cosmic variance from mode coupling - umich.edu · cosmic variance from mode coupling ... bramante,...

Cosmic Variance from Mode Coupling

Sarah ShanderaPenn State University

Shandera, CAP, 23 Sept 2013

L

Us

Nelson, Shandera, 1212.4550 (PRL);LoVerde, Nelson, Shandera, 1303.3549 (JCAP);Bramante, Kumar, Nelson, Shandera, 1307.5083;

Work in progress (S. Watson; Sohyun Park)

Linde, Muhkanov; Salopek, Bond; Mollerach et al; Boubekeur, Lyth; Byrnes et al;papers related to anomaly...

today: Peloso, Khoury, LoVerde

Monday, September 23, 2013


The Plan

• Cosmic Variance from a generalized local ansatz

• Big Picture implications for inflation theory (important if we want to push observers/data analysis)



gNL = 105

Cosmic Variance and the local ansatz:

LoVerde, Nelson, Shandera, 1303.3549 (JCAP);Nelson, Shandera, 1212.4550 (PRL);



gNL = 105

Cosmic Variance and the local ansatz:

LoVerde, Nelson, Shandera, 1303.3549 (JCAP);Nelson, Shandera, 1212.4550 (PRL);

f(ψG)→ φG + fNL(B, f̃NL, g̃NL, . . . )φ2G + gNL(B, f̃NL, g̃NL, . . . )φ3

G + . . .



Re-interpreting Planck results




No detection of local NG means cosmic variance may not be too large

(whew!)




No detection of local NG means cosmic variance may not be too large

(whew!)

Planck says NG is small? Or, universe is very big?



Beyond the local ansatz:

Consider a simple scale dependence:

ζ(x) = φG(x) + σG(x) +35fNL � [σG(x)2 − �σG(x)2�]

+925

gNL � σG(x)3 + ...

Bramante, Kumar, Nelson, Shandera, 1307.5083;

fNL(k) = fNL(kp)�

k

kp

�nf


I. Consequences for the power spectrum



Subsampling the generalized local ansatz

P obsζ (k) = Pζ(k)

�1 +

125

fNL(k)σGl + 35f2

NL(k)(σ2Gl − �σ2

Gl�)1 + 36

25f2NL(k)�σ2

G(k)�

�,

Shift to observed spectral index




More simply

Different short wavelength modes couple with different strengths to the (locally constant) background:

Locally observed spectral index is biased in subvolumes

SL

Us



The spectral index


(solid lines show 0.5 sigma fluctuations)



The spectral index, cont’d




Model Building Consequences




How to rule cosmic variance of spectral index out .....




......of observational relevance:





Observationally rule out any significant blue tilt in f local

NL




Importance of smaller scale probes.


Observationally rule out any significant blue tilt in f local

NL



Generalizations

ζk = σG,k +�

L−1

d3p1

(2π)3d3p2

(2π)3(2π)3δ3(p1 + p2 − k)F (p1, p2, k)σG,p1σG,p2 + ...,

Effect of a general bispectrum on the power spectrum:



Generalizations

ζk = σG,k +�

L−1

d3p1

(2π)3d3p2



Equilateral bispectrum has no effectBispectrum can weight IR modes differently



Generalizations

If tensor modes have an independent clock: same story (eg, non Bunch Davies)

ζk = σG,k +�

L−1

d3p1

(2π)3d3p2



Equilateral bispectrum has no effectBispectrum can weight IR modes differently


II. Consequences for the bispectrum and

beyond



Scale-dependence in the bispectrum

ξs,m(k) = ξs,m(kp)�

k

kp

�n(s),(m)f

Ratio of contributions of each field

Self-interactions of one field

BΦ(k1,k2,k3) = ξs(k3)ξm(k1)ξm(k2)PΦ(k1)PΦ(k2) + 5 perm .



But...

nsq. ≡d lnBζ(kL, kS , kS)

d ln kL− (ns − 1)



But...



Just from shift to power spectrum:



But...




∆nsq.(k) ≡ nobssq. (k)− nLargeVol.

sq. (k)

≈ −65fNL(kL)σGl nf

1 + 65fNL(kL)σGl



But...




