Constraining dark energy and primordial non-gaussianity with large-scale-structure studies!

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1 Constraining dark energy and primordial non-gaussianity with large-scale-structure studies! Cristiano Porciani, AIfA, Bonn!

2 Research interests! Cosmology, large-scale structure, intergalactic medium! For what regards large-scale structure:! Structure formation (models + simulations)! Models of galaxy biasing! Analysis of galaxy surveys: 2dFGRS, 2Qz, ZCOSMOS (coordinator of the galaxy clustering working group)! Estimation of clustering statistics and of their uncertainties, covariances, etc.! Higher-order statistics (3pt function, bispectrum)! Structure identifiers (pattern recognition)!

3 Estimation of 2-point statistics! New method to estimate 2- point statistics which does not require modeling the observational sampling strategy (Porciani & Lilly 2009)! Particularly important for future dark energy missions using spectroscopic data (e.g. EUCLID)! TRR 33: B8!

4 Galaxy clustering and Dark Energy! MNRAS, 2004, 349, 281! Pre BAOs era! At present it is not realistic to place strong constraints on DE from observed galaxy clustering (strong degeneracy with halo occupation)! Future generation surveys with larger sky coverage when complemented by weak lensing measurements will provide direct constraints on the growth of density fluctuations!

5 Current state of the art! BAO detected with 99.74% confidence in combined sample using all of 2dfGRS + SDSS Main + SDSS LRGs! Combined with WMAP this gives Ω m = ± (68% CL)! PERCIVAL ET AL. (2007)

6 The current state of the art Bennett 2006

Telescope / Ongoing/Future Survey! N(Z) / 10BAO surveys! instrument! 6! Dates! Status! WiggleZ! AAT/AAΩ! 0.2! 2007-2010! In progress! FastSound! Subaru/FMOS! 0.6! 2010-2013! Proposal! BOSS! SDSS! 1.5!

7 Telescope / Ongoing/Future Survey! N(Z) / 10BAO surveys! instrument! 6! Dates! Status! WiggleZ! AAT/AAΩ! 0.2! ! In progress! FastSound! Subaru/FMOS! 0.6! ! Proposal! BOSS! SDSS! 1.5! ! Starting! HETDEX! HET/VIRUS! 1.0! ! Part funded! LAMOST-DE! LAMOST! t.b.d.! ?! Proposal! WFMOS-DE! Subaru/wfmos! >2! ! Funding?! EUCLID/JDEM! ESA/NASA/JDEM! >100! 2012+! Status?! SKA! SKA! >100! 2020+! FUTURE!

8 BAO survey comparison! complete, in-progress & future BAO SURVEYS HETDEX 1.9<z<3.5 [? ] FASTSOUND z=1.2 [? ] Courtesy: S. Maddox!

9 Non-linear evolution of BAOs! Crocce & Scoccimarro 2008! Jeong & Komatsu 2006!

10 Biasing and redshift distortions! As far as mass density fluctuations are concerned a few analytical methods are available: standard Eulerian perturbation theory (z>1), renormalized perturbation theory (2 flavors), renormalized Lagrangian perturbation theory! However, simulations tend to be expensive and no analytical method can successfully account for galaxy biasing and redshift distortions! Solving this problem is key to fully exploit the potential of the planned surveys (Interpolation of simulations? New models? Marginalization of meta parameters?)! TRR 33: B8!

11 Beyond 2-point statistics: preserving phase information Coles & Chiang 2000!

12 Tracing the cosmic web Hahn, CP et al. 2007a, 2007b Using the theory of dynamical systems (after getting inspired by the Zel dovich approximation), we have developed a very simple but efficient descriptor of the LSS.! Space is partitioned between structures of different dimensionality (voids, sheets, filaments and knots) based on the dimension of the stable manifold for the orbit of test particles.!

