Dark Energy
ΛCDM Recall the lectures on cosmology The universe is flat Total energy density is 1 We know matter and baryon density So far, we called the rest Dark Energy We treated DE in the Friedmann Equation DE gave exponential growth of scale factor 2
Cosmic Acceleration Hubble showed that the universe is expanding But the rate depends on the type of energy For matter and radiation, expansion slows down Expectation: slowing expansion In 1998, there was an astonishing discovery Expansion of the universe is speeding up Has been doing so for 5 billion years 3
Standard Candle Imagine that you have a standard candle You can spread calibrated 100W light bulbs throughout the universe In Euclidean space, the apparent brightness would decrease with 1/r2 But we can also calculate this in our curved spacetime We know that in the early universe, we transitioned from radiation to matter domination But let's assume that there is some unknown component of energy We won't call it dark energy yet Let's leave it arbitrary 4
Equation of State Recall the evolution of the energy density But from the equation of state, we had From which we get 5
Measuring Expansion Redshift (through luminosity distance) tells how far the light has traveled Luminosity from standard candle tells effective solid angle Measure redshift vs luminosity for standard candle 6
Type 1a Supernovae Explosion of white dwarf in binary system Accretes mass from partner Explodes when it becomes too heavy (1.4 solar masses) Standard Candle Very predictable light emission curve We know how much light was emitted We can use these supernovae to measure the expansion history Measure luminosity vs redshift Probe history to redshift ~2 (5 billion years) 7
Discovery of Dark Energy Measured distance modulus m is apparent magnitude (how bright it looks) Log scale Larger m means dimmer object M is absolute magnitude (how bright it is) Reference at 10 Pc Steepening at high z comes from dimming of distant Supernovae Due to accelerated expansion Measured in 1998 and 1999 Perlmutter, Schmidt, Reiss awarded 2012 Nobel Prize Heralded as discovery of Dark Energy 8
Equation of State We already saw measurement of energy density Total density equals one DE density = 0.7 Now we can constrain this in terms of w Measured w = -1 Consistent with Dark Energy 9
What is Dark Energy? We discussed dark energy during cosmology Equation of state w = -1 Scale factor grows exponentially Does w change with time? Will the exponential growth continue forever? What do different types of DE predict for past, present, future? DE could be a particle Time evolution could be abrupt Phase transition Like CMB release Could be gradual transition Requires new force Quintescence 10
Cosmological Constant Einstein Field Equations Relation of gravity to energy Can add a constant to the equation, Λ Could be due to vacuum energy Recall the Casimir effect Due to zero point energy of all fields in SM Gives density 120 orders of magnitude too large Extra source of energy SUSY Adds extra fields that cancel effect Broken symmetry makes cancellation imperfect Density 60 orders of magnitude too large Many open issues Extensions of SM try to address these while solving other problems 11
Scalar Field If Dark Energy is a particle Could be in an excited state Lifetime of decay to ground state very long Much, much longer than age of universe Would behave like cosmological constant today But effect would vary with time Strength depends on how much is in excited state Strong time-dependent implications Many different models Give different behavior for time dependence 12
Pseudo Nambu-Goldstone Boson Introduce new field to SM Develops non-zero vacuum expectation value Just like Higgs mechanism VEV is Dark Energy Energy in the vacuum Would give w=1 Holds for past and present But w would evolve in the future Current research on DE Measuring w Determining time evolution of w 13