Allowing gNL(k) adds another shift

∆nsq.(k) ≡ nobssq. (k)− nLargeVol.

sq. (k)

≈ −65fNL(kL)σGl nf

1 + 65fNL(kL)σGl



Scaling Patterns



Scaling Patterns

Mn,R =�δn

R�c

�δ2R�n/2

c



Scaling Patterns

Self-interactions; eg, local ansatz

Mn,R =�δn

R�c

�δ2R�n/2

c



Scaling Patterns


Hierarchical M(h)n = n! 2

n−3

�M(h)

36

�n−2

Mn,R =�δn

R�c

�δ2R�n/2

c



Scaling Patterns



n−3

�M(h)

36

�n−2

Mn,R =�δn

R�c

�δ2R�n/2

c

∝ fNLP1/2ζ



Scaling Patterns

Extra source, eg, gauge field

(Barnaby, Shandera; 1109.2985)


δA


n−3

�M(h)

36

�n−2

Mn,R =�δn

R�c

�δ2R�n/2

c

∝ fNLP1/2ζ



Scaling Patterns

Extra source, eg, gauge field

(Barnaby, Shandera; 1109.2985)


δA

Feeder M(f)n = (n− 1)! 2n−1

�M(f)

38

�n/3


n−3

�M(h)

36

�n−2

Mn,R =�δn

R�c

�δ2R�n/2

c

∝ fNLP1/2ζ



Hybrid

(Quasi-single field)

M(h)n ∝ (A)n (B)n−2

Scaling Patterns, cont’d

(Chen, Wang)



Cosmic Variance and scaling patterns?

Φ(�x) = φ(�x) + ψG(�x) + f̃NL

�ψG(�x)2 − �ψG(�x)2�

�0

Gives `feeder’ scaling non-Gaussianity

But: in biased subvolumes, back to hierarchical



Cosmic Variance and scaling patterns?

Φ(�x) = φ(�x) + ψG(�x) + f̃NL

�ψG(�x)2 − �ψG(�x)2�

�0

Gives `feeder’ scaling non-Gaussianity

But: in biased subvolumes, back to hierarchical

Biased subvolumes: Generate whole local ansatz series, with bias B controlling size of terms

Φ(�x) = φ(�x) + f̃NLψG(�x)p + . . .


Implications for Inflation Theory



Power spectrum:

Inflation

Spectrum of scale-invariant, adiabatic, super horizon modes as “initial conditions”



Power spectrum:

Inflation


Bispectrum, trispectrum, etc?



Power spectrum:

Inflation


Bispectrum, trispectrum, etc? Mathematically independent....



Power spectrum:

Inflation


Bispectrum, trispectrum, etc? Mathematically independent....

....up to relationships of the type τNL ≥ (6/5fNL)2

(Smith, LoVerde, Zaldarriaga)



Power spectrum:

Inflation


Bispectrum, trispectrum, etc?

Perturbation theory that obeys usual (effective) field theory notions: patterns

Non-zero NG, but no patterns in shape or size

Mathematically independent....

....up to relationships of the type τNL ≥ (6/5fNL)2

(Smith, LoVerde, Zaldarriaga)



Mode Coupling Cosmic Var:



Mode Coupling Cosmic Var:Derivations didn’t depend on where you got the fluctuations:




Good: can we find a “natural” pattern inflation does not predict? (If not, is that bad for inflation?)





Bad: a random pattern in a big universe may not look random to local observers



A familiar aspect of inflation, dressed up in different clothes: IC problem for our observable 60 e-folds region



Bad: a random pattern in a big universe may not look random to local observers



What about describing only our Hubble patch?

• Apply cosmological principle

• eg, 60 e-folds + non-Bunch Davies is fine tuned.

S =�

d4x√−gL(Xi,φi, A

µj , . . . )Local:



What about describing only our Hubble patch?

• Apply cosmological principle

• eg, 60 e-folds + non-Bunch Davies is fine tuned.

With local type mode-coupling, this line is blurred: observer’s version of the landscape needed

S =�

d4x√−gL(Xi,φi, A

µj , . . . )Local:



More work:



Easy to apply this to other models to check what level of confusion can occur (quasi-single field in progress)

More work:



Easy to apply this to other models to check what level of confusion can occur (quasi-single field in progress)

More work:

Is there a useful notion of landscape and measure here? (not quite ‘theory space’? Quantifiable route!)


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