Measuring Dark Energy and Primordial Non-Gaussianity: Things to (Or Not To?) Worry About!

UC Berkeley-LBNL Cosmology Group Seminar September 16, 2008 Outline Outline

Start With... Dark Energy

Why Pursue Dark Energy? DE Equation of State (EOS) DE from SNe Ia ++ Beware of Systematics Two Population Model Gravitational Lensing Outline

Start With... And Then... Dark Energy CMB Bispectrum

Why Pursue Dark Energy? Why Non-Gaussianity? DE Equation of State (EOS) Why in CMB Bispectrum?

DE from SNe Ia ++ The fNL Beware of Systematics WL of CMB Bispectrum Two Population Model Analytic Sketch Gravitational Lensing Numerical Results Outline

Start With... And Then... Dark Energy CMB Bispectrum

Why Pursue Dark Energy? Why Non-Gaussianity? DE Equation of State (EOS) Why in CMB Bispectrum?

DE from SNe Ia ++ The fNL Beware of Systematics WL of CMB Bispectrum Two Population Model Analytical Sketch Gravitational Lensing Numerical Results Credit: NASA/WMAP Science Team Credit: NASA/WMAP Science Team Credit: NASA/WMAP Science Team THE ASTRONOMICAL JOURNAL, 116:1009È1038, 1998 September ( 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.

OBSERVATIONAL EVIDENCE FROM SUPERNOVAE FOR AN ACCELERATING UNIVERSE AND A COSMOLOGICAL CONSTANT

ADAM G. RIESS,1 ALEXEI V. FILIPPENKO,1 PETER CHALLIS,2 ALEJANDRO CLOCCHIATTI,3 ALAN DIERCKS,4 PETER M. GARNAVICH,2 RON L. GILLILAND,5 CRAIG J. HOGAN,4 SAURABH JHA,2 ROBERT P. KIRSHNER,2 B. LEIBUNDGUT,6 M. M. PHILLIPS,7 DAVID REISS,4 BRIAN P. SCHMIDT,8,9 ROBERT A. SCHOMMER,7 R. CHRIS SMITH,7,10 J. SPYROMILIO,6 CHRISTOPHER STUBBS,4 NICHOLAS B. SUNTZEFF,7 AND JOHN TONRY11 Received 1998 March 13; revised 1998 May 6

ABSTRACT We present spectral and photometric observations of 10 Type Ia supernovae (SNe Ia) in the redshift range 0.16 ¹ z ¹ 0.62. The luminosity distances of these objects are determined by methods that employ relations between SN Ia luminosity and light curve shape. Combined with previous data from our High-z Supernova Search Team and recent results by Riess et al., this expanded set of 16 high-redshift supernovae and a set of 34 nearby supernovae are used to place constraints on the following cosmological parameters: the Hubble constant (H ), the mass density ()M), the cosmological constant (i.e., the vacuum energy density, ) ), the deceleration0 parameter (q ), and the dynamical age of the universe (t ). The distances of the high-redshift" SNe Ia are, on average, 10%0 È15% farther than expected in a low mass0 density ()M \ 0.2) universe without a cosmological constant. Di†erent light curve Ðtting methods, SN Ia subsamples, and prior constraints unanimously favor eternally expanding models with positive cosmological constant (i.e., ) [ 0) and a current acceleration of the expansion (i.e., q \ 0). With no prior " 0 constraint on mass density other than )M º 0, the spectroscopically conÐrmed SNe Ia are statistically consistent with q \ 0 at the 2.8 p and 3.9 p conÐdence levels, and with ) [ 0 at the 3.0 p and 4.0 p 0 " conÐdence levels, for two di†erent Ðtting methods, respectively. Fixing a ““ minimal ÏÏ mass density, )M \ 0.2, results in the weakest detection, ) [ 0 at the 3.0 p conÐdence level from one of the two methods. " For a Ñat universe prior ()M ] ) \ 1), the spectroscopically conÐrmed SNe Ia require ) [ 0 at 7 p and 9 p formal statistical signiÐcance" for the two di†erent Ðtting methods. A universe closed"by ordinary matter (i.e., )M \ 1) is formally ruled out at the 7 p to 8 p conÐdence level for the two di†erent Ðtting methods. We estimate the dynamical age of the universe to be 14.2 ^ 1.7 Gyr including systematic uncertainties in the current Cepheid distance scale. We estimate the likely e†ect of several sources of systematic error, including progenitor and metallicity evolution, extinction, sample selection bias, local perturbations in the expansion rate, gravitational lensing, and sample contamination. Presently, none of these e†ects appear to reconcile the data with ) \ 0 and q º 0. " 0 Key words: cosmology: observations È supernovae: general

ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ 1. INTRODUCTION 1 Department of Astronomy, University of California at Berkeley, Berkeley, CA 94720-3411. This paper reports observations of 10 new high-redshift 2 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Type Ia supernovae (SNe Ia) and the values of the cosmo- Cambridge, MA 02138. 3 Departamento de Astronom• a y Astrof• sica, PontiÐcia Universidad logical parameters derived from them. Together with the Cato lica, Casilla 104, Santiago 22, Chile. four high-redshift supernovae previously reported by our 4 Department of Astronomy, University of Washington, Box 351580, High-z Supernova Search Team (Schmidt et al. 1998; Seattle, WA 98195. Garnavich et al. 1998a) and two others (Riess et al. 1998b), 5 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218. the sample of 16 is now large enough to yield interesting 6 European Southern Observatory, Karl-Schwarzschild-Strasse 2, cosmological results of high statistical signiÐcance. Con- D-85748 Garching bei Mu nchen, Germany. Ðdence in these results depends not on increasing the 7 Cerro Tololo Inter-American Observatory, National Optical sample size but on improving our understanding of system- Astronomy Observatories, Casilla 603, La Serena, Chile. NOAO is oper- atic uncertainties. ated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. The time evolution of the cosmic scale factor depends on 8 Mount Stromlo and Siding Spring Observatories, Private Bag, the composition of mass-energy in the universe. While the Weston Creek, ACT 2611, Australia. universe is known to contain a signiÐcant amount of ordi- 9 Visiting Astronomer, Cerro Tololo Inter-American Observatory. nary matter, ) , which decelerates the expansion, its 10 Department of Astronomy, University of Michigan, 834 Dennison M Building, Ann Arbor, MI 48109. dynamics may also be signiÐcantly a†ected by more exotic 11 Institute for Astronomy, University of Hawaii, 2680 Woodlawn forms of energy. Preeminent among these is a possible Drive, Honolulu, HI 96822. energy of the vacuum () ), EinsteinÏs ““ cosmological con- " 1009 THE ASTROPHYSICAL JOURNAL, 517:565È586, 1999 June 1 ( 1999. The American Astronomical Society. All rights reserved. Printed in U.S.A.

