Cosmology 4: The Hairy Edge

""

`Would you tell me, please, which way I ought to go from here?' Alice speaks to Cheshire Cat

`That depends a good deal on where you want to get to,' said the Cat.

`I don't much care where--' said Alice.

`Then it doesn't matter which way you go,' said the Cat.

`--so long as I get somewhere,' Alice added as an explanation.

`Oh, you're sure to do that,' said the Cat, `if you only walk long enough.'

Alice felt that this could not be denied, so she tried another question. `What sort of people live about here?'

`In that direction,' the Cat said, waving its right paw round, `lives a Hatter: and in that direction,' waving the other paw, `lives a March Hare. Visit either you like: they're both mad.'

We have now understood (?) most of the basic ideas: however there are a number of very speculative ideas which may be confirmed over the next few years.....

This is a sampling......

Do we understand Gravity:

\color{red}{ F = \frac{{GMm}}{{r^2 }}}

Nature and Nature's Laws lay hid in Night
God said "Let Newton be" and All was Light
Alexander Pope

gives

Pioneer

One tiny experimental problem:
Pioneer 10 and 11 launched 1972/73: last telemetry received from Pioneer 10, on 27 April 2002, when it was at a heliocentric distance of 80 AU.
Anomalous acceleration of Pioneer 10 and 11 Note this does not seem to be distance dependent
"Our previous analyses of radio Doppler and ranging data from distant spacecraft The extended Pioneer 10 data set spans 3 January 1987 to 22 July 1998. [For Pioneer 11 the shorter span goes from 5 January 1987 to the time of loss of coherent data on 1 October 1990.] With these data sets and more detailed studies of all the systematics, we now give a result, of aP = (8.74 ±1.33) x 10-10 ms-2.

MOdified Newtonian Dynamics. There are a lot of modified gravity theories: MOND is interesting since it fixes much of the dark matter problems. Mordechai Milgrom (1983)
\color{red}{ F = ma \Rightarrow F = m\mu \left( {\frac{a}{{a_0 }}} \right)a,{\rm{ }}\mu \left( x \right) = \left\{ {\begin{array}{*{20}c} {1\left( {\left| x \right| > 1} \right)} \\ {\left| x \right|\left( {0 < \left| x \right| < 1} \right)} \\ \end{array}} \right.}
Hence for galaxy rotation curves
\color{red}{ m\mu \left( {\frac{a}{{a_0 }}} \right)a = \frac{{mv^2 }}{r}\mu \left( {\frac{{v^2 }}{{ra_0 }}} \right) = \left\{ {\begin{array}{*{20}c} {\frac{{GMmr}}{{R^3 }}\left( {r < R} \right)} \\ {\frac{{GMm}}{{r^2 }}\left( {r > R} \right)} \\ \end{array}} \right.}
with a0 = 3x10-10.
Note

The problems: Gravity in 21st Century

We have no good theory of quantum gravity: either so weak that the corrections are infinitesimal or so strong that it is non-linear and theories diverge
Unified theories: Roughly:
Electricity and Magnetism → Electromagnetism
\color{red}{ \mu _0 ,\varepsilon _0 \Rightarrow c}
Electromagnetism and Weak Interactions → Electroweak theory
\color{red}{ G_{Fermi} \sim \frac{\alpha }{{M_W^2 }}}
Hierarchy of theories: simplest at highest temps:

But gravity has a long way to go. Planck Mass: mass at which grav. interactions become as strong as the rest

\color{red}{ M_{planck} \approx \sqrt {10^{42} } m_{electron} }

Better: construct Planck energy from G, ħ and c ⇒Planck energy.
\color{red}{ E_P = M_p c^2 = \left( {\frac{{\hbar c^5 }}{G}} \right)^{1/2} = 1.2 \times 10^{19} GeV}
Hope of supergravity theory/TOE is to unify all forces
Now the real problems! Do you think straight lines stay straight over 40 orders of magnitude
However,
  • Higgs can also interact with any new particles.
  • any new theory of gravity must have new particles at around Planck Mass.
  • Hence
    \color{red}{ M_H^{} = M_H^{bare} + C'm_{Planck} }
  • and if C' = 10-15 (say) the masses we calculate are meaningless.
Options
In a 3-D universe
This means we can arrange to have Planck mass at much lower energy: e.g. 1-100 TeV

Major consequences:

Hence it is very interesting to look at gravity at distances of microns. Washington experiment: confirms Newton down to ~ 150μ

Topology of the universe

WMAP has one highly anomalous point at l=2: quadrupole, suggests points π/2 away in sky are strongly anti-correlated
Suggestion that this combined with Ω=1.01 is that we live in finite universe with symmetry of Poincaré dodecahedron. Can regard this either as a space filled with repeating doecahedra

Luminet et. al. Nature 425, 566-567
Result is that CMBR would have repeated patterns
Interesting but evidence is slim!

Non-Copernican universe

Assumption that we live in a homogeneous universe may be wrong.
Suppose (G. Ellis) we are at the centre of a large (very) void: then we'd see shells of material being accelerated outwards
Would give us local acceleration (and hence mimic dark energy) but suggests we are in special place in the universe
Could be less unpleasant than dark energy, and can be tested: See Chris Clarkson talk

Anthropic Priniciple

6) Fortunately there is a special place for us

And God said " Let us make man in our own image, after Our likeness, and let them have dominion....over all the earth
Genesis I.26

Not only is this the best of all possible worlds, it is the only (observable, ) of all possible universes.

Relatively small number of parameters describe universe
Parameter Value Definition Measured Comments
G 6.673x10-11 Grav. const Lab
c 2.998x108 Speed of Light Lab
H0 70±7 km s-1Mpc-1 Hubble Hubbles constant
TCMBR 2.726K COBE/WMAP CMBR temp
ΩB .03±.01 WMAP, nucleosynthesis Baryon density
η 5.0x10-10 baryon/photon ratio
Ων 3.4x10-5 CMBR + BBN Uncertainty due to ρc, assumes mν = 0
Ωdm .26±.02 Galaxy clusters CDM density
ΩΛ ?? Curvature energy
Ω0 1.01±.02 Total energy
mec2 511 keV Electron mass
mPc2 937 MeV Proton mass
mnc2 939 MeV neutron mass
Standard model in particle physics has 28 parameters (12 masses, 4 couplings, rest are mostly mixing angles) Where do these come from?
e.g. Could the forces in nature be any different?
e.g How Dense is the Universe?
Anthropic arguments extend all the way from the physical constants and the masses and charges of the fundamental particles, to the gross properties of the universe...
Aguirre at al have also constructed working universe

So what happened before?

Then was not non-existent nor existent
There was no realm of air, no sky beyond,
What covered in and where? and what gave shelter?
Who verily knows and who can here declare it
Whence it was born and whence came this creation
He, the first origin of creation,
whether he formed it all or did not form it.
He verily knows it, or perhaps he knows not.
The Rig Veda X.129 (Hindu)

Sakharov (1985) suggested that the rules of physics need not be the same in going from one universe to the next: (e.g.) the electromagnetic coupling could be set arbitrarily in the first 10-30 s

Which takes us to...

Superstrings and the like:

We have seen that gravity curves space: in a sense, this is going to a larger number of dimensions.

Kalusza-Klein showed that one could include E-M along with gravity by adding a fifth dimension, but making it compact

To include all the other forces in nature (strong and weak) we need to go to a 10-dimensional space.

Ekpyrotic Universe

If we take the idea of extra dimensions seriously .....

And so finally

8) What a beautiful story!