• Successful determinations of the

Smithsonian Astrophysical Observatory University of Texas, Austin

Lockheed Martin

Cosmology Seminar@UIUC December 2, 2005

Eiichiro Komatsu

(University of Texas at Austin)

Cosmology - Exciting, but Embarrassing Situation

• Successful determinations of the

cosmological parameters have revealed

that we don’t understand most of the

How much we don’t know about the universe

~10^-34 sec Inflation Dark Energy I

<30,000 yrs Radiation Era Radiation

<8 billion yrs Matter Era Dark Matter

<now Dark Energy Era Dark Energy II

Log(Time)

Four Big Questions in Cosmology

• The nature of dark matter

 What are they? How many of them?

• The nature of dark energy

 What is it?

 Modification to gravity? Another form of energy?

• The origin of baryons

 Physics of Baryogenesis?

• The physics of inflation

 Did it happen at all? ^CIP

Why Inflation?

• Inflation saves the Big Bang Model

• The isotropy of the cosmic background radiation (T/T ~ 10^-5 ).

• The flatness of the universe (_ =1).

• The origin of cosmic structure.

By exponentially expanding a small region, Inflation naturally solves several problems not addressed by the Big Bang model:

Inflationary Universe

•

The expansion of the universe decelerates whe n matter or radiation dominates

•

When a certain condition between energy densit y and pressure is satisfied, the expansion will ac celerate  INFLATION

•

“A certain condition”: For p=w, w<-1/3

 Matter: w=0, Radiation: w=1/3

 What is w<-1/3?

3 ( 1 )

2

)

( t t ^w

a  ^

w<-1/3

• As the universe expands,

 Matter density (w=0) ~ a^-3

 Radiation density (w=1/3) ~ a^-4

• If w<-1/3, its energy density decreases slower than a

^-2

 E.g., for the cosmological constant (w=-1), the energy density is constant.

) 1

(

) 3

( a  a ^{  w}



A. Starobinsky (1979)

• Matter or radiation dominates  the universe will decelerate.

• In the early universe, quantum gravity effects should be important. In a nutshell,

 The Lagrangian of GR ~ R (Ricci scalar)

 When a quantum correction ~ R²/M_pl2 becomes im portant, the universe will accelerate!!

• Left-hand side of Einstein’s equation

K. Sato (1981)

•

In GUTs, a vacuum phase transition occurs at ~10¹³ TeV

 Will the phase transition affect the expansion of the unive

•

YES. If the phase transition is of the 1rse? ^st order, then t he universe will accelerate!

•

Right-hand side of Einstein’s equation

Alan Guth (1981)

• In GUTs the phase transition occurs.

• If the expansion accelerates,

 The observable universe becomes flat.

 Any anisotropy and inhomogeneity before t he acceleration will be wiped out, and the u niverse becomes homogeneous and isotro pic.

 Density of GUTs monopoles becomes exp onentially small  avoid over-closure of th e universe

• We need the accelerated expansion!!

Birth of Inflation

Observe Inflation

• Inflation generates primordial fluctuations in spacetime.

• (a) Fluctuations inherited in radiation

 Cosmic Microwave Background

 Temperature Anisotropy

 Polarization Anisotropy

• (b) Fluctuations inherited in matter

 Dark Matter Distribution (Gravitational Lensing)

 Galaxy Distribution (Redshift Surveys)

 Gas Distribution (Lyman-alpha clouds)

• (c) Fluctuations in spacetime itself

 Primordial Gravitational Waves

INFLATION

Inhomogeneous Homogeneous

x 100,000

Inside Horizon Exit Horizon

Enter Horizon Fluctuations conserved

outside the Horizon

Direct probe of physics of Inflation!!

Observe Inflation

Inside Horizon V()

V()

galac

tic size

COBE

Different wavelengths

measure different locations of V()

Need to cover a





Andrei Linde

• The number of papers whose title

contains “inflation” (as of today): 121

 New Inflation (1981, cited 1487 times)

 Chaotic Inflation (1983, cited 897 times ）

 Hybrid Inflation (1994, cited 458 times ）

• Dr. Inflationary Universe Dr. Inflationary Universe

But, which model is right?