MEASUREMENTS OF ) AND " FROM 42 HIGH-REDSHIFT SUPERNOVAE S. PERLMUTTER,1 G. ALDERING, G. GOLDHABER,1 R. A. KNOP, P. NUGENT, P. G. CASTRO,2 S. DEUSTUA, S. FABBRO,3 A. GOOBAR,4 D. E. GROOM, I. M. HOOK,5 A. G. KIM,1,6 M. Y. KIM, J. C. LEE,7 N. J. NUNES,2 R. PAIN,3 C. R. PENNYPACKER,8 AND R. QUIMBY Institute for Nuclear and Particle Astrophysics, E. O. Lawrence Berkeley National Laboratory, Berkeley, CA 94720 C. LIDMAN European Southern Observatory, La Silla, Chile R. S. ELLIS, M. IRWIN, AND R. G. MCMAHON Institute of Astronomy, Cambridge, England, UK P. RUIZ-LAPUENTE Department of Astronomy, University of Barcelona, Barcelona, Spain N. WALTON Isaac Newton Group, La Palma, Spain B. SCHAEFER Department of Astronomy, Yale University, New Haven, CT B. J. BOYLE Anglo-Australian Observatory, Sydney, Australia A. V FILIPPENKO AND T. MATHESON Department of Astronomy, University of California, Berkeley, CA A. S. FRUCHTER AND N. PANAGIA9 Space Telescope Science Institute, Baltimore, MD H. J. M. NEWBERG Fermi National Laboratory, Batavia, IL AND W. J. COUCH University of New South Wales, Sydney, Australia (THE SUPERNOVA COSMOLOGY PROJECT) Received 1998 September 8; accepted 1998 December 17 ABSTRACT We report measurements of the mass density, )M, and cosmological-constant energy density, ) , of the universe based on the analysis of 42 type Ia supernovae discovered by the Supernova Cosmology" Project. The magnitude-redshift data for these supernovae, at redshifts between 0.18 and 0.83, are Ðtted jointly with a set of supernovae from the Cala n/Tololo Supernova Survey, at redshifts below 0.1, to yield values for the cosmological parameters. All supernova peak magnitudes are standardized using a SN Ia light-curve width-luminosity relation. The measurement yields a joint probability distribution of the cosmological parameters that is approximated by the relation 0.8) [ 0.6) B [0.2 ^ 0.1 in the region M " of interest () [ 1.5). For a Ñat () ] ) \ 1) cosmology we Ðnd )flat \ 0.28`0.09 (1 p statistical) `0.05 M M " M ~0.08 ~0.04 (identiÐed systematics). The data are strongly inconsistent with a " \ 0 Ñat cosmology, the simplest inÑationary universe model. An open, " \ 0 cosmology also does not Ðt the data well: the data indicate that the cosmological constant is nonzero and positive, with a conÐdence of P(" [ 0) \ 99%, including the identiÐed systematic uncertainties. The best-Ðt age of the universe relative to the Hubble time is tflat \ 14.9`1.4(0.63/h) Gyr for a Ñat cosmology. The size of our sample allows us to perform a variety of statistical0 ~1.1tests to check for possible systematic errors and biases. We Ðnd no signiÐcant di†erences in either the host reddening distribution or Malmquist bias between the low-redshift Cala n/Tololo sample and our high-redshift sample. Excluding those few supernovae that are outliers in color excess or Ðt residual does not signiÐcantly change the results. The conclusions are also robust whether or not a width-luminosity relation is used to standardize the supernova peak magnitudes. We discuss and constrain, where possible, hypothetical alternatives to a cosmological constant. Subject headings: cosmology: observations È distance scale È supernovae: general

1 Center for Particle Astrophysics, University of California, Berkeley, California. 2 Instituto Superior Te cnico, Lisbon, Portugal. 3 LPNHE, CNRS-IN2P3, and University of Paris VI and VII, Paris, France. 4 Department of Physics, University of Stockholm, Stockholm, Sweden. 5 European Southern Observatory, Munich, Germany. 6 PCC, CNRS-IN2P3, and Colle` ge de France, Paris, France. 7 Institute of Astronomy, Cambridge, England, UK. 8 Space Sciences Laboratory, University of California, Berkeley, California. 9 Space Sciences Department, European Space Agency. 565 The Astrophysical Journal, 607:665–687, 2004 June 1 A # 2004. The American Astronomical Society. All rights reserved. Printed in U.S.A.

TYPE Ia SUPERNOVA DISCOVERIES AT Z > 1 FROM THE HUBBLE SPACE TELESCOPE: EVIDENCE FOR PAST DECELERATION AND CONSTRAINTS ON DARK ENERGY EVOLUTION1 Adam G. Riess,2 Louis-Gregory Strolger,2 John Tonry,3 Stefano Casertano,2 Henry C. Ferguson,2 Bahram Mobasher,2 Peter Challis,4 Alexei V. Filippenko,5 Saurabh Jha,5 Weidong Li,5 Ryan Chornock,5 Robert P. Kirshner,4 Bruno Leibundgut,6 Mark Dickinson,2 Mario Livio,2 Mauro Giavalisco,2 Charles C. Steidel,7 Txitxo Benı´tez,8 and Zlatan Tsvetanov8 Received 2004 January 20; accepted 2004 February 16

ABSTRACT We have discovered 16 Type Ia supernovae (SNe Ia) with the Hubble Space Telescope (HST ) and have used them to provide the first conclusive evidence for cosmic deceleration that preceded the current epoch of cosmic acceleration. These objects, discovered during the course of the GOODS ACS Treasury program, include 6 of the 7 highest redshift SNe Ia known, all at z > 1:25, and populate the Hubble diagram in unexplored territory. The luminosity distances to these objects and to 170 previously reported SNe Ia have been determined using empirical relations between light-curve shape and luminosity. A purely kinematic interpretation of the SN Ia sample provides evidence at the greater than 99% confidence level for a transition from deceleration to acceleration or, similarly, strong evidence for a cosmic jerk. Using a simple model of the expansion history, the transition between the two epochs is constrained to be at z 0:46 0:13. The data are consistent with the 2 ¼ Æ cosmic concordance model of M 0:3; Ã 0:7 ( dof 1:06) and are inconsistent with a simple model of evolution or dust as an alternative to dark energy. For a fla¼t universe with a cosmological constant, we measure 0:05 M 0:29 0:03 (equivalently, Ã 0:71). When combined with external flat-universe constraints, including the ¼ Æ ¼ 0:13 cosmic microwave background and large-scale structure, we find w 1:02 0:19 (and w < 0:76 at the 95% confidence level) for an assumed static equation of state of dark ener¼gy,ÀP wÆc2. Joint constÀraints on both the ¼ recent equation of state of dark energy, w0, and its time evolution, dw=dz, are a factor of 8 more precise than the first estimates and twice as precise as those without the SNe Ia discovered with HST. Our constraints are consistent with the static nature of and value of w expected for a cosmological constant (i.e., w0 1:0, dw=dz 0) and are inconsistent with very rapid evolution of dark energy. We address consequences of e¼voÀlving dark en¼ergy for the fate of the universe. Subject headings: cosmology: observations — distance scale — galaxies: distances and redshifts — supernovae: general On-line material: machine-readable tables

