Martin Bojowald- What happened before the big bang?

What happened before the big bang?

Martin Bojowald

The Pennsylvania State University

Institute for Gravitation and the Cosmos

University Park, PA

Before the big bang – p.1

Cosmic Expansion

1925–1929, Edwin Hubble:Precise distance measurement ofextra-galactic nebulae.

Escape velocity proportional to distance.

Space is expanding.

1915, General relativity: space dynamical, physical object;not absolute.

Galaxies appear to have come from dense, pointlike event.Simple explanation of the beginning of the universe?


Big bang model

1948, George Gamow, Ralph Alpher, Robert Herman:Dense, hot phase should be visible thanks to remnant radiation.

Current temperature predicted to be less than 5K (-268 ◦C).

1968, Penzias and Wilson: First (unintended) measurement ofthe predicted radiation, temperature: 2.7K.

1991: The satellite COBE showsisotropy of the radiation.(2006 Nobel Prize)

Now measured very precisely:WMAP, and soon Planck.


Symmetry

Detailed description of the whole universe seems hopeless.Possible only thanks to high degree of symmetry:Homogeneity and isotropy as shown by COBE.


Symmetry

Detailed description of the whole universe seems hopeless.Possible only thanks to high degree of symmetry:Homogeneity and isotropy as shown by COBE.

Time

Symmetry simplifies things, but often makes them lessinteresting.


visualization: David W. Hogg (NYU)with help from Blanton, Finkbeiner,

Padmanabhan, Schlegel, Wherry

data: Sloan Digital Sky Surveyand the Bright Star Catalog

Homogeneous, isotropic universe

For a homogeneous and isotropic universe, only size matters.Changes according to Friedmann equation:

a

t

(

∆a

∆t

)2

−

8πG

3

M

a= 0

Size a of the universe, mass M (excluding radiation), Newton’sconstant G for gravity. Kinetic and potential energies balanced.


Formation of structure

Falling temperature in an expanding universe:

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T

CMB released

ionizationenergy of H

thydrogen clouds seed galaxies

Initial phase not directly visible, but influences later stages.Before the big bang – p.7

Cosmic microwave background

Hot primordial plasma scatters electromagnetic radiation.

Radiation released about 400 000 years after densest moment.

WMAP

Nearly homogeneous (∼ 10−5). Overall picture consistent,very successful regarding many observations.


Weight problem

Different types of observations all in agreement, especially of→ Cosmic microwave background,→ Galaxy distribution,→ Supernovae redshifts.

Results in universe decomposition:→ 5% atoms (visible when hot)→ 23% Dark Matter (inferred from galaxy rotation curves)→ 72% Dark Energy (according to supernovae)

Origin of Dark Matter and Dark Energy unclear, but would beimportant to determine the future evolution of the universe.


The past

Friedmann equation:a

t

(

∆a

∆t

)2

−

8πG

3

M

a= 0

size a, mass M , Newton’s constant G

Vanishing extension some time ago. Whole universe collapsed,density infinite. Mathematical equations break down. Singularity.

Not just for this matter model, but generally (Hawking, Penrose).Before the big bang – p.10

What’s missing?

The singularity is a limit of the theory, and does not mean a limitof the world or its beginning.

Current theories must be improved.

Space is a physical object.

All physics is quantum,except general relativity.

Extend quantum mechanics to apply to space, too.

Combination with general relativity: quantum gravity.


Wave function

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Time

Quantum physics describes particles by wave functions, not aspointlike. Consequences:→ Properties (such as position) indistinct, spread-out.→ Quantum fluctuations.→ Many different ways for change, compared to simple motion

of a point. New forces.Before the big bang – p.12

Quantum fluctuations

For as its belt sparkled and glittered now in one partand now in another, and what was light one instant, atanother time was dark, so the figure itself fluctuated inits distinctness: being now a thing with one arm, nowwith one leg, now with twenty legs, now a pair of legswithout a head, now a head without a body: of whichdissolving parts, no outline would be visible in thedense gloom wherein they melted away. And in the verywonder of this, it would be itself again; distinct and clearas ever.

CHARLES DICKENS: A CHRISTMAS CAROL

Difficult to apply to a universe.


Discreteness

More indirect consequence of quantum mechanics:Quantum jumps, discreteness, atoms.

Important even for macroscopic behavior: Stability and structureof atoms, molecules, . . .

e

p


Atoms

1905, Albert Einstein: Analysis of Brownian motion asconvincing evidence for atoms.

Thomas Steiner


Atoms

1905, Albert Einstein: Analysis of Brownian motion asconvincing evidence for atoms.

Thomas Steiner

1955, Erwin Müller: First direct image of atoms using field ionmicroscopy.


Atoms of space?

Planck scale: gravitational constant G, speed of light c andPlanck’s constant ~ combine to

ℓP =√

G~/c3 ∼ 10−35m

Currently, smallest scale probed at particle accelerators:∼ 10−18m.

Planck density: a trillion suns compressed to the size of aproton.

No direct observation anytime soon.

Indirect observations require good theoretical understanding.

Even theory not complete, and different approaches exist.Before the big bang – p.16

Quantum gravity

Approaches:→ String theory describes

quantum excitations ofwaves on space-time,unification of forces.

→ Loop quantum gravityconstructs space fromatoms.

0

2

4

V

1

hVolume ladderBefore the big bang – p.17

Operators

Quantum mechanics:Possible energies of atoms discrete.

Discrete angular momentum (and spin)important for energy levels and transitions.

Molecules:many electrons/nuclei combined.

Quantum gravity:Volume is the crucial quantity (e.g. of the whole universe),becomes discrete.

Elementary variables mathematically behave like angularmomentum attached to all points in space.

Loop quantum gravity. −→ Space as a giant molecule.


Chainmail


Expand


Bounce

Discrete space provides limited energy storage.

Density remains finite:bounded by Planck density of about a trillionsolar masses in the size of a single proton.

No complete collapse, no singularity.The story continues.

C+ψn+1 + C0ψn + C−ψn−1 = H(n)ψn


Bounce


Cyclic universe

1930’s Richard Tolman postulates and analyzes cyclic universemodels.

1940’s–1960’s Alpher, Herman; Penzias, Wilson: Big bangmodel established.

1979 Novello, Salím; Melnikov, Orlov:First mechanisms for a bounce.

Since 1996, Durrer, Laukenmann; Peter, Pinto-Neto, . . . :cosmological consequences.

Since 2000: Loop quantum cosmology;

and Steinhardt, Turok, . . . : cyclic models in string theory.


Some open questions

Second law of thermodynamics: Entropy/disorder must increase.Why is there any order if this has been going on for infinite time?

Big bang: Quantum physics important even for space. Have tobring in fluctuations, . . .Can this help to establish order?

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Time


Observations?

Direct glance at big bang or at spatial atoms quite impossible,but indirect test possibilities exist.

Like a crystal, granular structure of space-time causes tinyvariations in propagation of waves, diffraction.May be magnified by long cosmic expansion.

Planck

LISA


References

Follow the Bouncing Universe, Scientific American, October2008

Once Before Time, Knopf Publishers, November 2010


Documents

Martin Bojowald- What happened before the big bang?