs. [3,4]. 3 So we cannot use tion has been made th less than one. 123518-2 background charge N of the warped sp izes the strength of the background. T namics is described by the DBI–Chern S M2 Pl 2 Z d4 x g p R Z d4 x g p 4 1 4 g s 4 V : In the nonrelativistic limit, this action r minimal form. We start the inflaton near 0 thr sition.1 Without the warped space, the roll down the steep potential ( * 1) a 1 This initial condition can be naturally o ing 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 that gy effects become significant or where the relativistic ating is happening in a relatively deep warped space so cosmological rescaling [9] takes effect. We discuss the in Sec. IV. II. THE IR MODEL this section, we study the non-Gaussianity in the plest IR DBI inflation model. We begin with a brief ew on the model. Details can be found in Refs. [3,4]. he inflaton potential is parametrized as V V0 1 2m2 2 V0 1 2 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 these els, such a potential is too steep to support a long od of slow-roll inflation. This is the well-known lem which plagues slow-roll inflation [10]. owever, it is shown [4] that, with warped space, the inflation can happen for both small and large t generates a scale-invariant spectrum for the density urbations with a tilt independent of the parameter . In case, the steepness of the potential does not play such mportant role. The inflaton stays on the potential due to arping in the internal space tion impossible. To obtain inflation, it is natural to e that the speed limit should be nearly saturated. In solving the equations of motion, we find p t 9 p 2 2 H2 1 t3 ; t H 1 ; where the time t is chosen to run from 1. The in travels ultrarelativistically with a Lorentz contractio tor 1 _ 2 = 4 1=2: Nonetheless, the coordinate speed of light is very sma to the large warping near 0, and in such a wa inflaton achieves ‘‘slow rolling.’’ The potential stays n constant during the inflation, and we have a peri exponential expansion with the Hubble constant _a=a V0 p = 3 p MPl. There is no lower bound on the tionary scale, and the approximations that H is co and dominated by the potential energy during infl require an upper bound on V [4], V M4 Pl 1 Ne : Generally speaking, this bound is not significant, sin get enough e-foldings, we need only * 104. How for some specific models, such as the simplest one th focus on in this paper, is determined by density p As shown in Table 21 ndard deviation shows asets. That means that ant, as they do not bias t increase the variance MB primordial signal. l − fclean NL on a map-by- ion. This is used as an realization due to the ed from the negligible wo samples, the vari- o very small: Table 21 6 for any given shape, for that shape. As an ed values of flocal NL for ILC samples, compar- evident also from this including residuals is ween the two compo- ice. m the comparison be- hods in Sect. 7, we can eground-cleaned maps n this work provide a s The DBI class contains two possibilities based on string con- structions. In ultraviolet (UV) DBI models, the inflaton field moves under a quadratic potential from the UV side of a warped background 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). Our results strongly limit the relativistic r´egime of these models even without 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 to the UV side, and the inflaton potential is V(φ) = V0 − 1 2 βH2 φ2 , with a wide range 0.1 β 109 allowed in principle. In previous work (Bean et al. 2008) a 95% CL limit of β 3.7 was 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 an amplitude fDBI NL = −(35/108) [(β2 N2 /9) − 1]. For this model, the range N ≥ 60 is compatible with Planck’s 3σ limits on ns (Planck Collaboration XXII 2013). Marginalizing over 60 ≤ 43 Planck Collaboration: Pl N ≤ 90, we find β ≤ 0.7 95% CL , dramatically restricting the allowed parameter s model. Power-law k-inflation: These models (Armendariz 1999; Chen et al. 2007b) predict f equil NL = −170/( (non-canonical kinetic term) Constraints on the amplitude of the predicted bispectrum Constraints on the model parameters