1. INTRODUCTION reinforced the statistical significance of this result (Knop et al. 2003), while others have also extended the SN Ia sample to Observations of Type Ia supernovae (SNe Ia) at redshift z 1 (Tonry et al. 2003; Barris et al. 2004). Observations of z < 1 provide startling and puzzling evidence that the ex- large-scale structure (LSS), when combined with measure- pansion of the universe at the present time appears to be ments of the characteristic angular size of fluctuations in the accelerating, behavior attributed to ‘‘dark energy’’ with neg- cosmic microwave background (CMB), provide independent ative pressure (Riess et al., 1998; Perlmutter et al. 1999; for (although indirect) evidence for a dark energy component (e.g., reviews, see Riess 2000; Filippenko 2001, 2004; Leibundgut 2001). Direct evidence comes from the apparent faintness of Spergel et al. 2003). An independent, albeit more tentative, investigation via the integrated Sachs-Wolfe (ISW) effect also SNe Ia at z 0:5: Recently expanded samples of SNe Ia have provides evidence for dark energy (Scranton et al. 2003). The magnitude of the observed acceleration was not anticipated by 1 Based on observations with the NASA/ESA Hubble Space Telescope, theory and continues to defy a post facto explanation. Candi- obtained at the Space Telescope Science Institute, which is operated by AURA, dates for the dark energy include Einstein’s cosmological Inc., under NASA contract NAS5-26555. 2 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, constant Ã (with a phenomenally small value), evolving scalar MD 21218. fields (modern cousins of the inflation field; Caldwell et al. 3 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, 1998; Peebles & Ratra 2003), and a weakening of gravity in Honolulu, HI 96822. 4 our 3 1 dimensions by leaking into the higher dimensions Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, requireþd in string theories (Deffayet et al. 2002). These expla- Cambridge, MA 02138. 5 Department of Astronomy, 601 Campbell Hall, University of California, nations bear so greatly on fundamental physics that observers Berkeley, CA 94720-3411. have been stimulated to make extraordinary efforts to con- 6 European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 firm the initial results on dark energy, test possible sources Garching, Germany. of error, and extend our empirical knowledge of this newly 7 Department of Astronomy, 105-24, California Institute of Technology, Pasadena, CA 91125. discovered component of the universe. 8 Department of Physics and Astronomy, Johns Hopkins University, Astrophysical effects could imitate the direct evidence from Baltimore, MD 21218. SNe Ia for an accelerating universe. A pervasive screen of 665 The Astrophysical Journal, 607:665–687, 2004 June 1 A # 2004. The American Astronomical Society. All rights reserved. Printed in U.S.A.

ABSTRACT We have discovered 16 Type Ia supernovae (SNe Ia) with the Hubble Space Telescope (HST ) and have used them to provide th45e first conclusive evidence for cosmic deceleration that preceded the current epoch of cosmic acceleration. These objects, discovered during the course of the GOODS ACS Treasury program, include 6 of the 7 highest redshift SNe Ia known, all at z > 1:25, and populate the Hubble diagram in unexplored territory. The luminosity distances to these objects and to 170 previously reported SNe Ia have been determined using empirical relations between light-curve shape and luminosity. A purely kinematic interpretation of the SN Ia sample provides evidence at the greater than 99% confidence level for a transition from deceleration to acceleration or, similar40ly, strong evidence for a cosmic jerk. Using a simple model of the expansion history, the transition betwµ een the two epochs is constrained to be at z 0:46 0:13. The data are consistent with the 2 ¼ Æ cosmic concordance model of M 0:3; Ã 0:7 ( dof 1:06) and are inconsistent with a simple model of evolution or dust as an alternative to dark energy. For a fla¼t universe with a cosmological constant, we measure 0:05 M 0:29 0:03 (equivalently, Ã 0:71). When combined with external flat-universe constraints, including the ¼ Æ ¼ 0:13 cosmic microwave35background and large-scale structure, we find w 1:02 0:19 (and w < 0:76 at the 95% confidence level) for an assumed static equation of state of dark ener¼gy,ÀP wÆc2. Joint constÀraints on both the ¼ recent equation of state of dark energy, w0, and its time evolution, dw=dzHST, are aDiscoveredfactor of 8 more precise than the first estimates and twice as precise as those without the SNe Ia dGroundiscovere dDiscoveredwith HST. Our constraints are consistent with the static nature of and value of w expected for a cosmological constant (i.e., w0 1:0, dw=dz 0) and ar30e inconsistent with very rapid evolution of dark energy. We address consequences of e¼voÀlving ¼ dark energy for the fate of the universe0.5. 1.0 1.5 2.0 Subject headings: cosmology: observations — distance scale — galaxies: distances and redshifts — supernovae: general z On-line material: machine-readable tables

1.0 ABSTRACT

We 0.5have discovered 16 Type Ia supernovae (SNe Ia) with the Hubble Space Telescope (HST ) and have used them to provide the ﬁrst conclusive evidence for cosmic deceleration that preceded the current epoch of cosmic acceleration. These objects, discovered during the course of the GOODS ACS Treasury program, include 6 of the 0.0 7 highest redshift SNe Ia known, all at z > 1:25, and populate the Hubble diagram in unexplored territory. The

lumi(m-M) (mag) nosity distances to these objects and to 170 previously reported SNe Ia have been determined using emp! ir-0.5ical relations between light-curve shape and luminosity. A purely kinematic interpretation of the SN Ia sample providesGroundevidenc Discoverede at the greater than 99% confidence level for a transition from deceleration to accel- HST Discovered eratio-1.0n or, similarly, strong evidence for a cosmic jerk. Using a simple model of the expansion history, the transition between the two epochs is constrained to be at z 0:46 0:13. The data are consistent with the 2 ¼ Æ cosmic1.0concordance model of M 0:3; 0:7 ( 1:06) and are inconsistent with a simple model of Ã dof ¼ =0) evolution orq(z)=qdust as0+z(dq/dz)an alternative to dark energy. For a flat universe with a cosmo=-,log idq/dz=0cal consta (jnt0, we measure 0:05 0 M 0.50:29 0:03 (equivalently, Ã 0:71). When coConstantmbined wi thAcceleration,external flat-u nqiverse constraints, including the ¼ Æ ¼ 0:13 cosmic microwave background and large-scale structure, we find w 1:02 0:19 (and w < 0:76 at the 95% confidence level) for an assumed static equation of state of dark ener¼gy,ÀP wÆc2. Joint constÀraints on both the 0.0 ¼ recent equation of state of dark energy, w0, and its time evolution, dw=dz, are a factor of 8 more precise than Constant Deceleration, q the fi(m-M) (mag) rst estimates and twice as precise as those without the SNe Ia discovered with HST. Our constraints ! 0=+, dq/dz=0 (j are co-0.5nsistent withCoasting,the static n q(z)=0ature of and value of w expected for a cosmological constant (i.e.,0=0)w0 1:0, dw=dz 0) and areAcceleration+Deceleration,inconsistent with very rapid ev oqlu0=-,tion dq/dz=++of dark energy. We address consequences of e¼voÀlving ¼ Acceleration+Jerk, q0=-, j0=++ dark e-1.0nergy for the fate of the universe. Subject headings: cosmology: observations — distance scale — galaxies: distances and redshifts — 0.0 0.5 1.0 1.5 2.0 supernovae: general z On-line material: machine-readable tables

1. INTRODUCTION reinforced the statistical significance of this result (Knop et al. 2003), while others have also extended the SN Ia sample to Observations of Type Ia supernovae (SNe Ia) at redshift z 1 (Tonry et al. 2003; Barris et al. 2004). Observations of z < 1 provide startling and puzzling evidence that the ex- large-scale structure (LSS), when combined with measure- pansion of the universe at the present time appears to be ments of the characteristic angular size of fluctuations in the accelerating, behavior attributed to ‘‘dark energy’’ with neg- cosmic microwave background (CMB), provide independent ative pressure (Riess et al., 1998; Perlmutter et al. 1999; for (although indirect) evidence for a dark energy component (e.g., reviews, see Riess 2000; Filippenko 2001, 2004; Leibundgut 2001). Direct evidence comes from the apparent faintness of Spergel et al. 2003). An independent, albeit more tentative, investigation via the integrated Sachs-Wolfe (ISW) effect also SNe Ia at z 0:5: Recently expanded samples of SNe Ia have provides evidence for dark energy (Scranton et al. 2003). The magnitude of the observed acceleration was not anticipated by 1 Based on observations with the NASA/ESA Hubble Space Telescope, theory and continues to defy a post facto explanation. Candi- obtained at the Space Telescope Science Institute, which is operated by AURA, dates for the dark energy include Einstein’s cosmological Inc., under NASA contract NAS5-26555. 2 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, constant Ã (with a phenomenally small value), evolving scalar MD 21218. fields (modern cousins of the inflation field; Caldwell et al. 3 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, 1998; Peebles & Ratra 2003), and a weakening of gravity in Honolulu, HI 96822. 4 our 3 1 dimensions by leaking into the higher dimensions Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, requireþd in string theories (Deffayet et al. 2002). These expla- Cambridge, MA 02138. 5 Department of Astronomy, 601 Campbell Hall, University of California, nations bear so greatly on fundamental physics that observers Berkeley, CA 94720-3411. have been stimulated to make extraordinary efforts to con- 6 European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 firm the initial results on dark energy, test possible sources Garching, Germany. of error, and extend our empirical knowledge of this newly 7 Department of Astronomy, 105-24, California Institute of Technology, Pasadena, CA 91125. discovered component of the universe. 8 Department of Physics and Astronomy, Johns Hopkins University, Astrophysical effects could imitate the direct evidence from Baltimore, MD 21218. SNe Ia for an accelerating universe. A pervasive screen of 665 +0.027 +0.036 Supernova Cosmology Project ΩΛ = 0.713 0.029(stat) 0.039(sys) Kowalski, et al., Ap.J. (2008) − − 50 Supernova Cosmology Project Kowalski, et al., Ap.J. (2008) 1.5 45 Union 08 SN Ia compilation