13 Anisotropic correlations! Higher-order statistic and anisotropic correlations depend on the underlying cosmology. Not clear yet what the sensitivity to dark energy is.! Lee, Hahn, CP, 2009!

14 Primordial non-gaussianity! (extra parameters for dark energy studies?)!

15 The origin of structure! One of the major unsolved mysteries in cosmology! Many competing theories that differ in their predictions some of which are accessible to astronomical observations today!

16 Canonical inflation! Our universe derives from the exponential expansion of a tiny causally connected patch! The accelerated expansion is driven by a spatially homogeneous scalar field (the inflaton) which is slowly rolling down its potential! Introduced to address problems that were eating away at the foundations of the hot bigbang model (flatness, horizon, relic density, expansion)! V(ϕ)! ϕ!

17 Perturbations and inflation! Small quantum fluctuations of the inflaton are naturally produced! The exponential expansion rapidly stretches them to longer and longer wavelengths! On super-hubble scales, fluctuations become overdamped, leading to curvature perturbations that can be described as classical! Courtesy of Prof. Sir M. Berry!

18 D-term! oscillating! tachyon! old! hybrid! chaotic! eternal! Inflationary zoo! curvaton! brane! curvaton scenario! new! Two scalar fields: one drives the accelerated expansion (the inflaton) and the second one is responsible for the formation of structure with its quantum fluctuations (the curvaton)! ghost! R 2! extended! natural! super-natural! extra-natural! double! F-term! multi-field!

19 Ekpyrotic/cyclic models! Inspired by heterotic! M-theory! Khoury et al. 2001, 2002, Steinhardt & Turok 2002! The collision of 2 parallel branes embedded in an extradimensional bulk marks the beginning of the hot, expanding phase of the universe! Prior to the collision the universe is contracting, perturbations are generated during this phase!

20 Model predictions! Canonical inflation! Curvaton scenario! Ekpyrotic universe!! Geometry! Flat Flat! Flat! WMAP! WMAP! WMAP! Spectrum of perturbations! Statistics of perturbations! Nearly scaleinvariant! Nearly scaleinvariant! Nearly scaleinvariant! WMAP! WMAP! WMAP! Nearly Non-Gaussian! Non-Gaussian! Gaussian!

21 Spectra and multi-spectra! φ( r k 1 )φ( r k 2 ) = (2π) 3 δ( r k 1 + r k 2 )P(k 1 ) Power spectrum! φ( r k 1 )φ( r k 2 )φ( r k 3 ) = (2π) 3 δ( r k 1 + r k 2 + r k 3 )B(k 1,k 2,k 3 ) For a Gaussian field, B=0! Bispectrum!

22 Shape of non-gaussianity! Depending on the properties of the bispectrum of the gravitational potential, non-gaussianity can be broadly classified into two classes (Babich et al. 2004):! NG of the local (squeezed) form, where B(k 1, k 2, k 3 ) is dominated by the configurations with k 1 «k 2 k 3! (curvaton models, Ekpyrotic/cyclic models)! NG of the equilateral form, where! B(k 1, k 2, k 3 ) is dominated by the configurations with k 1 k 2 k 3! (ghost inflation, DBI inflation)!

23 A particularly simple model! Most of the local models can be reduced to the simple form (Salopek & Bond 1990; Falk et al. 1993; Gangui et al. 1994):! Φ r x [ ] ( ) = φ( x r r ) + f NL φ 2 ( x ) φ 2 Bardeen s potential auxiliary non-linearity parameter! Gaussian field (a real number)! Fractional non-gaussian corrections are 10-5 f NL!

24 Expected non-gaussianity! f NL! Model! References! (n s -1)/4! 0.01! canonical inflation! Maldacena 2003! Acquaviva et al. 2003! -5/(4r)! >10! curvaton! Lyth et al. 2003! 100! multi-field inflation! Linde & Mukhanov 1997! ! new ekpyrotic models! Buchbinder et al. 2007, Creminelli & Senatore 2007, Koyama et al. 2007! 100 (equilateral)! DBI inflation! Alishahiha et al. 2004! 100 (equilateral)! ghost inflation! Arkani-Hamed et al. 2004!