  19. 19. Effective Field Theory of Inflation Cheung et al. 2008) provides a general way to scan the NG pa- rameter space of inflationary perturbations. For example, one can expand the Lagrangian of the dynamically relevant degrees of freedom into the dominant operators satisfying some under- lying symmetries. We will focus on general single-field models parametrized by the following operators (up to cubic order) S = d4 x √ −g  − M2 Pl ˙H c2 s ˙π2 − c2 s (∂iπ)2 a2 (97) − M2 Pl ˙H(1 − c−2 s )˙π (∂iπ)2 a2 + M2 Pl ˙H(1 − c−2 s ) − 4 3 M4 3 ˙π3 where π is the scalar degree of freedom (ζ = −Hπ). The mea- surements on f equil NL and fortho NL can be used to constrain the mag- nitude of the inflaton interaction terms ˙π(∂iπ)2 and (˙π)3 which give respectively fEFT1 NL = −(85/324)(c−2 s − 1) and fEFT2 NL = −(10/243)(c−2 s − 1) ˜c3 + (3/2)c2 s (Senatore et al. 2010, see also Chen et al. 2007b; Chen 2010b). These two operators give rise to shapes that peak in the equilateral configuration that are, nevertheless, slightly different, so that the total NG signal will be a linear combination of the two, possibly leading also to an orthogonal shape. There are two relevant NG parameters, cs, the sound speed of the the inflaton fluctuations, and M3 which characterizes the amplitude of the other operator ˙π3 . 10−2 −2000 Fig. 23. 68%, 95 field inflation pa the change of va Following Senat less parameter ˜c inflationary mod non-interacting m M3 = 0 (or ˜c3(c− s The mean va onal NG amplitu f equil NL = 1 − c2 s c2 s ( fortho NL = 1 − c2 s c2 s ( eld Theory of Inflation ch to inflation (Weinberg 2008; eneral way to scan the NG pa- erturbations. For example, one e dynamically relevant degrees perators satisfying some under- on general single-field models perators (up to cubic order) c2 s (∂iπ)2 a2 (97) M2 Pl ˙H(1 − c−2 s ) − 4 3 M4 3 ˙π3 reedom (ζ = −Hπ). The mea- n be used to constrain the mag- terms ˙π(∂iπ)2 and (˙π)3 which 5/324)(c−2 s − 1) and fEFT2 NL = (Senatore et al. 2010, see also These two operators give rise ilateral configuration that are, o that the total NG signal will two, possibly leading also to two relevant NG parameters, inflaton fluctuations, and M3 3 10−2 10−1 100 cs −20000− Fig. 23. 68%, 95%, and 99.7% confidence regions in the single- field inflation parameter space (cs, ˜c3), obtained from Fig. 22 via the change of variables in Eq. (98). Following Senatore et al. (2010) we will focus on the dimension- less parameter ˜c3(c−2 s − 1) = 2M4 3c2 s /( ˙HM2 Pl). For example, DBI inflationary models corresponds to ˜c3 = 3(1 − c2 s )/2, while the non-interacting model (vanishing NG) correspond to cs = 1 and M3 = 0 (or ˜c3(c−2 s − 1) = 0). The mean values of the estimators for equilateral and orthog- onal NG amplitudes are given in terms of cs and ˜c3 by f equil NL = 1 − c2 s c2 s (−0.275 + 0.0780A) fortho NL = 1 − c2 s (0.0159 − 0.0167A) (98) one scalar DF e Field Theory of Inflation proach to inflation (Weinberg 2008; a general way to scan the NG pa- y perturbations. For example, one of the dynamically relevant degrees nt operators satisfying some under- ocus on general single-field models g operators (up to cubic order) π2 − c2 s (∂iπ)2 a2 (97) + M2 Pl ˙H(1 − c−2 s ) − 4 3 M4 3 ˙π3 of freedom (ζ = −Hπ). The mea- can be used to constrain the mag- ction terms ˙π(∂iπ)2 and (˙π)3 which −(85/324)(c−2 s − 1) and fEFT2 NL = 2)c2 s (Senatore et al. 2010, see also 0b). These two operators give rise equilateral configuration that are, nt, so that the total NG signal will 10−2 10−1 cs −20000−10 ˜c3 Fig. 23. 