µ 40

Hamuy et al. (1996) Krisciunas et al. (2005) Riess et al. (1996) Jha et al. (2006) SCP: This Work 35 Riess et al. (1998) + HZT SCP: Perlmutter et al. (1999) Tonry et al. (2003) 1.0 Barris et al. (2003) SCP: Knop et al. (2003) Riess et al. (2006) Astier et al. (2006) SNe Miknaitis et al. (2007) 30 0.0 1.0 2.0 Redshift

0.5

CMB

Flat BAO

0.0 0.0 0.5 1.0 m WMAP Cosmic Acceleration

Modiﬁed Gravity Dark Energy

2 H 8πG H = (ρ + ρV ) − rc 3

Modiﬁcation of Friedmann Vacuum Energy equation (5D Gravity) (Cosmological Constant)

Phenomenological Scalar Fields modiﬁcation to the GR Evolving Equation of State Lagrangian

New Physics/Surprises? Dark Energy Equation Of State

T ν = diag(ρ, p, p, p) p = wρ µ − − −

w = 1/3 w = 0 w < 1/3 − For Cosmological Constant... w = 1 − DE EOS Revisited: Different Approaches...

(A) Parameterize w(z) [Adopted by the DETF] w(a) = w + (1 a)w Chevallier & Polarski (2001) 0 − a (Linder 2003) DE EOS Revisited: Different Approaches...

(A) Parameterize w(z) [Adopted by the DETF]

Chevallier & Polarski (2001) w(z) = w0 + waz/(1 + z) (Linder 2003) DE EOS Revisited: Different Approaches...

(A) Parameterize w(z) [Adopted by the DETF]

Chevallier & Polarski (2001) w(z) = w0 + waz/(1 + z) (Linder 2003)

(B) Non-Parametric w(z)

Unbiased Estimate of DE Density (Wang & Lovelace 2001) Principal Component Approach (Huterer & Starkman 2003) Uncorrelated Estimates (Huterer & Cooray 2005)

...

For a review: Please see Sahni and Starobinsky (2006) [arXiv:astro-ph/0610026] “Seeing” The Dark Energy ...via its effect on the expansion of the Universe 1/2 H(z) = H Ω (1 + z)3 + Ω (1 + z)2 + (1 Ω Ω )F (z) 0 m k − k − m ! " “Seeing” The Dark Energy ...via its effect on the expansion of the Universe 1/2 H(z) = H Ω (1 + z)3 + Ω (1 + z)2 + (1 Ω Ω )F (z) 0 m k − k − m z ! 1 + w(z!) " F (z) = exp 3 dz! 1 + z ! "0 ! # “Seeing” The Dark Energy ...via its effect on the expansion of the Universe 1/2 H(z) = H Ω (1 + z)3 + Ω (1 + z)2 + (1 Ω Ω )F (z) 0 m k − k − m z ! 1 + w(z!) " F (z) = exp 3 dz! 1 + z ! "0 ! # Approaches... Standard Candles: Luminosity Distance of SNe Standard Rulers: Angular Diameter Distance via BAO Distance to the Last Scattering Surface Weak Lensing Tomography Binned Estimates: Future n 1 − 3(1+wn) 3(wi wi+1) w F (zn > z > zn 1) = (1 + z) (1 + zi) − 1 0-.07 − i=0 ! w2 .07-.15

w3 0.15-.3

w4 0.3-0.6

w5 0.6-1.2

w6 1.2-2.0

D.S., S. Sullivan, S. Joudaki, A. Amblard, D. Holz, A. Cooray; PRL, 100, 241302 (2008) Binned Estimates: Future n 1 − 3(1+wn) 3(wi wi+1) w F (zn > z > zn 1) = (1 + z) (1 + zi) − 1 0-.07 − i=0 ! w2 .07-.15

w3 0.15-.3

w4 0.3-0.6

w5 0.6-1.2

w6 1.2-2.0

D.S., S. Sullivan, S. Joudaki, A. Amblard, D. Holz, A. Cooray; PRL, 100, 241302 (2008)

Outline

Dark Energy CMB Bispectrum

Why Pursue Dark Energy? Why Non-Gaussianity? DE Equation of State (EOS) Why in CMB Bispectrum?

DE from SNe Ia ++ The fNL Beware of Systematics WL of CMB Bispectrum Two Population Model Analytical Sketch Gravitational Lensing Numerical Results Systematic Matters! Supernova Cosmology Project Supernova Cosmology Project Kowalski, et al., Ap.J. (2008) Kowalski, et al., Ap.J. (2008) 0.0 2

BAO Union 08 w i SN Ia 0 th s compilation y s -0.5 CMB te SNe m a t + BAO ic s w wa -2 + CMB

-1.0 -4 Union 08 SNe SN Ia compilation -1.5 -6 0.0 0.1 0.2 0.3 0.4 0.5 -2.0 -1.5 -1.0 -0.5 0.0 ! m w0 Kowalski et al. (2008)

+0.027 +0.036 ΩΛ = 0.713 0.029(stat) 0.039(sys) − − +0.059 +0.063 w = 0.969 0.063(stat) 0.066(sys) − − − Outline

Dark Energy CMB Bispectrum

Why Pursue Dark Energy? Why Non-Gaussianity? DE Equation of State (EOS) Why in CMB Bispectrum?

DE from SNe Ia ++ The fNL Beware of Systematics WL of CMB Bispectrum Two Population Model Analytical Sketch Gravitational Lensing Numerical Results Cosmology with SNe Ia: Revisited

SNAP DESTINY

Advantages Direct measure of accl. Small dispersion Single objects (easier!) Can be observed over wide z Not cosmic variance limited Straightforward tests of sys.

