Nishant Agarwal PROBING THE INITIAL CONDITIONS OF THE

32 Pages·2013·1.1 MB·English

P
ROBING THE INITIAL CONDITIONS
U LSS
OF THE NIVERSE USING

Nishant Agarwal

McWilliams Center for Cosmology
Carnegie Mellon University
Cosmology After Planck Workshop, Michigan, September 25, 2013
• What is the initial state of the fluctuations
generated during inflation?

• Can we observe the effects of general initial
states in the CMB and large scale structure?
N. Agarwal, R. Holman, A. J. Tolley, and J. Lin, JHEP 2013
N. Agarwal, R. Holman, and A. J. Tolley, IJMPD 2013
N. Agarwal, S. Ho, A. D. Myers, et al, arXiv:1309.2954
N. Agarwal, S. Ho, and S. Shandera, In preparation
S. Ho, N. Agarwal, A. D. Myers, et al, In preparation
• Introduction
• General initial states
Introduction
• Large scale structure
• Conclusions
-
• Introduction
• General initial states
Introduction
• Large scale structure
• Conclusions
• The primary means of learning the physics of
inflation is through the statistics of the curvature
perturbation, –
𝜁

2𝜁(𝑡,𝑥⃗) 2
𝑖𝑖 𝑖𝑖
𝑔 (𝑡, 𝑥⃗) = 𝑒 𝑎 𝑡 𝛿
• Introduction
• General initial states
Introduction
• Large scale structure
• Conclusions
Inflaton fluctuations,

Curvature perturbation𝛿s𝛿,
Transfer functions, Growth function
𝜁

CMB matter
𝛿𝑇 𝛿𝜌
Planck SDSS
• Introduction
• General initial states
Introduction
• Large scale structure
• Conclusions
Statistics of

• Gaussian perturbations
𝜁
(2-point function)

𝑥 𝑦
– Power spectrum

• Non-Gaussian perturbations
𝜁 𝑥⃗ 𝜁 𝑦⃗ (𝑡)
( -point functions 𝑧

– Bispectrum
𝑛 )

𝑥 𝑦
𝜁 𝑥⃗ 𝜁 𝑦⃗ 𝜁 𝑧⃗ (𝑡)
• Introduction
• General initial states
Introduction
• Large scale structure
• Conclusions
• -point functions of will leave observable
effects in the CMB and in LSS
𝑛 𝜁
• Introduction
• General initial states
Introduction
• Large scale structure
• Conclusions
• -point functions of will leave observable
effects in the CMB and in LSS
𝑛 𝜁

• How do general initial states for the
perturbations affect the -point functions of ?

𝑛 𝜁
• Do the modified -point functions of leave
distinct signatures in the CMB and LSS?
𝑛 𝜁
• Introduction
• General initial states
General initial states
• Non-Gaussianity
• Halo bias
• Time dependent expectation values of operators
– In-in formalism
(J. S. Schwinger 1961; L. Keldysh 1964)

• For BD initial states,
• For general initial states, is quadratic at
0
𝜌 𝑡 = 1
lowest order (no initial state non-Gaussianity)
0
𝜌 𝑡
• Introduction
• General initial states
General initial states
• Large scale structure
• Conclusions
• We can write the following generating
functional for the correlation functions