SLACbisp ectrum). f NL is de ned b y = g + f NL 2 g; where is the Ba rdeen p otential. Note that nongaussian ... po w er in B-mo des to the (scala r) densit y p

Inflation and the SLAC Theory Group1979{1980

I was a one-year visitor from a postdoc position at Cornell.

My research problem (working with Henry Tye back at Cornell): Why were sofew magnetic monopoles produced by the big bang?

SLAC group (with visitors):Sidney Coleman (visiting from Harvard)Lenny Susskind (recently arrived)Paul Langacker (visiting from Penn, working on GUTs review)So-Young PiErick Weinberg (visited spring term, from Columbia)Marvin WeinsteinHelen QuinnStan Brodsky: : :

Alan Guth

Massachusetts Institute of Technology

Sid Drell Symposium, January 12, 2018 {1{

Inflation and the SLAC Theory Group1979{1980

I was a one-year visitor from a postdoc position at Cornell.

My research problem (working with Henry Tye back at Cornell): Why were sofew magnetic monopoles produced by the big bang?

SLAC group (with visitors):Sidney Coleman (visiting from Harvard)Lenny Susskind (recently arrived)Paul Langacker (visiting from Penn, working on GUTs review)So-Young PiErick Weinberg (visited spring term, from Columbia)Marvin WeinsteinHelen QuinnStan Brodsky: : :

Alan Guth



Inflation as Applied Particle Theorywith General Relativity

For a scalar �eld �(x), the pressure

p = �1

2@��@

�� V (�) :

If the potential energy dominates, then p � �V (�).

Positive energy density V (�) =) negative pressure.

GR: Negative pressure =) gravitational repulsion.

New In ation

Linde, 1982

Albrecht & Steinhardt

Chaotic In ation

Linde, 1983

Alan Guth





p = �1

2@��@

�� V (�) :




New In ation

Linde, 1982


Chaotic In ation

Linde, 1983

Alan Guth





p = �1

2@��@

�� V (�) :




New In ation

Linde, 1982


Chaotic In ation

Linde, 1983

Alan Guth



Successes of Inflation

1) Horizon / Uniformity Problem: The universe appears to beuniform (to a few parts in 105) on length scales � the horizondistance of classical cosmology. With in ation, uniformity canbe established before in ation, on tiny length scales. In ationstretches these tiny length scales to cosmological proportions.

2) Flatness / Mass Density Problem:

Pre-1998: �Mass density

Critical mass density� 0:3 :

Planck 2015:

= 0:999� 0:004 (95%con�dence).

Alan Guth



Successes of Inflation

1) Horizon / Uniformity Problem: The universe appears to beuniform (to a few parts in 105) on length scales � the horizondistance of classical cosmology. With in ation, uniformity canbe established before in ation, on tiny length scales. In ationstretches these tiny length scales to cosmological proportions.

2) Flatness / Mass Density Problem:

Pre-1998: �Mass density

Critical mass density� 0:3 :

Planck 2015:

= 0:999� 0:004 (95%con�dence).

Alan Guth



3) Cosmological Density Fluctuations |A Mind-Boggling Success Story

The Time-Delay Description:

Expansion of universe is described by scale factora(t), which grows with time.

Field equation for the in aton scalar �eld:

Given one solution �0(t), the general solution is

�(~x; t) = �0

�t� Æt(~x)

�= �0(t)� _�0 Æt(~x) � �0(t) + Æ�(~x; t) :

Perturbations in rolling scalar �eld are characterized

by a time delay Æt(~x) = �Æ�(~x; t)_�0(t)

{4{






�(~x; t) = �0

�t� Æt(~x)

�= �0(t)� _�0 Æt(~x) � �0(t) + Æ�(~x; t) :



{4{






�(~x; t) = �0

�t� Æt(~x)

�= �0(t)� _�0 Æt(~x) � �0(t) + Æ�(~x; t) :



{4{






�(~x; t) = �0

�t� Æt(~x)

�= �0(t) � _�0 Æt(~x) : � �0(t) + Æ�(~x; t) :



{4{






�(~x; t) = �0

�t� Æt(~x)

�= �0(t)� _�0 Æt(~x) � �0(t) + Æ�(~x; t) :



{4{

Initial State: Bunch-Davies/Gibbons-Hawking Vacuum

Fourier expand the scalar �eld, as an operator, in terms of Fourier modeoperators ~�(~k; t):

�(~x; t) =1

(2�)3

Zd3k ei

~k�~x~�(~k; t) :

For each Fourier mode ~k, the physical wavelength is

�phys(t) = a(t)2�

j~kj:

At asymptotically early times, � is very small, the frequency is very high, andthe expansion of the universe is comparatively very slow | it looks more andmore like Minkowski space at earlier and earlier times.

The \vacuum" is the state in which each mode is in its Minkowski groundstate (i.e., harmonic oscillator ground state) as t! �1:

Alan Guth



The End of Inflation

Key properties:

1) Nearly scale invariant spectrum:V (�) and V 0(�) change very littlewhile the visible modes are gener-ated.

2) Nearly Gaussian: it's a nearly freequantum �eld theory.

3) Adiabatic(all components|photons, baryons,dark matter|are compressed by thesame factor): the uctuations aregenerated before the components aredi�erentiated.

Alan Guth



Ripples in the Cosmic Microwave Background

{7{

Spectrum of CMB Ripples

{8{

Planck 2015 TE Power Spectrum

{9{

Planck 2015 EE Power Spectrum

{10{

Gaussianity of the CMB

Nongaussianites are measured by fNL, where Planck 2015 set thebounds

f localNL = 0:8� 5:0 ;

fequil

NL = �4� 43 ;

f orthoNL = �26� 21 (68% CL statistical).

Local, equil, and ortho refer to three di�erent \shapes" for the 3-pointfunction (bispectrum). fNL is de�ned by

� = �g + fNL�2g;

where � is the Bardeen potential. Note that the nongaussian termwill be comparable to the gaussian term when fNL � 105, so the limitsimply that the CMB is VERY gaussian.

Alan Guth



B-Modes (Gravitational Waves)

Modes to describe the polarization of the CMB fall in two classes,E-modes and B-modes. The B-modes cannot be generated inlinear approximation by density perturbations.

BUT: can be generated by (nonlinear) scattering from dust.

Intensity measured by the tensor-scalar ratio r, the ratio of thepower in B-modes to the power in (scalar) density perturbations.

Currently, r < 0:7 at 95% con�dence.

The search is on! CMB Stage 4 proposes to reach a sensitiviy of0.001.

A primordial B-mode observation would pin down the energy scaleof in ation.

Alan Guth



Summary

In ation is a consequence of the dynamics of a scalar �eld. It's a very naturalconsequence of any extension of known physics to higher energies.

Successes of in ation include:

Explanation of the homogeneity of the universe.

Explanation of why the total mass density is so close to the critical value.

Gives very successful predictions for the spectrum of density perturbationsobserved in the CMB. Also predicts polarization patterns, and Gaussianity.

The sensitivity for primordial B-modes is improving dramatically. If they can befound, they will give a powerful new tool for studying the early universe.

Alan Guth



Documents

SLACbisp ectrum). f NL is de ned b y = g + f NL 2 g; where is the Ba rdeen p otential. Note that nongaussian ... po w er in B-mo des to the (scala r) densit y p