SNAP DESTINY

Advantages Challenges Direct measure of accl. Dust extinction Small dispersion Photometric calibration (Vega) Single objects (easier!) Malmquist bias Can be observed over wide z K-corrections Not cosmic variance limited Evolution, chemical comp. Straightforward tests of sys. Population bias + Grav. Lensing

Credit: This clip was prepared by the Supernova Cosmology Project (P. Nugent: spectral sequence; A. Conley: image sequence) with the help of Lawrence Berkeley National Laboratory's Computer Visualization Laboratory (N. Johnston: animation) at the National Energy Research Scientiﬁc Computing Center. Challenges: Systematic Uncertainties source of common sample- treatment uncertainty (mag) dep.(mag) Multi-band photometry Extinction 0.013 - including near-IR Calibration of standard stars Calibration 0.021 0.021 (optical thru near-IR) to <1% High S/N lightcurves & spectra; Malmquist - 0.020 requirement of pre-rise data SN spectra with broad λ , Lightcurve 0.028 - temporal coverage Evolution 0.015 - High-resolution spectroscopy Kowalski et al. (2008), Carnegie Supernova Project: W. Freedman 2-Population Lensing Evolution based on Two SN Populations

Scannapieco & Bildsten (2005)

SNRIa(t) M˙ (t) M (t) ∗ ∗ 1 = B 10 1 + A 10 (100yr)− 10 M Gyr− 10 M ! ◦ " # ◦ $

Also: Hamuy et al. 1995 Livio 2000 Evolution based on Two SN Populations

Bimodal Delay Time Distribution Belczynski et al. 2005 Mannucci et al. 2006 Data From: Mannucci et al. 2005 Strolger et al. 2003 Dahlen et al. 2004

Total

Prompt Delayed/Extended/Tardy Evolution based on Two SN Populations

20 µB = mB∗ M + α(s 1) βc B component − − − star forming Tripp (1998), Guy et al. (2005) 15 hosts

10 PROMPT Number

5 12% Dfference

0 in

6 Intrinsic Luminosity A component 5 passive hosts = + ∆ LP LE L 4 DELAYED

Number 3

2 Howell et al. 2007 1

0 Data Source: Sullivan et al. 2006 (SNLS) 0.6 0.8 1.0 1.2 1.4 Stretch Evolution based on Two SN Populations

+,-./0123'2/44353.63 !!&# !!&" !&! !&" !&#

!&!'(')'('!&* 758+90 % :3;,<32 $ Median Redshift: 0.026 # N=50 " ! !&*'(')'('!&?> "! *> Median Redshift: 0.55 *! C1+D35 N=99 > ! $ !&?>'(')'('*&> > # Median Redshift: 1.12 = N=20 " * ! Howell et al. 2007 !&? !&% !&@ *&! *&* *&" *&= A05306B Is there a Signature in the Hubble Diagram? Is there a Signature in the Hubble Diagram?

d m M = 5 log L + 25 + − Mpc M ! " Is there a Signature in the Hubble Diagram?

d m M = 5 log L + 25 + + δ f (z) − Mpc M D ∗ D ! " Is there a Signature in the Hubble Diagram?

d m M = 5 log L + 25 + + δ f (z) − Mpc M D ∗ D ! "

With current data (192 SNe from Davis et al. 2007), the residual is δP δD consistent with zero: δ (5 9)% D ∼ ± With future data, one will be able to constrain the residual much better.

D.S., A. Amblard, A. Cooray, and D. Holz; ApJL, 684, L13 (2008) Effect on the EOS Estimates: Bias in “w”

Generate Mock Datasets

δD = 0.025

D.S., A. Amblard, A. Cooray, and D. Holz; ApJL, 684, L13 (2008) Effect on the EOS Estimates: Bias in “w”

200 indep. mocks analyzed δD = 0.025

~1-sigma bias in “w” Correlation While model-fitting the data: δ = 0 1σ bias in w D ⇒ ∼ δ = FREE NO bias in w, BUT Error bar increased by 2.5 times D ⇒ Best situation: Constrain δD <= 2% with confidence D.S., A. Amblard, A. Cooray, and D. Holz; ApJL, 684, L13 (2008) Challenges: Systematic Uncertainties source of common sample- treatment uncertainty (mag) dep.(mag) Multi-band photometry Extinction 0.013 - including near-IR Calibration of standard stars Calibration 0.021 0.021 (optical thru near-IR) to <1% High S/N lightcurves & spectra; Malmquist - 0.020 requirement of pre-rise data SN spectra with broad λ , Lightcurve 0.028 - temporal coverage Evolution 0.015 - High-resolution spectroscopy Kowalski et al. (2008), Carnegie Supernova Project: W. Freedman Constrain the systematics to < 2% level to have the bias on 2-Population “w” less than 1-sigma level without increasing error bar! Lensing Influence of Gravitational Lensing? Influence of Gravitational Lensing? Influence of Gravitational Lensing?

obs,lensed(z, nˆ) = µ(z, nˆ) obs,true(z) F F Inﬂuence of Gravitational Lensing?

obs,lensed(z, nˆ) = µ(z, nˆ) obs,true(z) F F Weak lensing can modify the SNa ﬂux & bias estimates of w AmpliﬁcationAmplification Probability Probability Distribution Distribution 18 "P_mu-PLOT-z-1.dat" "P_mu-PLOT-z-2.dat" 16 "P_mu-PLOT-z-3.dat"

14 obs,lensed(z, nˆ) = µ(z, nˆ) obs,true(z) 12 F F

mu Valid for all cosmologies P 8 and at all redshifts

0 0.8 0.9 1 1.1 1.2 1.3 mu Wang, Y., Holz, D. E., & Munshi, D., 2002, ApJ, 572, L15 Our Analysis with Mock Catalogs

N = 2000 D.S., A. Amblard, D. Holz, A. Cooray; ApJ, 678, 1 (2008) Ωm = 0.3 w = 1 ; w = 0 0 − 1

[∆(m M)] = 2.5 log(µ) − lensing − (m M)data(z) = (m M)fid(z) + [∆(m M)] − − − int +[∆(m M)] − lensing Effect of Weak Lensing on Estimates of “w”

10,000 Realizations 10,000 SNe

2000 SNe 300 SNe

D.S., A. Amblard, D. Holz, A. Cooray; ApJ, 678, 1 (2008) Effect of Removing the Outliers

10,000 Realizations

Outliers (25%) Removed ~ 50 SNe Whole Dataset Used... 2000 SNe

D.S., A. Amblard, D. Holz, A. Cooray; ApJ, 678, 1 (2008) Challenges: Systematic Uncertainties source of common sample- treatment uncertainty (mag) dep.(mag) Multi-band photometry Extinction 0.013 - including near-IR Calibration of standard stars Calibration 0.021 0.021 (optical thru near-IR) to <1% High S/N lightcurves & spectra; Malmquist - 0.020 requirement of pre-rise data SN spectra with broad λ , Lightcurve 0.028 - temporal coverage Evolution 0.015 - High-resolution spectroscopy Kowalski et al. (2008), Carnegie Supernova Project: W. Freedman Constrain the systematics to < 2% level to have the bias on 2-Population “w” less than 1-sigma level without increasing error bar! Lensing Need a large # of SNe per redshift bin to keep bias < 1% Outline

Dark Energy CMB Bispectrum

Why Pursue Dark Energy? Why Non-Gaussianity? DE Equation of State (EOS) Why in CMB Bispectrum?

DE from SNe Ia ++ The fNL Beware of Systematics WL of CMB Bispectrum Two Population Model Analytical Sketch Gravitational Lensing Numerical Results Outline

Dark Energy CMB Bispectrum

Why Pursue Dark Energy? Why Non-Gaussianity? DE Equation of State (EOS) Why in CMB Bispectrum?