25 The state of the art! f NL (95% CL)! Data! Method! Estimator! Reference! -58<f NL <134! WMAP 1yr! bispectrum! KSW! Komatsu et al. 2003! -27<f NL <121! WMAP 1yr! bispectrum! C+! Creminelli et al. 2006! -54<f NL <114! WMAP 3yr! bispectrum! KSW! Spergel et al. 2007! -36<f NL <100! WMAP 3yr! bispectrum! C+! Creminelli et al. 2006! 27<f NL <147! WMAP 3yr! bispectrum! YW! Yadav & Wandelt 2008! -9<f NL <111! WMAP 5yr! bispectrum! YW! Komatsu et al. 2008! -4<f NL <80! WMAP 5yr! bispectrum! SZ! Smith et al. 2009! -70<f NL <91! WMAP 3yr! Minkowski functionals! -! Hikage et al. 2008! 23<f NL <75! WMAP 3yr! 1-point PDF! -! Jeong & Smoot 2007! -178<f NL <64! WMAP 5yr! Minkowski functionals! -8<f NL <111! WMAP 5yr! wavelet decomposition! -! Komatsu et al. 2008! -! Curto et al. 2008!

26 Summary of CMB studies! Current 95% limits from bispectrum: -9<f NL <111 and -4<f NL <80! Most-likely value f NL 40-60! 7 per cent chance that a Gaussian map gives a higher mostlikely value! Two studies claim detection of non-gaussianity at high confidence! Topological methods give somewhat different results!

27 The near future: Planck! The Planck satellite (a new European CMB probe) will be launched this Spring! The expected Cramer-Rao limit is Δf NL 5 from temperature anisotropies (Komatsu & Spergel 2001)! This reduces to Δf NL 3 from the joint analysis of temperature and polarization maps (Yadav, Komatsu & Wandelt 2007)! Smaller angular scales!

28 Other probes of non-gaussianity?! It would be important to cross-check results against probes with different systematics! What about the large-scale structure? E.g. the galaxy bispectrum?! Unfortunately the non-linear growth of perturbations superimposes a much stronger non-gaussian signal onto the primordial one that is then difficult to recover! (Verde et al. 2000, Scoccimarro et al. 2004, Sefusatti & Komatsu 2007).!

29 Back to life in 2008! The large-scale clustering of collapsed objects (galaxies, galaxy clusters) as measured by the power spectrum depends linearly on f NL!!! Dalal et al. 2008! An approximated model based on linear theory captures all the relevant physics (Dalal et al. 2008, Matarrese & Verde 2008, Slosar et al. 2008, Afshordi & Tolley 2008, McDonald 2008)!

30 Afshordi & Tolley 2008! How does it work?! Gaussian case:! long and short wavelength modes of the density field are independent! Non-Gaussian case:! the long modes modulate the amplitude of the short ones via the gravitational potential! δ s = δ G [1+ 2 f NL φ l /g(z)]

31 Competitive with CMB! Fitting the best datasets for galaxy clustering with the approximated model, gives:! -29<f NL <70 at 95% CL! Slosar et al. 2008! This is competitive with the WMAP 5yr results!! Combined: 0<f NL <69! Caveat: how accurate is the first-order model?!

32 Numerical simulations! We thus decided to run a series of high-resolution simulations of structure formation from non- Gaussian initial conditions! Box-sizes from 150 h -1 Mpc to 1200 h -1 Mpc! 600,000 CPU hours at the Swiss National Super Computing Centre in Manno (CH)!

