Part III
“How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?”
Sherlock Holmes in The Sign of the Four
DARK ENERGY
Evidence for Dark Energy
The Cosmological Constant Problem
Evidence for Dark Energy
• Brightness of very distant supernovae
• Flatness of the
universe as a
whole
Evidence for Dark Energy
• Brightness of very distant supernovae
• Flatness of the universe as a whole
Very distant objects should not precisely follow Hubble’s Law because gravitational attraction should decelerate the universal expansion.
This can be tested by looking for deviations from Hubble’s Law for very distant supernovae.
Evidence for Dark Energy
• Brightness of very distant supernovae
• Flatness of the
universe as a
whole
Evidence for Dark Energy
• Brightness of very distant supernovae
• Flatness of the universe as a whole
The universal expansion should be decelerating due to gravitational attraction
Expect this:
Evidence for Dark Energy
• Brightness of very distant supernovae
• Flatness of the universe as a whole
Courtesy: Ned Wright’s Cosmology Page
Tonrey et.al., 2003
Evidence for Dark Energy
• Brightness of very distant supernovae
• Flatness of the universe as a whole
Courtesy: Ned Wright’s Cosmology Page
Tonrey et.al., 2003
Amount of Dark Matter
Evidence for Dark Energy
WMAP collaboration Small temperature variations, at the level of one part in 100,000, are visible in the CMB
• Brightness of very distant supernovae
• Flatness of the
universe as a
whole
Evidence for Dark Energy
WMAP collaboration
These are due to sound waves in the primordial gas which emitted this light.
• Brightness of very distant supernovae
• Flatness of the
universe as a
whole
Evidence for Dark Energy
• Brightness of very distant supernovae
• Flatness of the universe as a whole
The CMB allows the inference of the properties of the later universe through which these photons pass.
Evidence for Dark Energy
• Brightness of very distant supernovae
• Flatness of the universe as a whole
Courtesy: Ned Wright’s Cosmology Page
Measurements of CMB and Dark Matter
and universal expansion and acceleration are consistent
Amount of Dark Matter
Concordance Cosmology
Can also count ordinary atoms even if they cannot be seen!
Nucleosynthesis
Properties of the CMB
Courtesy: Ned Wright’s Cosmology Page
The cosmological term
• Einstein’s equations as initially written preclude the existence of a static Universe
Taipei June 2014
𝐺
𝜇𝜈+ 𝜆 𝑔
𝜇𝜈= 8𝜋𝐺 𝑇
𝜇𝜈𝐺
𝜇𝜈= 8𝜋𝐺 𝑇
𝜇𝜈• This conclusion can be avoided if they are modified to include a ‘cosmological term’ which acts as a repulsive counterforce to gravity’s attraction
• The requirement for the cosmological term was removed once the Universe was found to be expanding.
Cosmological term as Dark Energy
• The cosmological term provides an excellent description of the Dark Energy, since its repulsive nature can drive the observed cosmological acceleration
• Interpreted as a stress-energy the cosmological term looks like constant positive energy density and negative pressure
8𝜋𝐺 𝑇
𝜇𝜈= −𝜆 𝑔
𝜇𝜈−𝑝 = 𝜌 = 𝜆
8𝜋𝐺
Einstein’s error
• Was Einstein’s greatest error introducing the cosmological term, or discarding it before Dark Energy was discovered?
Taipei June 2014
𝐺
𝜇𝜈= 8𝜋𝐺 𝑇
𝜇𝜈− 𝜆 𝑔
𝜇𝜈= 8𝜋𝐺 (𝑇
𝜇𝜈+ 𝑡
𝜇𝜈)
• Modern point of view: Neither! His error was to believe he gets to choose...
• The cosmological term is precisely what a vacuum energy, 𝑡𝜇𝜈, would look like, and we should be able to compute its
properties if we understand the vacuum.
Vacuum Energy as Dark Energy
• The success of special relativity requires the
vacuum energy density to be constant and its pressure to be negative, as required to be Dark Energy.
• Negative pressure keeps the vacuum energy density
constant as the universe expands.