DE from SNe Ia ++ The fNL Beware of Systematics WL of CMB Bispectrum Two Population Model Analytical Sketch Gravitational Lensing Numerical Results Primordial Non-Gaussianity: Primary CMB Bispectrum

Gaussian Quantum Fluctuation 1 2 Starobinsky (1986) Falk et al. (1993) δφ g η + m− f η ∼ δφ pl η Gangui et al. (1994) Non-Gaussian !Inﬂation Fluctuation"

1 1 2 Salopek & Bond Φ m− g δφ + m− f δφ ∼ pl Φ pl δφ (1990) Non-Gaussian Cur! vature Perturbation" ∆T g Φ + f Φ2 Pyne & Carroll (1996) T ∼ T Φ Non-Gaussian CMB! Anisotr" opy Primordial Non-Gaussianity: Primary CMB Bispectrum

Combining all the contributions: ∆T (x) g Φ(x) T ∼ T where: Φ(x) = Φ (x) + f Φ2 (x) Φ2 (x) L NL L − " L # ! " Non-Linear Coupling Parameter Measurement of non-Gaussian CMB anisotropies potentially constrains non-linearity, “slow-rollness”, and “adiabaticity” in inﬂation. - Komatsu 2002 Primordial Non-Gaussianity: Primary CMB Bispectrum

Non-Gaussianity from the simplest inﬂation model is very small: f 0.01 1 NL ∼ − Much higher level of primordial non-Gaussianity is predicted by

Models with multiple scalar ﬁelds Non-Adiabatic Fluctuations Features in the inﬂation potential Non-canonical kinetic terms ...

Review: N. Bartolo, E. Komatsu, S. Matarrese, and A. Riotto, Phys. Rep. 402, 103 (2004). Primary CMB Bispectrum

The CMB Temperature Perturbation in the Sky:

∆T (nˆ) Θ(nˆ) = Θ Y m(nˆ) ≡ T lm l !lm Power Spectrum:

Θ Θ = δ δ CΘΘ ! lm l!m! " l,l! m,m! l Angular Bispectrum:

l1 l2 l3 Θ Θl1m1 Θl2m2 Θl3m3 = Bl l l ! " m1 m2 m3 1 2 3 ! " Measurement of primordial non-Gaussianity

P H Y S I C A L R E V I E W L E T T E R S week ending PRL 100, 181301 (2008) 9 MAY 2008

Evidence of Primordial Non-Gaussianity (fNL) in the Wilkinson Microwave Anisotropy Probe 3-Year Data at 2:8

Amit P. S. Yadav1 and Benjamin D. Wandelt1,2 1Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 W. Green Street, Urbana, Illinois 61801, USA 2Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green Street, Urbana, Illinois 61801, USA (Received 7 December 2007; revised manuscript received 6 March 2008; published 7 May 2008)

We present evidence for primordial non-Gaussianity of the local type (fNL) in the temperature anisotropy of the cosmic microwave background. Analyzing the bispectrum of the Wilkinson Microwave Anisotropy Probe 3-year data up to ‘max 750 we find 27 < fNL < 147 (95% C.L.). This amounts to a rejection of f 0 at 2:8, disfavoring canonical single-field slow-roll inflation. The NL signal is robust to variations in lmax, frequency and masks. No known foreground, instrument systematic, Submitted toro tsecondaryhe Astropanisotropyhysical Joexurnplainsal Suit.pplWeme eexplont Sereriethes impact of several analysis choices on the quoted A Preprint typesignificanceset using LTEXandstyfindle em2u:l5ateatopj bev. 0conserv8/13/06ative.

DOI: 10.1103/PhysRevLett.100.181301 PACS numbers: 98.70.Vc, 98.80.Es

FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP1) OBSERVATIONS: COSMOLOGICAL INTERPRETATION It is now widely accepted that tests of primordial non- Gaussianity where F k1; k2; k3 is large for the configura- 1 2,3,4 5 6 6 7 2 EGaussianity. Komatsu, parameterized, J. Dunkley by the, M.nonlinearityR. Nolta ,parameterC. L. Bennettiont ,whenB. Gokl1d ,k2G. Hki3n.shaw , N. Jarosik , D. Larson 6f, M,.promiseLimon 8toLbe. Paguniquee 2, Dprobe. N. Spoferthegelearly3,9, MUni. Hversealpe[rn1]. 10, R. TheS. Hlocalill 11,formA. Karisesogutfrom7, S. aS.nonlinearMeyer 1relation2, G. S. betweenTucker NL 13 10 7 14 Although the non-Gaussianity from, J. Lthe. Wsimplesteiland inflation, E. Wollacinflatonk , andandE.curvL. Waturerighperturbationst [2,3], curvaton models models is very small, f 0:01 Su1b[m2i–tte4d],totherethe Aisstarovperyhysical J[o9u],rnoraltheSupekpyroticplement Semodelsries [7]. The equilateral form arises NL ÿ large class of more general models, e.g., models AwithBSTRAfromCT noncanonical kinetic terms such as the Dirac-Born- multiple scalar fields, features in inflation potential, non- Infeld action [10], the ghost condensation [11], or any The WMAP 5-year data provide stringent limits on deqeuilviations from the minimal, 6-parameter adiabatic fluctuations, noncanonical9 < fkineticlocal werful1 is discriminantdisfavored ebetweenven whenekpyr-gravitational waves are included, which constrains the NL models of inflation that can produce significant gratemperaturevitational waanisotropiesves, such asalonechaotwasic orintroducedpower-law in [14]. otic models and standard slow-roll inflation. As such, the inflation models, or a blue spectrum, such as hybrid Theinflaideation ofmoaddingdels. Waelinearobtaitermn tigtoht,reducesimultexcessaneousvariance search forlimprimordialits on thenon-Gaussianity(constant) equaisticomplementaryon of state of dtoark endueergytoanoisend theinhomogeneityspatial curvatfolloure owedf theinu[n15iv].ersAppliede: to the search for the inflationary gravitational wave back- WMAP 0.11 < 1 + w < 0.14 (95% CL) and 0.0175 < Ωk dark matter, arXiv:0803.0547v1 [astro-ph] 4 Mar 2008 F k1; k2; k3 is large for the configurations in which k1 We used the generalized bispectrum estimator of pri- space vehicles, space vehicles: instruments, instrumentation: detectors, telescopes k2, k3. Second, the nonlocal, ‘‘equilateral’’, non- mordial non-Gaussianity of local type described in [17].

1. INTRODUCTION E0031-9007lectronic ad=d08ress=:100(18)komatsu=@181301(4)astro.as.utexas.edu 181301-1  2008 The American Physical Society 1 WMAP is the result of a partnership between Princeton Uni- Measurements of microwave background ﬂuctua- versity and NASA’s Goddard Space Flight Center. Scientiﬁc guid- tions by the Cosmic Background Explorer (COBE ance is provided by the WMAP Science Team. ; Smoot et al. 1992; Bennett et al. 1994, 1996), the 1 Univ. of Texas, Austin, Dept. of Astronomy, 2511 Speedway, RLM 15.306, Austin, TX 78712 2 Dept. of Physics, Jadwin Hall, Princeton University, Prince- Code 5247, New York, NY 10027-6902 ton, NJ 08544-0708 9 Princeton Center for Theoretical Physics, Princeton Univer- 3 Dept. of Astrophysical Sciences, Peyton Hall, Princeton Uni- sity, Princeton, NJ 08544 versity, Princeton, NJ 08544-1001 10 Dept. of Physics and Astronomy, University of British 4 Astrophysics, University of Oxford, Keble Road, Oxford, OX1 Columbia, Vancouver, BC Canada V6T 1Z1 3RH, UK 11 Adnet Systems, Inc., 7515 Mission Dr., Suite A100 Lanham, 5 Canadian Institute for Theoretical Astrophysics, 60 St. George Maryland 20706 St, University of Toronto, Toronto, ON Canada M5S 3H8 12 Depts. of Astrophysics and Physics, KICP and EFI, Univer- 6 Dept. of Physics & Astronomy, The Johns Hopkins University, sity of Chicago, Chicago, IL 60637 3400 N. Charles St., Baltimore, MD 21218-2686 13 Dept. of Physics, Brown University, 182 Hope St., Providence, 7 Code 665, NASA/Goddard Space Flight Center, Greenbelt, RI 02912-1843 MD 20771 14 UCLA Physics & Astronomy, PO Box 951547, Los Angeles, 8 Columbia Astrophysics Laboratory, 550 W. 120th St., Mail CA 90095–1547 Measurement of primordial non-Gaussianity

