the nuts and bolts of inflation richard barrett. dark energy seminarglasgow 29/11/2003 inflation...

The Nuts and Bolts of Inflation

Richard Barrett

Dark Energy Seminar Glasgow 29/11/2003

Inflation

• What is inflation? What is dark energy?

• Why was inflation ‘invented’?

• Some basic gravity physics

• The physics of inflation

• Sources of dark energy

• Branes and inflation


Inflation

Inflation is

• Any time when expansion of universe accelerates

• Originally meant inflation in the very early universe but now applies also to current inflationary epoch

• Both caused by same thing (scalar fields)

• The scalar field causing inflation now is called dark energy (because no-one’s seen it)


Inflation

Why was inflation ‘invented’?

• The horizon problem

• The flatness problem

Inflation invented by Alan Guth in 1981 to solve some serious problems with ‘standard’ cosmology:

Now known to be important at the present epoch

Happens in the very early universe


Inflation

How do we explain the isotropy of the CMBR, when opposite sides of the sky were ‘causally disconnected’ when the CMBR photons were emitted?

The horizon problem

From Guth (1997)

CMBR

Big Bang

time

space

Our world line

Now

A B

Our past light cone


Inflation

The flatness problem

In ‘standard’ cosmology:

• =1 means universe is flat• If 1, moves quickly away from 1 after big bang• Today universe is close to flat


Inflation

Present day ‘closeness’ of matter density to the critical density appears to require an incredible degree of ‘fine tuning’ in the very early universe.

This is the FLATNESS PROBLEM

Solution (first proposed by Alan Guth in 1981) is…

INFLATIONINFLATION

…a period of accelerated expansion in the very early universe.

Small, causallyconnected region

Limit of observable Universe today

INFLATION

Inflationary solution to the Horizon Problem

From Guth (1997)

Inflationary solution to the Flatness Problem

From Guth (1997)


Inflation

Basic gravity physics: matter and gravity

• No ‘force field’ for gravity: matter falls freely through (curved) spacetime

• BUT: matter generates the curvature

• ‘Normal’ matter always makes curvature that causes two objects to move towards each other

gravity is always attractive


Inflation

More mass (density) = more spacetime curvature:

Black holeThe sun Neutron starFlat space


Inflation

More curvature means stronger attraction:


Inflation

Basic gravity physics: the EP

• All matter moves in the same way under gravity (because gravity is just the shape of spacetime)

• So, if some matter generates gravity, all other matter feels it

The Equivalence Principle (EP) says


Inflation

Basic gravity physics: pressure

• ‘Normal’ cosmic matter is a gas with pressure (just like air pressure on earth): the gas pushes on itself

• Only pressure gradients give a net force on gas


Inflation

Gas elements

No net force Net force =

Forces

Pressure

Position Position


Inflation


• In a homogeneous universe pressure is the same everywhere

pressure doesn’t push matter at all

Can’t make matter expand using pressure


Inflation

• Pressure = Energy

• Energy = Mass (E = mc2 )

• Mass generates gravity that’s attractive

• So: pressure makes matter attract itself


Does pressure have any effect?

High pressure slows the expansion of the universe


Inflation

• Gas particles move (they have momentum)• Momentum transferred to walls gives force• BUT: Moving particles have kinetic energy too (E = 1/2 mv2)• Also works for photons, by special relativity (E = cp)


Inflation

Inflating the universe

• What if we could make matter (‘gas’) with negative pressure?

• Would generate gravity that’s repulsive

• Universe would expand even faster

INFLATION


Inflation

Inflating the universe

• Not possible with ‘normal’ matter

• Need something a bit exotic

A SCALAR FIELD

(Physically scalar field isn’t really like a gas, it only makes curvature in the same way as a gas, but like a gas with negative pressure would)


Inflation

The physics of inflation

• ‘Field’ means something that is distributed smoothly through space (like electric field), rather than made of particles

• ‘Scalar’ just means the value of the field at any point is just a number (in contrast, the electric field is like an arrow at each point)

• Call this value . can vary from place to place and from time to time: = (x,t)


Inflation


How does a scalar field generate curvature (gravity)?

• All matter generates gravity through its stress-energy tensor Tab

• Einstein’s equations are Gab = 8Tab (CURVATURE = MATTER DENSITY)

• Tab has the same form for gases and scalar fields

• Scalar fields are only like gases in terms of their gravity


Inflation

Scalar field: Tab = a b - [a a/2 + V()]gab

Normal gas: Tab = (+p)uaub + pgab

Energy part Pressure part

• The important bit is V(), the scalar potential. Its value at any point just depends on

• It does exactly what pressure p does for gases

• For gases p must be positive, BUT: V() can have any value at all

• We get negative pressures with the right V()


Inflation


To get inflation we need V() to be large.

How can this happen?

• Spontaneous Symmetry Breaking (in the very early universe)

• Scalar fields (dilatons) predicted by string theory can have inflationary potentials


Inflation

Spontaneous Symmetry Breaking• At high energies (early universe) laws of physics have

high symmetry

• At lower energies the preferred state has less symmetry

• Some scalar field that previously was at the minimum of V() is now not at the minimum

• The scalar field has vacuum energy, V() > 0

moves to the new minimum and symmetry is broken

• This is a phase transition

• Inflation occurs


Inflation

Spontaneous Symmetry Breaking

Original inflation Slow-roll inflation

• V() has a minimum at = 0 before SSB

• V() has a minimum at > 0 after SSB

quantum tunnels from 0 to the new minimum


Inflation

The cosmological constant

• Original explanation of inflation was in term of the cosmological constant

• This is just like a scalar field = that is constant everywhere at all times

• Gives pressure p = -


Inflation

Sources of dark energy

• Observational evidence (SNIa, CMBR, SDSS,) provides a consistent picture: the expansion is accelerating

• We must have a scalar field in action

• This is the mysterious dark energy

• Where does it come from?


Inflation

Sources of dark energy

• Spontaneous symmetry breaking phase transition (like in the early universe)?

• String theory: all predict a scalar field (the dilaton) in the ‘low-energy limit’ that could act as an inflaton

• Branes: string theory also suggests that our universe is a brane in a higher dimensional space, and that a scalar field that could cause inflation


Inflation

Branes and inflation

• String theories predict universe actually has 4 space dimensions

• Our universe is a 3D brane moving in this 4D ‘bulk’ (a 3D sheet floating in 4D space)

• Gravity propagates in the bulk (4D), other forces only on the brane

• The inflaton scalar field comes from the part of gravity propagating through the bulk


Inflation

A brane is ‘soliton’ (a stable solution of the string theory equationswhere matter and the nongravitational fields are nonzero only in a very thin layer)

All the physics that we are familiar with happens on this brane


Inflation


In one string theory the universe is a 4D bulk with a 3D brane at each end:

• One brane is the real universe, the other a ‘mirror world’

• We are aware of the mirror world only through its gravity

• This gravity looks like a scalar field to us• The two branes can get closer together (and

even cross over)• This gives rise to the cyclic model of Steinhardt

and Turok


Inflation


Brane cosmology simulation

the nuts and bolts of inflation richard barrett. dark energy seminarglasgow 29/11/2003 inflation...

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