Lecture 25Problems with the Big Bang

Inflation ASTR 340

Fall 2006

Dennis Papadopoulos

The cosmic concordance

• What is our universe like?– Matter content?– Geometry (flat, spherical, hyperbolic)?– Anything else strange?

• Remarkable agreement between different experimental techniques:

“Cosmic concordance” parameters

Measurements of the matter content of the Universe (recap)

• Primordial nucleosynthesis– Theory predicts how present light element

abundances (4He, 3He, D, 7Li) depend on mean baryon density

– Observed abundances B0.04

• Galaxy/galaxy-cluster dynamics– Look at motions of stars in galaxies, or galaxies in

galaxy clusters…– Infer presence of large quantities of “dark matter”

which gravitationally affects observed objects but cannot be seen with any telescope

Nucleosynthesis

• Analysis of galaxy motions suggests a total matter density of Matter0.3

• Same conclusion from gravitational lensing by clusters (light from background objects is bent due to GR effects)

• First stunning conclusion:– Compare B0.04 and Matter0.3

– Normal matter only accounts for about 1/8 of the total matter that’s out there!

– Dark matter provides DM0.26

– We’re made of the minority stuff!

• Can be confirmed by taking an inventory of a cluster, where diffuse gas is hot and emits X-rays…– Find that about 1/8 of a

cluster’s mass is in baryons– We believe that clusters

should be representative samples of the universe…

– Confirms DM0.26

MEASURING THE GEOMETRY OF THE UNIVERSE

• Recall that universe with different curvature has different geometric properties

• Adding up the angles in a triangle,– Flat universe(k=0): angles sum to 180– Spherical universe (k=+1): angles sum to >180– Hyperbolic universe (k=-1): angles sum to <180

• Similarly, for a known length L at a given distance D, the angular size on the sky varies depending on the curvature of space– Flat universe (k=0): angular size =L/D– Spherical universe (k=+1): angular size >L/D– Hyperbolic universe (k=-1): angular size <L/D

D

L

k=0 k=+1 k=-1

L L

Angular size of fluctuations in the CBR

• Remember the cosmic microwave background…

• It has fluctuations, with average separations corresponding to a known scale L at the distance where light last interacted with matter (matter/radiation decoupling)

• Distance D to this “surface of last scattering” is also known

• Can use apparent angular separations of fluctuations compared to L/D to infer geometry of Universe

Surface of last scattering

us

D L

Flat universe!• Result:

– The universe is flat– In terms of omega curvature parameter,

k=0, i.e k=0– Recall that the sum of all three omega parameters as

measured at present time must be 1:

– How do we reconcile k=0 with our measurement of the matter density, which indicates M=0.3?

– There must be a nonzero cosmological constant, =0.7!

1M k

M 0

crit

0

(3H02 /8G)

k kc 2

R02H0

2

3H02

Non-zero • Recall that with a non-zero, positive value of

the universe expands more rapidly than it would if it contained just matter

• Are there other indications of nonzero ?• Yes, from direct measurement of “deceleration

parameter” q0

• Recall q0 = (d2R/dt2 )/(RH2) measures the rate of change of the Hubble parameter (expansion rate)

• The relation between q0 , , and M is

q0 =0.5 M

• If M =0.3 and =0.7, would expect q0 =-0.55• More generally, any negative q0 means acceleration

rather than deceleration in the cosmic expansion rate, and would imply > M /2=0.15

• Direct measurement of q0 would be able to confirm finding that is nonzero…

The accelerating Universe

• Huge clue came from observations of Type-1a Supernovae (SN1a)– Very good “standard candles”– Can use them to measure relative

distances very accurately

Type 1A Supernovae

• In the normal life of a star (main sequence)…– nuclear fusion turns

Hydrogen into Helium

• In the late stages of the life of a massive star…– Helium converted into

heavier elements (carbon, oxygen, …, iron)

– At end of star’s life, get an onion-like structure (see picture to right)

• What’s special about iron?– Iron has the most stable nucleus– Fusing hydrogen to (eventually) iron releases energy

(thus powers the star)– Further fusion of iron to give heavier elements

requires energy to be put in…– Can only happen in the energetic environment of a

supernova explosion– So, all heavier elements are created during

supernova explosions

Supernovae

• What produces a SN1a?– Start off with a binary star system– One star comes to end of its life – forms a “white

dwarf” (made of helium, or carbon/oxygen)– White Dwarf starts to pull matter off other star… this

adds to mass of white dwarf (accretion)– White dwarfs have a maximum possible mass… the

Chandrasekhar Mass (1.4 MSun)– If accretion pushes White Dwarf over the

Chandrasekhar Mass, it starts to collapse.

• White Dwarf starts to collapse…– Rapidly compresses matter in white dwarf– Initiated runaway thermonuclear reactions – star

turns to iron/nickel in few seconds– Liberated energy blows star apart– Resulting explosion briefly outshines rest of

galaxy containing it… these are the SN1a events

• SN1a– No remnant (neutron star or black hole) left– Since white dwarf always has same mass when it

explodes, these are “standard candles” (i.e. bombs with a fixed yield, hence fixed luminosity)

H0 and q0 with SN1a’s

• The program:– Search for SN1a in

distant galaxies– Compare expected

power with observed brightness to determine distance

– Measure velocity using redshift

• “Low redshift” galaxies give measurement of H0

• “High redshift” galaxies allows you to look for deceleration of universe

The results…• This program gives

accurate value for Hubble’s constant– H=72 km/s/Mpc

• Find acceleration, not deceleration, at large distance!– Very subtle, but really

is there in the data!– Profound result!