Approaching the

Inflationary Paradigm

• ⁰

^th

order test: did inflation happen?

1. Is the observable universe flat?

2. Are fluctuations Gaussian?

3. Are fluctuations nearly scale independent?

4. Are fluctuations adiabatic?

• ¹

^st

order test: which model is right?

1. Deviation from Gaussianity?

2. Deviation from scale independence?

Deviation from adiabaticity?

Did Inflation Happen?

• ^{Flatness ( }

^tot

^{= 1): }

^tot

= 1.02 ± 0.02

• Gaussianity ( ƒ

_NL

~1): -58 < ƒ

_NL

< 134

• Scale invariance ( n

s

~1): n

s

= 0.99 ± 0.04

• Adiabaticity (  T/T=(1/3)*  ): deviation <

30%

  ^{x   }

_gaus

  ^{x   f}

_NL

^

²_gaus

  ^{x }



1 3

  k

^ns 

k

Spergel, Verde, Peiris, Komatsu et al. (2003)

Komatsu et al. (2003)

Spergel, Verde, Peiris, Komatsu et al. (2003)

Peiris, Komatsu et al. (2003)

Dev. from Scale Invariance

•

Different wave- numbers probe different parts of potential.

•

We need to cover many decades in wave-number to

determine the shape of potential

 Require a variety of probes.

P(k) to

V(phi)

The Current State-of-the-Art

V()









Toward “the” Inflation Model

• What is necessary?

 More accurate measurements of P(k)

 Not just statistical error! Minimum systematic error

 Sample more k-modes

• One solution = A galaxy survey at high-z

 Why high-z? Less non-linear power!

As the universe ages, gravitational effects distort initial power spectrum on increasingly larger scales

• At z=6, non-linear contribution at k=1 Mpc^-1 is about 15%.

High Sensitivity Calls for

Better Theory

Modeling Non-linearity:

Analytical Approach

Modeling Non-linearity:

Analytical Approach

Non-linear Bias

• The largest systematic errors will be the effect of galaxy bias on the shape of the power spectrum. If bias is linear it is easy to

correct, but it won’t be linear when the

underlying matter

clustering is non-linear.

How do we correct for

it?

Non-linear Bias: Analytical

Approach

Achieving 1% accuracy drives the observing strategy

Science Drivers:

To best constrain inflation and overlap with CMB, need adequate statistics on scales from 1 Mpc to 100 Mpc

H is an ideal line due to its strength

CIP is stationed at L2 to achieve proper passive cooling.

Neutrino Mass

•Free-streaming of non-relativistic

neutrinos suppress the amplitude of the matter power spectrum at small scales.

•The total suppression

depends only on the total neutrino mass.

•The free-

streaming scale depends on

individual

neutrinos mass.

Parameter Forecast

•CIP, in combination with the CMB data from Planck, will determine the tile and running to a few x 10^-3 level!

•The running predicted by a very simple inflationary model (a massive scalar field with self-interaction) predicts the running of (0.8-1.2) x 10^-3, which is not very far away from CIP’s sensitivity.

•More years of operation, or a larger FOV may allow us to measure the running from the simplest inflationary models.

•The limit on neutrino masses will be 20-40 times better than the current

Neutrinos don’t affect the

determination of P(k)

CIP will nail it!

V()









MESSAGE FROM CIP

• CIP will measure the inflationary parameters do wn to:

 Tilt: +- 0.0030

 Running: +- 0.0024

• As a bonus, it will lift massive degeneracies bet ween these parameters and the other inflationar y parameters constrained by CMB:

 Gravity wave amplitude

 Deviation from adiabatic fluctuations

• Hopefully, CIP, in combination with CMB experi

ments, will nail “the” inflationary model.