68%, 95%, and 99.7% confidence regions in th field inflation parameter space (cs, ˜c3), obtained from Fi the change of variables in Eq. (98). Following Senatore et al. (2010) we will focus on the dim less parameter ˜c3(c−2 s − 1) = 2M4 3c2 s /( ˙HM2 Pl). For exam inflationary models corresponds to ˜c3 = 3(1 − c2 s )/2, w non-interacting model (vanishing NG) correspond to cs M3 = 0 (or ˜c3(c−2 s − 1) = 0). The mean values of the estimators for equilateral an onal NG amplitudes are given in terms of cs and ˜c3 by equil 1 − c2 s Equilateral -192 fNL 108 Orthogonal -103 fNL 53 S = d4 x √ −g − M2 Pl ˙H c2 s ˙π2 − c2 s (∂iπ)2 a2 − M2 Pl ˙H(1 − c−2 s )˙π (∂iπ)2 a2 + M2 Pl ˙H(1 − c where π is the scalar degree of freedom (ζ surements on f equil NL and fortho NL can be used t nitude of the inflaton interaction terms ˙π(∂ give respectively fEFT1 NL = −(85/324)(c−2 s −(10/243)(c−2 s − 1) ˜c3 + (3/2)c2 s (Senatore Chen et al. 2007b; Chen 2010b). These two to shapes that peak in the equilateral co nevertheless, slightly different, so that the be a linear combination of the two, poss an orthogonal shape. There are two relev cs, the sound speed of the the inflaton fl which characterizes the amplitude of the 44 Implications of Planck’s results: an example
  20. 20. Implications of Planck’s results: an example Senatore et al. (2010)
  21. 21. 10−2 10−1 100 cs −20000−10000010000 ˜c3(c−2 s−1) Implications of Planck’s results: an example Senatore et al. (2010), PLANCK (2013)
  22. 22. Beyond fNL Running non-Gaussianity A scale-dependent fNL 2 parameters: amplitude (fNL) and running (nNG) fNL(k) = fNL k kP nNG The level of non-Gaussianity could be different at different scales sh a on us w pr m la co an ta Lo Verder et al. (2008), ES, Liguori, Yadav, Jackson, Pajer (2009) Becker Huterer (2009) from WMAP data
  23. 23. Beyond fNL The 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 trispectrum No evidence so far! However ... !#$ #% #% ##% #% '##% '#% (##% )*+,%0345,6% Fig. 8. Modal bispectrum coefficients βR n for the mode expansion (Eq. (63)) obtained from Planck foreground-cleaned maps using hybrid Fourier modes. The different component separation meth- ods, SMICA, NILC and SEVEM exhibit remarkable agreement. The variance from 200 simulated noise maps was nearly constant for each of the 300 modes, with the average ±1σ variation shown in red. !!#$!!#%!!#!!#'!!# !# (!!# $!!# )!!# %!!# *!!# !!# +,-./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 Structure No direct access to matter perturbations ... ... but a large volume to explore, with several observables: 1. galaxies 2. weak lensing 3. clusters 4. Ly-alpha forest 5. 21 cm (?) Predictions are challenging!
  26. 26. The Matter Power Spectrum matter overdensity: δm ≡ ρm(x) − ¯ρm ¯ρm δk1 δk2 ≡ δD(k1 + k2) Pm(k1) 0.01 0.1 1 10 0.01 1 100 k h Mpc1 k4ΠPkk3 Nbody nonlinear linear matter power spectrum
  27. 27. 0.01 0.1 1 10 0.01 1 100 k h Mpc1 k4ΠPkk3 Nbody nonlinear linear TextLarge scales: initial conditions, inflation matter overdensity: δm ≡ ρm(x) − ¯ρm ¯ρm δk1 δk2 ≡ δD(k1 + k2) Pm(k1) matter power spectrum The Matter Galaxy Power Spectrum Pg(k) b2 Pm(k) galaxy power spectrum
  28. 28. fNL = - 5000 fNL = - 500 fNL = + 500 fNL = + 5000 Ωm 0.271+0.005 −0.004 0.271+0.001 −0.001 σ8 0.808+0.005 −0.005 0.808+0.003 −0.003 h 0.703+0.004 −0.004 0.703+0.001 −0.001 0.96 0.965 0.97 0.975 !0.01 0 0.01 ns s Planck + EUCLID Planck 0.26 0.27 0.79 0.8 0.81 0.82 #m $8 Plan Plan Figure 3.1: The marginalized likelihood contours (68.3% and 95.4% CL) for Pla The Galaxy Power Spectrum Forecasted constraints on spectral index and its running for EUCLID Amendola et al. (2012) Constraints on the initial power spectrum:
  29. 29. The Galaxy Power Spectrum using the halo auto spectra to compute results as the cross spectra; i.e. we stochasticity. Examples of the variou resulting bias factors are plotted in F As can be seen, we numerically co predicted scale dependence. Becau statistics of rare objects, the errors on simulations plotted in Fig. 8 are lar tempt to improve the statistics on the bining the bias measurements from Figure 8 plots the average ratio betwe in our simulations and our analytic using c ¼ 1:686 as predicted from t model [78]. In computing the average we used a uniform weighting across IMPRINTS OF PRIMORDIAL NON-GAUSSIANITIES ON . . . PHYSICAL REVIEW The bias of galaxies receives a significant scale-dependent correction for NG initial conditions of the local type Dalal et al. (2008) “Gaussian” bias Scale-dependent correction due to local non-Gaussianity Large effect on large scales! Pg(k) = [b1 + ∆b1(fNL, k)]2 P(k) ∆b1,NG(fNL, k) ∼ fNL D(z) k2 Constraints 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 Spectrum Pg(k) = [b1 + ∆b1(fNL, k)]2 P(k) The bias of galaxies receives a significant scale-dependent correction for NG initial conditions of the local type Constraints 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 Spectrum Pg(k) = [b1 + ∆b1(fNL, k)]2 P(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 a significant scale-dependent correction for NG initial conditions of the local type Constraints on the initial bispectrum:
  32. 32. The Galaxy Bispectrum Future, large volume surveys could provide: ΔfNL local ~ 5 and ΔfNL eq ~ 10 i.e. competitive constraints for all types of non-Gaussianity ES Komatsu (2007), ES, Crocce Desjacques (2012) The galaxy 3-point function is the natural equivalent of the CMB bispectrum Bgal b3 1 [Binitial + Bgravity] + b2 1 b2 P2 m
  33. 33. 0.02 0.04 0.06 0.08 0.10 5 10 20 50 100 kmax h Mpc1 fNL V 10 h3 Gpc3 , z 1 kmin 0.009 h Mpc1 b1 2, b2 0.8 P B PB FIG. 15: One-σ uncertainty on the fNL parameter, mar A Fisher matrix analysis for Galaxy correlators The uncertainty on fNL (local) from Power Spectrum Bispectrum ( both) marginalized (b1, b2)
  34. 34. • Abundance of galaxy clusters Other probes PNG affects the high-mass tail of the cluster mass function 2 Williamson, et al. 10 SZ M500 (1014 Msol /h70) 1 10 LX/E(z)1.85 (1044 ergs-1 h70 -2 ;0.5-2.0keV) Fig. 4.— The X-ray luminosity and SZ inferred masses 500(ρcrit) for our cluster sample. We plot statistical uncertainties ly, and note that the statistical uncertainty of the SZ mass esti- ate is limited by the assumed scatter in the SZ significance-mass ation. Clusters from the shallow fields are in blue, and clusters m the deep fields are in red. We also show the best-fit relations Pratt 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 exceedingly Fig. 5.— A Mortonson et al. (2010)-style plot showing the mass M200(ρmean) and redshift of the clusters presented in this paper. Some of the most extreme objects in the catalog are annotated with the R.A. portion of their object name. The red solid line shows the mass above which a cluster at a given redshift is less than 5% 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 blue open data point (redshift slightly offset for clarity) denotes the mass estimate for SPT-CL J2106-5844 from combined X-ray and SZ measurements in Foley et al. (2011). That work concludes that this cluster is less than 5% likely in 32% of the ΛCDM parameter probability distribution, and we show the corresponding Mortonson Williamson et al. (2011) Sample of the most massive clusters in the SPT catalog vs the “probability of their existence” JCAP04(200 Effects of scale-dependent non-Gaussianity on cosmological structures LoVerde et al. (2008)
  35. 35. • Abundance of galaxy clusters • Weak Lensing • ... • 21cm (?) • μ-distorsions of the CMB spectrum (??) Other probes PNG affects the high-mass tail of the cluster mass function PNG affects also the nonlinear evolution of the matter power spectrum at small scales All probes present significant theoretical and numerical challenges!
