Repulsive Gravity & the Cosmological Constant
Outline

Observational Evidence

repulsive gravity in General Relativity

Inflation
Observational Evidence for Accelerating Expansion

Hubble showed that the Universe is expanding

But, is it speeding up or slowing down?

normal matter + gravity should make it slow down

but how do we know for sure?

improved "Hubble Diagram"

here's Hubble's original:

xaxis is distance, yaxis is velocity

How to do a better job

get a more accurate distance indicator

which can be seen at very large distances

Supernovae of type Ia

these are white dwarfs in binary systems which accrete mass
from their partner

when M grows to ~ M_{ch}= 1.4M_{sun}, the
carbonoxygen white dwarf has a spectacular nuclear explosion that totally
disrupts the star

probably always happens at the same mass

no outer layers to make things messy

the core collapse Supernovae (type II) are messy because
of the outer layers of the massive star

making a Hubble diagram:

1st, find some supernovae at high redshift (here's
an example from HST )

(note: HST is not actually used for a SN search  discoveries
come from the ground)

confirm that the supernovae are of type Ia with a spectrum
(usually with the Keck 10m telescope)

use that same spectrum to measure the redshift

measure the brightness of the supernova as it brightens and
then fades and compare to nearby supernovae like this one:

Here are some SN brightness measurements. The curves are
the best fit SN light curve as determined from nearby supernovae

Now determine the distance to the SN using
or

Plot d vs. v to get a Hubble diagram

here's one from the Highz Supernovae Search Team:

The "distance modulus" plotted on the yaxis is a peculiar distance
unit used by astronomers. It is equal to 5*log(distance/10 pc) so the
most distant SN on this plot is at about 7.6 billion pc.)

for equal time, here's one from the Supernova Cosmology Project:

both plots show redshift z vs. a logarithmic measure
of brightness (and therefore distance)

So, what's the result?

Why is Saul Permuter (leader of the SN Cosmology Project)
so happy?

It's not because his preliminary conclusion from the supernova
video has been confirmed!

perhaps its because the SN result is Science Magazine's Breakthrough
of the Year for 1998:

To be fair, this is a discovery by two groups. Here's Brian
Schmidt, leader of the Highz SN Search:

Prof. Peter Garnavich is also a member of the Highz SN Search

So, what's going on here?

Take a look at the bottom panel of the HighZ Hubble diagram:

This plot has the brightnesses scaled to the expectation
for an empty Universe

the white straight line represents an empty
= 0, = 0 Universe

note that =
+ is the total density in
ordinary matter

the magenta line
curving upward represents a
= 0, = 1 Universe

the SN appear to be slightly fainter than in the empty Universe
case

expansion is accelerating

the green line
curving downward represents a
= 1, = 0 Universe

the SN appear to be slightly fainter than in the brighter
Universe case

expansion is slowing down

this was the expected case a few years ago

Conclusion, the Universe seems to be that the expansion of
the Universe is accelerating, but not as fast as the empty Universe

this is good, because the Universe isn't empty!

Here are the results from the SCP and the HiZ SN for a fit
to the best values of
& :

Both groups prefer =
0.3 & = 0.7.

theory seems to prefer +
= 1 (a flat Universe)
Repulsion in Einstein Theory of Gravity

How can we understand gravitational repulsion in Einstein's
theory?

isn't gravity just an attractive force? (i.e. doesn't it
just suck?)

Gravity doesn't just depend on mass, but it depends of velocity,
too.

gravitational acceleration

or
in our usual notation

the density,
> 0 for any type of matter

the presure, p = 0 for normal slowly moving matter

and p/c^{2} = /3
for radiation (matter moving at v=c)

for radiation +
3p/c^{2} = 2, so radiation
yields a stronger gravitational attraction than ordinary matter moving
at v << c.

if we had negative pressure, we might get +
3p/c^{2} < 0 which would give a positive acceleration.

What is negative pressure?

it pulls instead of pushes

stretch a rubber band and it pulls, so it has negative pressure

but p/c^{2} <<
for a rubber band, so the modification of the gravitational force is tiny

when you let it go, the tension quickly converts into energy
of motion which gives a positive pressure.

a hypothetical cosmic string is like a rubber band with a
very high tension

stretch it and let it go, and it will oscillate at v ~
c.

it only pulls in 1 of 3 directions, so it has p/c^{2}
= (1/3)

or + 3p/c^{2}
= 0, so a stationary cosmic string causes no gravitational acceleration

if you stretch it and let it go, it develops a high velocity
which gives a positive contribution to the pressure

so an oscillating loop of cosmic string will give an attractive
gravitational force.

To get gravitational repulsion, we need something with a
very strong tension in 2 or 3 dimensions

3 dimensions is best, and stuff that has the maximal amount
of tension in 3 dimensions is called "false vacuum"

"false vacuum" has p/c^{2} = 
or + 3p/c^{2}
= 2

this is the most negative pressure that is allowed by General
Relativity

What does this negative pressure mean?

"false vacuum" has the peculiar property that the energy
density is a constant

suppose you have a piston full of ordinary matter.

squeeze the piston and the density of matter increases

you must input a lot of energy to squeeze it because the
pressure of the ordinary matter is pushing against you

now, suppose you have a piston full of "false vacuum"
matter

you don't need to squeeze it because the negative pressure
will cause it to squeeze itself

the "false vacuum" can produce energy  it will pull you
with the piston if you are holding on

the "false vacuum's" mass energy is proportional to its volume
(i.e. through E=mc^{2})

it is 100% efficient at convering mass to energy (compared
to < 1% for nuclear reactions)

Why is it called false vacuum?

vacuum means essentially nothing

a false vacuum is like a vacuum (i.e. no oridinary matter
or radiation)

but, it has this extra energy density

if space was filled with a false vacuum we couldn't easily
tell

energy only comes out if we convert the false vacuum to something
else