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Primordial physics from large-‐scale structure beyond the power spectrum
Roland de PutterCaltech
CosmoStat21, València – May 25, 2018
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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
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multifield inflation
Was inflation driven by a single field or by multiple fields?
ϕ
V(ϕ,χ)
χ
inflatonpotential
single-‐field inflation
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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
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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
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Current best constraints come from CMB bispectra
fNL = 0.8 +/-‐ 5.0 (68% CL)Planck 2015, paper XVII
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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
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Time
Large-‐scale structure surveys provide exciting opportunity to measure primordial non-‐Gaussianity
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ΦL
1. Primordial non-‐Gaussianity leads to scale-‐dependent halo bias
δnh> 0δnh< 0
Dalal et al 2008
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Dalal et al 2008, de Putter & Doré 2017
scale-‐dependent galaxy bias
1. Primordial non-‐Gaussianity leads to scale-‐dependent halo bias
smaller scales
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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
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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
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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
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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
=
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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
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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
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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
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“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
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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
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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!
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EUCLID
Bla Bla
WFIRST
SPHEREx (proposed)
www.nasa.gov/wfirst
spherex.caltech.edu (1412.4872)
www.euclid-‐ec.org
1. Exciting times ahead!
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• 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