P H Y S I C A L R E V I E W L E T T E R S week ending PRL 100, 181301 (2008) 9 MAY 2008

Evidence of Primordial Non-Gaussianity (fNL) in the Wilkinson Microwave Anisotropy Probe 3-Year Data at 2:8

We present evidence for primordial non-Gaussianity of the local type (fNL) in the temperature anisotropy of the cosmic microwave background. Analyzing the bispectrum of the Wilkinson Microwave Anisotropy Probe 3-year data up to ‘max 750 we find 27 < fNL < 147 (95% C.L.). This amounts to a rejection of f 0 at 2:8, disfavoring canonical single-field slow-roll inflation. The NL signal is robust to variations in lmax, frequency and masks. No known foreground, instrument systematic, or secondary anisotropy explains it. We explore the impact of several analysis choices on the quoted significance and find 2:5 to be conservative.

DOI: 10.1103/PhysRevLett.100.181301 PACS numbers: 98.70.Vc, 98.80.Es

ItCisononwstwidelyraintsacceptedon lothatcaltestspriofmprimordialordial nnon-on-GaGaussianityussianitwherey froFmk ;lkar;gk e issclargeale forstrtheucconfigura-ture 1 2 3 Gaussianity, parameterized by the nonlinearity parameter tion when k1 k2 k3. 1 2 3, 4 5 6 fNL, promiseAnˇzetoSbelosaauniquer, Chproberistopofhether HearlyirataUni, vUerseroˇs[1S].eljak, TheShlocalirleyformHo, arisesand fromNikhailnonlinearPadmanrelationabhan between Although the non-Gaussianity from the simplest inflation inflaton and curvature perturbations [2,3], curvaton models 1Berkeley Center for Cosmological Physics, Physics Department and Lawrence Berkeley National Laboratory, models is very small, fNL 0:01 1 [2–4], there29( is65)a very< f [9<],+70(+93)or the ekpyrotic models [7]. The equilateral form arises Uniÿversity of−Cali−fornia, BeNrkLeley California 94720, USA large class of more general 2models,Caltech Me.g.,/C models130-33,withPasadenfroma, Cnoncanonicalalifornia 9112kinetic5, USAterms such as the Dirac-Born- multiple scalar fields,3Infeaturesstitute finor inflationTheoretipotential,cal Physicnon-s, UniveInfeldrsity oactionf Zuric[h10, ],Zutherichghost, Switcondensationzerland [11], or any adiabatic fluctuations,4Physnoncanonicalics Departmekineticnt, Uniterms,versitydeovia-f Califootherrnia, single-fieldBerkeley, Cmodelsaliforninia which94720,theUSscalarA field acquires tions from the Bunch-Davies vacuum,5Deparamongtment oothers,f Astrothatphysicaal lSocwienspeedces, Pofeysoundton H[a12ll,]. While we focus on the local predict substantially higherPrleinvceeltoonf Uprimordialniversity, Pnon-rincetonform, Neinw thisJersletterey 0,8i5t4is4,straightforwardUSA to repeat our analy- Gaussianity6(seeLawr[e5n] cfore Baerekvieelew).y National Laboratory,Universsisityforof theCalequilateralifornia, Beform.rkeley CA 94720, USA Recent calculations of the perturbations arising(Datined:theAugust The6, 20local08) form of non-Gaussianity may be parametrized ekpyrotic or cyclic cosmological scenarios [6] have con- in real space as [1,3,13] Recent work has shown that the local non-Gaussianity parameter fNL induces a scale-dependent cluded that these scenarios can predict fNL much larger 2 2 bias, whose amplitude is growing with scale. Here we first re derrive this resultfwithin rthe contexrt o;f (2) than single-field slow-roll inflation [7]. Detailed calcula- L NL L ÿ h L i tions in ptheseeak-bmodelsackgrouarend sfraughtplit formwithalismdifficultiesand showcon-that it only depends on the assumption of universality of mass function, assuming halo bias only depends owheren masfs.NLWcharacterizese then use exthetenamplitudeded Press-ofSchprimordialechter non- nected to matching the perturbations through the formalism to argue that this assumption may be vioGaussianitylated and t.hNotee scalthate deptheendNeentwtonianbias wilpotentiall depend has the cosmological singularity at the bounce. However, current on other properties, such as merging history of haloopposites. In pasignrticuoflarBardeen’, in the slimcurvit oaturef recperturbation,ent mergers . calculations suggest that primordial non-Gaussianity of the we find the effect is suppressed. Next we use these prTheedictfirstions fastin cobispectrumnjunction wbasedith a cfoNLmpeestimatorndium using f type could be a powerful discriminant between ekpyr- NL of large scale data to put a limit on the value of fNLtemperature. When comanisotropiesbining all daaloneta assuwasminintroducedg that halo in [14]. otic modelsoccuandpatstandardion depenslodsw-rollonly inflation.on halo mAsasssuch,, we gtheet a liThemit ideaof of29adding( 65) astructure formation, these could be present at a subdom- [1, 2, 3, 4], which has been tremendously successful in inant level and if detected would rule out the simplest describing a very large number of very distinct data-sets 0031-9007=08=100(18)=181301(4) 181301-1models of inflation2008[15,The16, American17, 18]. Physical Society (see e.g. [5]). Inflationary models generically predict a A fourth direction, and the one we focus on in this flat universe and nearly scale-invariant spectrum of ini- paper, is non-Gaussianity in initial conditions. Stan- tial fluctuations [6, 7, 8, 9, 10], both of which seem to be dard single field inflation predicts that the departures confirmed by observations. Consequently, a lot of effort is from Gaussianity are very small and not accessible to being put into constraining observables that might actu- arXiv:0805.3580v2 [astro-ph] 6 Aug 2008 the current observational constraints. Most of the models ally distinguish between different models of inflation. At predict that non-Gaussianity is of the local type, mean- the moment, this is done as a multi-pronged effort: first, ing that it depends on the local value of the potential measurement of the primordial power spectrum gives a only. A standard parameterization of the primordial direct measure of the inflationary potential shape and non-Gaussianity is the so-called scale-independent f inflationary models differ on the actual slope, some pre- NL parameterization, in which one includes a quadratic cor- dicting red and some blue spectrum. Moreover, inflation rection to the potential [19, 20]: predicts that the primordial slope should only be chang- 2 ing with scale very slowly and any deviation from this Φ = φ + fNLφ , (1) prediction would be a surprise in need of an explanation. Second, a detection of B-mode polarization in the where φ is the primordial potential assumed to be a Gaus- cosmic microwave background, if interpreted as gravita- sian random field and fNL describes the amplitude of the tional waves from the early Universe, will effectively de- correction. A typical value of fNL for standard slow roll termine the energy scale of inflation and rule out a major inflation is of the order of slow roll parameter and thus class of inflationary models that predict inflation occurs of order 10−2 [21], but this is likely to be swamped by at a low energy scale [11]. Alternatives to inflation, such the contribution from nonlinear transformation between as ekpyrotic models [11, 12, 13, 14], differ from inflation- the primordial field fluctuation (assumed to be Gaussian Weak Lensing of the Primary Bispectrum