log r
log a
0
r p
The Cosmological Constant Problem
• The vacuum energy is calculable within any theory of
elementary particles, such as the Standard Model of particle physics, and the observed vacuum energy is the sum of a classical energy and an enormous quantum energy
𝜌
𝑣𝑎𝑐= 𝜆 + 𝑚
44𝜋
2• So what? Can always choose classical 𝜆 to ensure the
Universe accelerates by the right amount, even if 𝜌𝑣𝑎𝑐 is much smaller than 𝑚4
Hierarchy problems
• The electroweak hierarchy
• The cosmological constant
𝐿
𝑆𝑀= 𝜇
20+ 𝑚
20𝐻
∗𝐻 + 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠 𝜇
2= 𝜇
20+ ℎ𝑖𝑔ℎ𝑒𝑟 𝑜𝑟𝑑𝑒𝑟
me ~ 106 eV
m 10-2 eV mw ~1011 eV
m ~ 108 eV
Modern picture: no unique
‘classical’ theory; instead many ‘effective’ theories
𝜌
𝑣𝑎𝑐= 𝜆
0+ 𝑘
𝜐𝑚
𝜐 4Hierarchy problems
• The electroweak hierarchy
• The cosmological constant
𝐿
𝑆𝑀= 𝜇
20+ 𝑚
20𝐻
∗𝐻 + 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠 𝜇
2= 𝜇
20+ ℎ𝑖𝑔ℎ𝑒𝑟 𝑜𝑟𝑑𝑒𝑟
me ~ 106 eV
m 10-2 eV mw ~1011 eV
m ~ 108 eV
Modern picture: no unique
‘classical’ theory; instead many ‘effective’ theories
𝜌
𝑣𝑎𝑐= 𝜆
1+ 𝑘
𝑒𝑚
𝑒 4+ 𝑘
𝜈𝑚
𝜈 4𝜌
𝑣𝑎𝑐= 𝜆
0+ 𝑘
𝜈𝑚
𝜈 4Hierarchy problems
• The electroweak hierarchy
• The cosmological constant
𝐿
𝑆𝑀= 𝜇
20+ 𝑚
20𝐻
∗𝐻 + 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠 𝜇
2= 𝜇
20+ ℎ𝑖𝑔ℎ𝑒𝑟 𝑜𝑟𝑑𝑒𝑟
me ~ 106 eV
m 10-2 eV mw ~1011 eV
m ~ 108 eV
Modern picture: no unique
‘classical’ theory; instead many ‘effective’ theories
𝜌
𝑣𝑎𝑐= 𝜆
1+ 𝑘
𝑒𝑚
𝑒 4+ 𝑘
𝜈𝑚
𝜈 4𝜌
𝑣𝑎𝑐= 𝜆
0+ 𝑘
𝜈𝑚
𝜈 4Must cancel to 32
decimal places!!
What We’re Looking For
• Our picture of the physics of ordinary particles must already be wrong at energies higher than 1 eV, or distances shorter than 1 micron.
• Whatever the change is, it must change gravity in such a way as to produce a small response to the vacuum energy.
• It must not alter other interactions.
• Is this possible? Party line says “no”.
What We’re Looking For
• Our picture of the physics of ordinary particles must already be wrong at energies higher than 1 eV, or distances shorter than 1 micron.
• Whatever the change is, it must change gravity in such a way as to produce a small response to the vacuum energy.
• It must not alter other interactions.
• Is this possible? Party line says “no”.
• Remarkably, it may be!
Helpful extra dimensions
• The Problem:
• Einstein’s equations make a lorentz-invariant vacuum energy (which is generically large) an obstruction to a close-to-flat spacetime (which we see around us)
𝑇
𝜇𝜈= 𝜆 𝑔
𝜇𝜈𝐺
𝜇𝜈= 8𝜋𝐺 𝑇
𝜇𝜈Helpful extra dimensions
• The Problem:
• Einstein’s equations make a lorentz-invariant vacuum energy (which is generically large) an obstruction to a close-to-flat spacetime (which we see around us)
𝑇
𝜇𝜈= 𝜆 𝑔
𝜇𝜈𝐺
𝜇𝜈= 8𝜋𝐺 𝑇
𝜇𝜈Arkani-Hamed et al Kachru et al Carroll & Guica Aghababaie et al
But this need not be true if there are
more than 4 dimensions!!
Helpful extra dimensions
• Why not?
• Extra dimensions need not be lorentz invariant
• Vacuum energy might curve extra dimensions, rather than the ones we see in cosmology
Vilenkin et al
e.g. gravitational field of a cosmic string
Helpful extra dimensions
• A higher-dimensional analog:
• Similar (classical) examples also with a 4D brane in two extra dimensions: e.g. the rugby ball and related solutions
Carroll & Guica Aghababaie et al
Opportunities & Concerns
• If true, many striking implications:
• Micron deviations from inverse square law
• Missing energy at the LHC and in astrophysics:
requires Mg > 10 TeV
• Probably a vanilla SM Higgs
• Excited string states (or QG) at LHC below 10 TeV
• Low energy SUSY without the MSSM
• Very light Brans-Dicke-like scalars
• Sterile neutrinos from the bulk?
“…when you have eliminated the impossible, whatever remains, however improbable, must be the truth.”
A. Conan Doyle
Outlook
• Cosmological observations are now redundantly testing the Hot Big Bang model.
• Observations support the ‘Concordance Cosmology’.
Outlook
• Cosmological observations are now redundantly testing the Hot Big Bang model.
• Observations support the ‘Concordance Cosmology’.
• The concordance involves several lines of independent evidence for both Dark Matter and Dark Energy.
• Neither can be dark forms of ordinary atoms.