  36. 36. Conclusions • After the first PLANCK results the simplest model of inflation is alive and kicking: no indication of any departure from a single-field, slow roll inflation with canonical kinetic term from a Bunch-Davies vacuum • PLACK will further improve its constraints by adding polarization information • Constraints on non-Gaussianity can, in some cases, severely reduce the parameter space of many non-minimal models (without, however, ruling them out) • Future cosmological observations will focus on the large-scale structure: the large volume available makes them, in principle, an even more powerful probe of the initial conditions than the CMB • However, the analysis of its several observables is challenging: we have to deal with the nonlinear evolution of structures and the complex baryon physics (to mention two among many problems ...!)
  37. 37. New Light in Cosmology from the CMB SCHOOL WORKSHOP 22 - 26 July 2013 29 July - 2 August 2013 Miramare, Trieste, Italy TOPICS of the School: • EARLY UNIVERSE • CMB THEORY • CMB EXPERIMENTS • PLANCK PRODUCTS • LENSING ISW • BIG SCIENCE FROM SMALL SCALES The purpose of the School is to provide the theoretical and computational tools to study the implications of the 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 the experimental CMB results in all their aspects, their relation with other probes and the future prospects. PARTICIPATION Scientists and students from all countries which are members of the United Nations, UNESCO or IAEA may attend the School and Workshop. As it will be conducted in English, participants should have an adequate working knowledge of this language. Although the main purpose of the Centre is to help research workers from developing countries, through a programme of training activities within a framework of international cooperation, 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 entire activity. 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?2474 Once in the website, comprehensive instructions will guide you step-by-step, on how to fill out and submit the application forms. SCHOOL WORKSHOP SECRETARIAT: Telephone: +39 040 2240 363 - Telefax: +39 040 2240 7363 - E-mail: smr2474@ictp.it ICTP Home Page: http://www.ictp.it/ IN COLLABORATION WITH THE ITALIAN INSTITUTE FOR NUCLEAR PHYSICS ORGANIZERS: 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) DEADLINE for requesting participation 15 April 2013 extended to 28 April 2013 January 2013 Deadline in 2 days!
  38. 38. 2000 2002 2004 2006 2008 2010 2012 0 20 40 60 80 100 120 140 PNG in the last 10 years ? # of articles with “Non-Gaussian” in the title on the ADS data base
  39. 39. PNG in the last 10 years ? # of articles with “Non-Gaussian” in the title on the ADS data base 2000 2002 2004 2006 2008 2010 2012 0 20 40 60 80 100 120 140 non-primordial NG
  40. 40. 2000 2002 2004 2006 2008 2010 2012 0 20 40 60 80 100 120 140 PNG in the last 10 years COBE (≪1σ) WMAP1 (0.8 σ) WMAP3 (0.7 σ) WMAP7 (1.5 σ) ? non-primordial NG # of articles with “Non-Gaussian” in the title on the ADS data base WMAP5 (1.7 σ) Yadav Wandelt (2.8σ ?)
  41. 41. 2000 2002 2004 2006 2008 2010 2012 0 20 40 60 80 100 120 140 PNG in the last 10 years Inflation / Theory non-primordial NG # of articles with “Non-Gaussian” in the title on the ADS data base COBE (≪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 2012 0 20 40 60 80 100 120 140 PNG in the last 10 years Inflation / Theory non-primordial NG # of articles with “Non-Gaussian” in the title on the ADS data base CMB 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 2012 0 20 40 60 80 100 120 140 PNG in the last 10 years Inflation / Theory non-primordial NG # of articles with “Non-Gaussian” in the title on the ADS data base Large-Scale Structure CMB 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 2012 0 20 40 60 80 100 120 140 PNG in the last 10 years Inflation / Theory non-primordial NG # of articles with “Non-Gaussian” in the title on the ADS data base Large-Scale Structure CMB COBE (≪1σ) WMAP1 (0.8 σ) WMAP3 (0.7 σ) WMAP7 (1.5 σ) ? WMAP5 (1.7 σ) Yadav Wandelt (2.8σ ?) Planck fNL = 0? Dalal et al.

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