33 The large-scale structure! 250 h -1 Mpc! f NL = 0 f NL = 750!

34 Testing the model! Good news: the clustering dependence on f NL is clearly present in the simulations! Pillepich, CP & Hahn 2009! Bad news: The simple model overestimates the effect by a scale-dependent amount! An accurate fitting formula has been extracted from the simulations.! see also Desjacques et al. 2009,! Grossi et al. 2009!

35 Higher-order models! Can we do better allowing more model complexity?! Giannantonio & Porciani 2009! Third-order perturbation theory (Feynman diagrams) + model for halo formation (small scales) + model for background evolution (large-scales)!

36 Future prospects! Predicted uncertainties for detection (not for measurement)! q 0.8! Dalal et al. 2008, Carbone et al. 2008, McDonald 2008, Afshordi & Tolley 2008!

37 Degeneracies, degeneracies everywhere! p-euclid, weak lensing: Δf NL =5 for a fixed WMAP5 cosmology but:! CP + Amara, Carron, Giannantonio, Pillepich!

38 Mass power spectrum! Pillepich, CP & Hahn 2009! Primordial non-gaussianity modifies the mass power spectrum on the scales probed by BAO and weak-lensing studies!! How does this impact dark energy studies?!

39 Forecasting: p-euclid! CP + Amara, Carron, Giannantonio, Pillepich! DETF FoM: ! (no priors) no f NL f NL! Primordial non- Gaussianity changes the matter power spectrum! Constraints on the dark-energy equation of state from weak lensing are severely weakened! TRR 33: B5!

40 Forecasting: p-euclid! CMB studies help. Using Planck priors, FoM=200!

41 Forecasting EUCLID! However, the spectroscopic survey in EUCLID will provide additional constraints on f NL from galaxy clustering! The combined dataset would thus be able to constrain both dark energy and f NL at an unprecedented level! TRR33: B8!

42 The large-scale structure! 250 h -1 Mpc! f NL = 0 f NL = 750!

43 Zooming in! 160 h -1 Mpc! f NL = 0 f NL = 750!

44 A massive galaxy cluster! 40 h -1 Mpc! f NL = 0 f NL = 750!

45 f NL from rare events! Rare events have the advantage that they maximize deviations from the Gaussian case! However, they have the obvious disadvantage of being rare!! Early attempts inconclusive due to small number statistics (e.g. Willick 2000)!

46 Mass function! Pillepich, CP & Hahn 2009! We have derived an accurate fitting formula for the mass distribution of galaxy clusters and groups as a function of f NL! The halo mass function extracted from the simulations provides a benchmark for future determinations of f NL with galaxy-cluster surveys!

Forecasting: erosita! First imaging all-sky survey in the medium energy X-ray range up to 10 KeV with unprecedented angular resolution (10 5 galaxy clusters!)!

47 Forecasting: erosita! First imaging all-sky survey in the medium energy X-ray range up to 10 KeV with unprecedented angular resolution (10 5 galaxy clusters!)! We are currently deriving the expected constraints on dark energy, dark matter and f NL from cluster counts and clustering properties - with A. Pillepich (ETHZ) and T. Reiprich (AIfA).! TRR 33: B7!

48 Dark-energy clustering! The effective sound speed of dark energy determines the scale at which DE can cluster (this can be pretty small for phantom energy, k-essence field)! Takada 2006! Can we measure this?! ISW? Hubble diagram as a function of direction on the sky? Galaxy redshift surveys?!

49 ISW effect! Tommaso Giannantonio:! Combined measurement of the ISW effect at 4.5σ! Giannantonio et al. 2008! Applications to dark energy, modified gravity - DGP, f(r) - and primordial non- Gaussianity! TRR 33: B4!

50 Thanks for your attention!

WMAP 5-Year Results: Measurement of fnl

WMAP 5-Year Results: Measurement of fnl Eiichiro Komatsu (Department of Astronomy, UT Austin) Non-Gaussianity From Inflation, Cambridge, September 8, 2008 1 Why is Non-Gaussianity Important? Because a