Primordial  physics  from  large-­‐scale  structure  beyond  the  power  spectrum

Roland de  PutterCaltech

CosmoStat21,  València – May  25,  2018

Time

• understand  initial  conditions  of  Universe• probe  particle  physics  beyond  the  standard  model  at  extremely  high  energies

What  is  the  physics  behind  inflation?Motivation:

E  ~  1015 GeV (?)cf.  LHC:  ~  103 GeV

inflation

multifield inflation

Was  inflation  driven  by  a  single  field  or  by  multiple  fields?

ϕ

V(ϕ,χ)

χ

inflatonpotential

single-­‐field  inflation

Local  non-­‐Gaussianitymodulation  of  small-­‐scale  perturbations  by  long  mode,  “mode  coupling”

δS δS

long-­‐wavelength  curvature/metric  perturbation  

local  short-­‐wavelength  fluctuations

ΦL

~    fNL

multifield inflation

ϕ

V(ϕ,χ)

χ

inflatonpotential

single-­‐field  inflation

fNL =  0 (*) fNL non-­‐zero

Local  non-­‐Gaussianity distinguishes  between  single-­‐ and  multifield

Maldacena 2003

Current  best  constraints  come  from  CMB  bispectra

fNL =  0.8  +/-­‐ 5.0  (68%  CL)Planck  2015,  paper  XVII

If  primordial  perturbations  generated  by  second  field,  expect  |fNL|~  1de  Putter,  Gleyzes,  Doré 2017

Results  based  on  MCMC  runs  with  current  CMB  temperature  and  polarization  power  spectra  (Planck  2015)  

TARGETPRECISION:σ(fNL)  <  1

Time

Large-­‐scale  structure  surveys  provide  exciting  opportunity  to  measure  primordial  non-­‐Gaussianity

ΦL

1.  Primordial  non-­‐Gaussianity leads  to  scale-­‐dependent  halo  bias

δnh>  0δnh<  0

Dalal et  al  2008

Dalal et  al  2008,  de  Putter  &  Doré 2017

scale-­‐dependent  galaxy  bias

1.  Primordial  non-­‐Gaussianity leads  to  scale-­‐dependent  halo  bias

smaller  scales

2.  Primordial  non-­‐Gaussianity is  imprinted  on  higher  order  statistics

δ(kL)

Region  A  (overdense) Region  B  (underdense)

PA(kS)                          >                      PB(kS)local  power  spectrum  of  short  modes

modulated  by  long  mode

Correlations  of  the  position-­‐dependent  power  spectrum  constrain  fNL

BISPECTRUM(squeezed)  

δP(kS;kL ) δ(−kL )pos-­‐depP(kS)

x overdensity

=long  modeshort  mode

PA(kS) PB(kS) δ(kL)

Region  A  (overdense) Region  B  (underdense)

Chiang  et  al  2014,  Dai,  Pajer &  Schmidt  2015,  Chiang  2017,  de  Putter  2018

Position-­‐dependent  power  spectrum  approach  equivalent  to  bispectrum and  trispectrum

BISPECTRUM(squeezed)  

δP(kS;kL ) δ(−kL )

δP(kS;kL ) δP(k 'S;−kL )

pos-­‐depP(kS)

x overdensity

long  modeshort  mode

=pos-­‐depP(kS)

pos-­‐depP(kS’)

x TRISPECTRUM(collapsed)  

=

Chiang  et  al  2014,  Dai,  Pajer &  Schmidt  2015,  Chiang  2017,  de  Putter  2018

BISPECTRUM(squeezed)  

δP(kS;kL ) δ(−kL )pos-­‐depP(kS)

x overdensity

long  modeshort  mode

ANALYSIS/FORECASTS  HARD

Bispectrum analysis  challenging  because  of  large  number  of  (correlated)  triangles

=

δP(kS;kL ) δ(−kL )pos-­‐depP(kS)

x overdensity

long  modeshort  mode

ANALYSIS/FORECASTS  EASIER

de  Putter  2018

δ lnP(kS;kL ) = b δ(kL )+ε

Position-­‐dependent  power  spectrum  approach  allows  for  quick,  analytic  computation  of  complicated    higher-­‐order  statistics

PA(kS) PB(kS) δ(kL)

δ lnP(kS;kL ) = b δ(kL )+ε

modulation  contains  primordial  mode-­‐coupling  (signal!)  and  mode-­‐coupling  from  non-­‐lin evolution  (CV  noise)

stoch. noise due  to  finite  number  of  short  modes

The  position-­‐dependent  power  spectra  are  biased  tracers  of  the  matter  density

de  Putter  2018

Non-­‐Gaussian  covariance  between  triangles  is  important,  but  ameliorated  by “cosmic  variance  cancellation”

includes  correlations  between  triangles

“medium-­‐volume”  surveyV  =  100  (h-­‐1 Gpc)3 at  z  =  1

matter  case

smaller  scales

δ lnP(kS;kL ) = b δ(kL )+ε

modulation  contains  primordial  mode-­‐coupling  (signal!)  and  mode-­‐coupling  from  non-­‐linevolution  (CV  noise)

stoch. noisedue  to  finite  number  of  

short  modes

de  Putter  2018

“medium-­‐volume”  surveyV  =  100  (h-­‐1 Gpc)3 at  z  =  1

matter  case

The  trispectrum adds  information  

smaller  scales

δ lnP(kS;kL ) = b δ(kL )+ε

modulation  contains  primordial  mode-­‐coupling  (signal!)  and  mode-­‐coupling  from  non-­‐linevolution  (CV  noise)

stoch. noisedue  to  finite  number  of  

short  modes

Going  from  matter  to  galaxy/halo  higher  order  statistics

“medium-­‐volume”  surveyV  =  100  (h-­‐1 Gpc)3 at  z  =  1

galaxy/halo  case

smaller  scales

Halo  bispectrum&  trispectrum:    signal  from  scale-­‐dependent  bias  andfrom  explicit  primordial  mode-­‐coupling

How  to  probe  primordial  non-­‐Gaussianity

• Position-­‐dependent  power  spectrum  approach  allows  for  quick,  analytic  results,  useful  for  trade  studies  and  survey  optimization

• Both  probes  require  large-­‐volume  surveys

• Bispectrum requires  small  scales,  i.e.  high  accuracy  redshifts

• Galaxy  power  spectrum  and  bispectrumare  strong,  complementary  probes,  with  different  systematics!

EUCLID

Bla Bla

WFIRST

SPHEREx (proposed)

www.nasa.gov/wfirst

spherex.caltech.edu (1412.4872)

www.euclid-­‐ec.org

1.  Exciting  times  ahead!

• Nature  of  inflation  is  a  big  fundamental  physics  mystery,  that  can  be  addressed  with  cosmological  large-­‐scale  structure  data.

• Using  scale-­‐dependent  bias  and  explicit  mode-­‐coupling,  the  galaxy  power  spectrum,  bispectrum and  trispectrum are  complementary  probes  of  inflation.

Summary

• Future  data  (from  e.g.  SPHEREx)  may  answer  whether  inflation  driven  by  a  single,  or  multiple  fields