Θ˜ (nˆ) = Θ[nˆ + αˆ] = Θ[nˆ + φ(nˆ)] ∇ i 1 i j Θ(nˆ) + φ(nˆ) Θ(nˆ)+ iφ(nˆ) jφ(nˆ) Θ(nˆ) ≈ ∇i ∇ 2∇ ∇ ∇ ∇

˜Θ l1 l2 l3 ˜ ˜ ˜ Bl l l = Θl1m1 Θl2m2 Θl3m3 1 2 3 m1 m2 m3 ! " m m m 1!2 3 " # CMB Bispectrum of the Equilateral Case 101

Primary (fNL=1) Lensed l l 100 LOCAL l ) MODEL 18 !1 Increase in the ! 10 Amplitude (x10 2 ) ! 10!2 /(2 l,l,l B 4 l

10!3 Decrease in the Amplitude 10!4 0 500 1000 1500 2000 2500 3000 l A. Cooray, D.S., P. Serra; PRD, 77, 123006 (2008) CMB Bispectrum of the Squeezed Case(s)

6 l2 Primary (f =1) NL 100 5 Lensed

) l=l1 l3=l+l2 15 ! 3 (x10 2 ) ! 2 /(2

l,10,l+10 1 B 4 l 3

0 Decrease in the Primary (fNL=1) Amplitude Lensed !1 0 500 1000 1500 2000 2500 3000 2

l ) 17 ! (x10 2

) 1 ! /(2

1 3 2 l,100,l+100 0

l=l l =l+l B 4 l Decrease in the Amplitude !1 10 0 500 1000 1500 2000 2500 3000 l2 l A. Cooray, D.S., P. Serra; PRD, 77, 123006 (2008) Reduction in the S/N due to Lensing

S 2 (BΘ )2 S 2 S 2 l1l2l3 d N lensed N unlensed = tot tot tot − N 6Cl Cl Cl l1l2l3 1 2 3 ! d log l d log l $ ! " # " # max " # min

Primary (fNL=1) Lensing

10!2 1/2 ] 3 /dl 2

10!3 [d(S/N) Planck

WMAP

10!4 0 500 1000 1500 2000 2500 3000

l3 A. Cooray, D.S., P. Serra; PRD, 77, 123006 (2008) Bias in the Non-Gaussianity Parameter

true Θ 2 Θ ∆f f fˆ B σ− B˜ NL − NL = 1 l1l2l3 l1l2l3 ˆ ≡ ˆ − BΘ σ 2BΘ fNL fNL ! l1l2l3 − l1l2l3

100 ! (!) 100 WMAP Primary 30%

10!1 6% 10!1 Planck (+) 1 ! NL WMAP | !2

)f 10 3 bias NL f !

Lensed | !3 !2 (S/N)(

10!4

(!) PLANCK !3 10 10!5 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000

l3 l Minimum detectable value of fNL 7 (instead of 5) for Planck A. Cooray, D.S., P. Serra; PRD, 77, 123006 (2008) At the End of 50 Minutes...

Dark Energy CMB Bispectrum

Why Pursue Dark Energy? Why Non-Gaussianity? DE Equation of State (EOS) Why in CMB Bispectrum?

DE from SNe Ia ++ The fNL Beware of Systematics WL of CMB Bispectrum Two Population Model Analytical Sketch Gravitational Lensing Numerical Results At the End of 50 Minutes...

Dark Energy CMB Bispectrum

Why Pursue Dark Energy? Why Non-Gaussianity? DE Equation of State (EOS) Why in CMB Bispectrum?

DE from SNe Ia ++ The fNL Beware of Systematics WL of CMB Bispectrum Two Population Model Analytical Sketch Gravitational Lensing Numerical Results Summary Summary We have shown that the next-generation surveys will be able to constrain the dark energy equation of state in three or more independent redshift bins to better than 10%.

We have found that a post-calibration shift in the standard candle brightness between delayed and prompt SNe can introduce bias in the best-ﬁt dark energy parameters. By controlling the magnitude of any resulting two-population difference to better than 0.025 mag, the bias can be kept under 1-σ for a JDEM-like survey without signiﬁcantly degrading the accuracy of the dark energy measurements.

For a JDEM-like survey, we have shown that the bias in the equation of state measurement is less than a percent level (so long as all the SNe are used in the Hubble diagram).

We have discussed the lensing modiﬁcation to the CMB bispectrum and demonstrated that lensing leads to an overall decrease in the amplitude of the primary bispectrum at multipoles of interest between 100 and 2000 through additional smoothing introduced by lensing. For a high resolution experiment such as Planck, the lensing modiﬁcation to the bispectrum must be properly included when attempting to estimate the primordial non-Gaussianity. An ignorance will bias the estimate at the level of 30%. ORG S R A R D A K

dulissa.wordpress.com DSARKAR.ORG Summary We have shown that the next-generation surveys will be able to constrain the dark energy equation of state in three or more independent redshift bins to better than 10%.

For a JDEM-like survey, we have shown that the bias in the equation of state measurement is less than a percent level (so long as all the SNe are used in the Hubble diagram).

rs dA(rs r!) φ(nˆ) = 2 dr! − Φ(x(nˆ), r!) − d (r )d (r ) !0 A s A ! Lensing Power Spectrum

φ φ(nˆ) = φ Y m(nˆ) φ φ = δ δ C lm l ! lm l!m! " l,l! m,m! l !lm 2 Cφ = k2dkP (k)[Ilen(k)]2 l π Φ l !

len len Il (k) = drW (r)jl(kr) ! d (r r) W len(r) = 2F (r) A s − − dA(r)dA(rs) Uncertainty in Star Formation: Bias in “w”

Delayed Fraction Bias in “w”

D.S., A. Amblard, A. Cooray, and D. Holz; ApJL, 684, L13 (2008) Effect of Weak Lensing on Estimates of “w” 10,000 Realizations 10,000 SNe

Magnitude 2000 SNe Analysis 300 SNe

10,000 Realizations 10,000 SNe

Flux Averaging 2000 SNe Technique 300 SNe

D.S., A. Amblard, D. Holz, A. Cooray; ApJ, 678, 1 (2008) A Little Bit of History J. E. Gunn and B. M. Tinsley, Nature, 257, 454 (1975) “New data on the Hubble diagram, combined with constraints on the density of the Universe and the ages of galaxies, suggest that the most plausible cosmological models have a positive cosmological constant, are closed, too dense to make deuterium in the big bang, and will expand for ever. Possible errors in the supporting arguments are discussed.” G. Efstathiou, W. J. Sutherland, and S. J. Maddox, Nature, 348, 705 (1990) “...We argue here that the successes of the CDM theory can be retained and the new observations accommodated in a spatially ﬂat cosmology in which as much as 80% of the critical density is provided by a positive cosmological constant, which is dynamically equivalent to endowing the vacuum with a nonzero energy density. In such a universe, expansion was dominated by CDM until a recent epoch, but is now governed by the cosmological constant ...” J. P. Ostriker and P. J. Steinhardt, Nature, 377, 600 (1995) “OBSERVATIONS are providing progressively tighter constraints on cosmological models advanced to explain the formation of large-scale structure in the Universe ... The observations do not yet rule out the possibility that we live in an ever-expanding open Universe, but a Universe having the critical energy density and a large cosmological constant appears to be favoured.” J. S. Bagla, T. Padmanabhan, and J. V. Narlikar, Comments Astrophys., 18, 275 (1996) “... the conclusion today is inescapable that the standard big bang models without the cosmological constant are effectively ruled out.”