• What does the future hold? Increasingly rapid expansion!

Dark Energy

• There is an “energy” in the Universe that is making it accelerate– Call this “Dark Energy”– This makes up the rest of the gravitating energy in the

Universe, and causes it to be flat!– Completely distinct from “Dark Matter”

• Remember Einstein’s cosmological constant…?– Dark Energy has precisely the same effect as

Einstein’s cosmological constant– So, he was probably right all along!

What is “dark energy”?

• An “energy” that is an inherent component of space…

• Consider a region of vacuum– Take away all of the radiation– Take away all of the matter– What’s left? Dark energy!– But we have little idea what it is…

The Age of the Universe• Using this cosmological model, we can figure

out the age of the Universe.– Answer – 13.7 billion years

• Prediction…– There should be no object in the Universe that is

older than 14 Gyr.– This agrees with what’s seen!– This was a big problem with old cosmological

models that didn’t include dark energy:• e.g age of the universe in M =1, k =0, =0 model is 9

billion years• But there are globular star clusters whose estimated ages

are 12-14 billion years!• This was troubling since universe must be at least as old

as the oldest stars it contains!

Concordance modelIn summary, the parameters for our Universe,

using best available data…

• Hubble constant: H0=72 km/s/Mpc

• Geometry: k =0 (flat)

• Deceleration parameter: q0=0.55

• Baryon density: B=0.04

• Dark matter density: DM=0.26

• Cosmological constant: =0.7

• Age: t0=13.7 billion years

Deceleration –Acceleration

The Saga Continues

…although we are far from understanding all the properties of the Universe, recent observations are bringing us to the “era of precision cosmology!”

Observing the Big Bang for Yourself

• Olber’s Paradox• Why is the darkness of the night sky

evidence for the Big Bang?

Why is the darkness of the night sky evidence for the Big Bang?

Olbers’ Paradox

If universe were

1) infinite

2) unchanging

3) everywhere the same

Then, stars would cover the night sky

Olbers’ Paradox

If universe were

1) infinite

2) unchanging

3) everywhere the same

Then, stars would cover the night sky

Night sky is dark because the universe changes with time

As we look out in space, we can look back to a time when there were no stars

Night sky is dark because the universe changes with time

As we look out in space, we can look back to a time when there were no stars

• Why is the darkness of the night sky evidence for the Big Bang?– If the universe were eternal, unchanging,

and everywhere the same, the entire night sky would be covered with stars

– The night sky is dark because we can see back to a time when there were no stars

What aspects of the universe were originally unexplained with

the Big Bang theory?

Inflation

• What aspects of the universe were originally unexplained with the Big Bang theory?

• How does inflation explain these features?• How can we test the idea of inflation?

What is Inflation

• Power law expansion – rate of change R gets longer as the Universe expands. i.e. if R was 50% smaller 10 Gyars ago it will be a factor of 2 bigger 30 Gyears later

• Rate of change of R constant – expansion exponential- Universe could expand by a factor of 1050 in a fe10-30 seconds

• In GR rate of expansion(doubling time~1/

Mysteries Needing Explanation

1) Where does structure come from?

2) Why is the overall distribution of matter so uniform?

3) Why is the density of the universe so close to the critical density?

Mysteries Needing Explanation

1) Where does structure come from?

2) Why is the overall distribution of matter so uniform?

3) Why is the density of the universe so close to the critical density?

An early episode of rapid inflation can solve all three mysteries!

How does inflation explain these features?

1 meter

Inflation can make all the structure by stretching tiny quantum ripples to enormous size

These ripples in density then become the seeds for all structures

How can microwave temperature be nearly identical on opposite sides of the sky?

Regions now on opposite sides of the sky were close together before inflation pushed them far apart

Overall geometry of the universe is closely related to total density of matter & energy

Density = Critical

Density > Critical

Density < Critical

Inflation of universe flattens overall geometry like the inflation of a balloon, causing overall density of matter plus energy to be very close to critical density

How can we test the idea of inflation?

Patterns of structure observed by WMAP show us the “seeds” of universe

Observed patterns of structure in universe agree (so far) with the “seeds” that inflation would produce

“Seeds” Inferred from CMB

• Overall geometry is flat – Total mass+energy has critical density

• Ordinary matter ~ 4.4% of total• Total matter is ~ 27% of total

– Dark matter is ~ 23% of total– Dark energy is ~ 73% of total

• Age of 13.7 billion years

“Seeds” Inferred from CMB

• Overall geometry is flat – Total mass+energy has critical density

• Ordinary matter ~ 4.4% of total• Total matter is ~ 27% of total

– Dark matter is ~ 23% of total– Dark energy is ~ 73% of total

• Age of 13.7 billion years

In excellent agreement with observations of present-day universe and models involving inflation and WIMPs!

What have we learned?

• What aspects of the universe were originally unexplained with the Big Bang theory?– The origin of structure, the smoothness of the

universe on large scales, the nearly critical density of the universe

• How does inflation explain these features?– Structure comes from inflated quantum ripples– Observable universe became smooth before

inflation, when it was very tiny– Inflation flattened the curvature of space, bringing

expansion rate into balance with the overall density of mass-energy

What have we learned?

• How can we test the idea of inflation?– We can compare the structures we see in

detailed observations of the microwave background with predictions for the “seeds” that should have been planted by inflation

– So far, our observations of the universe agree well with models in which inflation planted the “seeds”