Cosmological Models John O Byrne School of Physics University of Sydney Using diagrams and pp slides from Seeds Foundations of Astronomy and the Supernova Cosmology Project http://www-supernova.lbl.gov Observation: Isotropy: On the largest scales, the local universe looks the same in any direction that one observes. Either: We occupy a special place in the universe (violating the Location Principle) or: On the largest scales, the universe has the same physical properties everywhere (Homogeneity) We adopt the latter as a fundamental assumption. This is the basis of Modern Cosmology The Cosmological Principle To this we usually add Universality: The laws of physics are the same everywhere in the universe. 1
The Anthropic Principle Notes that the universe is fine-tuned to our existence Fine-tuning. Strength of gravity Smoothness of the Big Bang Masses of sub-atomic particles Strength of the strong nuclear force Magnitude of the Cosmological Constant Controversial - Is it just an easy way out of difficult questions? Explanations? Chance Theory of Everything The Multiverse Cosmology and General Relativity The basis of any theory of cosmology is General Relativity. The equations of General Relativity permit a variety of different solutions - i.e. a variety of different structures and different histories of the universe Expanding, contracting and static universes, plus many combinations of these possibilities. 2
Observation: Hubble s Law Distant galaxies are receding from us with a speed proportional to distance - defined by the Hubble Constant Redshift What we actually observe is Redshift (z) 1+ z = observed emitted caused by the expansion of space 1+ z = R when observed R when emitted where R is a scale factor 3
The Expanding Universe On large scales, galaxies are moving apart, with velocity proportional to distance. It s not galaxies moving through space. Space is expanding, carrying the galaxies along! The galaxies themselves are not expanding! Redshift Redshift (z) is a Cosmological redshift and NOT a Doppler redshift It is NOT a velocity of galaxies through space and is NOT governed by Special Relativity Interpretation as a Doppler shift would make us a special centre of expansion and violate the location principle Conversion of observed redshift (except small values) to velocities or distances requires a particular model of the universe to be assumed 4
The Necessity of a Big Bang If galaxies are moving away from each other with a speed proportional to distance, there must have been a beginning, when everything was concentrated: The Big Bang!? Evidence for a Big Bang 1. The expansion of the universe 2. The cosmic microwave background 3. The abundance of the light elements 5
Looking Back Towards the Early Universe The more distant the objects we observe, the further back into the past of the universe we are looking. The Cosmic Background Radiation The radiation from the very early phase of the universe is detectable today as the Cosmic Microwave Background Blackbody radiation with a temperature of T = 2.73 K 6
Abundance of Light Elements Helium Model Universes Size scale of the Universe Maximum age of the universe: ~ 1/H 0 Current rate of expansion - given by the Hubble constant H 0 Time H ~ 72 km/s/mpc (±10%) 7
Traditional Model Universes Size scale of the Universe > c => Universe will collapse back < c => universe will expand forever = c Time If the density of matter/energy equaled the critical density, then (in traditional models) the universe would be on the border between collapse and expanding forever Also, the geometry of the universe would be flat! Meaning? Shape and Geometry of the Universe Take a 2-dimensional analogy: How can a 2-D creature investigate the geometry of the sphere? Measure curvature of its space! k = 0 (zero curvature) k = +1 (positive curvature) k = -1 (negative curvature) 8
Cosmological Parameters H - Hubble parameter (in km/s/mpc) k - spatial curvature R(t) - scale size a(t) - scale factor w i - equation of state i - density parameter d(t) - deceleration parameter (q>0 for deceleration) a(t) = R(t) R now = 1 1+ z w i = pressure i = 0 (matter) density i =1/3 (radiation) density i = i density critical Confused? Various parameters are related. Problems with the simple Big Bang 1) The flatness problem: The universe seems to be nearly flat. Why so close? Even a tiny deviation from perfect flatness at the time of the big bang should have been amplified to a huge deviation today. Extreme fine tuning required! 2) The isotropy of the cosmic background: If information can only travel through the universe at the speed of light, then structure in the cosmic background should not be correlated over large angular scales! Contradiction to almost perfect isotropy of the cosmic background! 9
Inflation Inflation: period of sudden expansion during the very early evolution of the universe Perhaps triggered by the sudden energy release from the decoupling of the strong and electroweak forces New favoured Model Hubble Constant H o 72 km/s/mpc ± 10% Cosmological density parameter o 1.02 ± 0.02 Baryon density parameter b 0.044 ± 0.004 Matter density parameter m 0.27 ± 0.04 Dark-energy density parameter 0.73 ± 0.04 Time since the Big Bang 13.7 ± 0.2 billion years Age of universe at Decoupling 379 ± 8 thousand years Redshift of the microwave background 1089 ± 1 Inflationary period at age ~ 10-35 s 10
New favoured Model Size scale of the Universe NEW favourite m = 0.3 = 0.7 Old favourite m = 1.0 = 0.0 Time Measuring the Deceleration of the Universe By observing type Ia supernovae, astronomers can measure the Hubble relation at large distances i.e. the Distance/redshift relation It was expected that this would measure the deceleration of the universe, but 11
The Accelerating Universe Other evidence: Fluctuations in the Cosmic Microwave Background Angular size of the CMB fluctuations allows us to probe the geometry of space-time! CMB fluctuations have a characteristic size of 1 degree. 12
Analysis of the Cosmic Background Fluctuations Analyze frequency of occurrence of fluctuations on a particular angular scale Universe has a flat geometry consistent with the new favourite model Other evidence:large Scale Structure A large survey of distant galaxies shows the largest structures in the universe: Filaments and walls of galaxy superclusters, and voids of largely empty space. - structure originating in the Cosmic Microwave Background 13
Other evidence:large Scale Structure The structure (technically the power spectrum) of both the CMB, and the distribution of galaxies suggest that m (the density of matter) ~ 0.27 The Accelerating Universe 14
Dark Matter Combined mass of all visible matter (i.e. emitting any kind of radiation) in the universe adds up to much less than the critical density. Galaxy rotation curves and Gravitational lensing shows that some clusters contain 10 times as much mass as is directly visible. There must be DARK matter The Nature of Dark Matter Can dark matter be composed of normal matter? If so, then its mass would mostly come from protons and neutrons ( baryons ) The density of baryons right after the big bang leaves a unique imprint in the abundances of deuterium and lithium. Density of baryonic matter is only ~ 4 % of critical density. Most dark matter must be non-baryonic! 15
Dark Energy negative pressure in spacetime has a repulsive effect to explain the acceleration - has been called dark energy any dark energy contributes to the energy density of the vacuum has the same effect as Einstein s Cosmological Constant, (upper-case lambda) is a free parameter in Einstein s fundamental equation of general relativity; previously believed to be 0 Energy corresponding to seems to account for the missing mass/energy needed to produce a flat space-time. Problems Many of the old problems seemed solved leaving just minor things like and what is dark matter? what is dark energy? Quantum field theory predicts energy density of the vacuum up to 10 120 greater than is observed Why is so close to zero? - the cosmological constant problem Why are and m so close now - a special epoch? 16
Modelling dark energy Matter and radiation have constant equations of state (w m = 0 and w r = 1/3) Cosmological constant has w = 1 Other options: Dark energy with constant w: e.g. strings w = -1/3, domain walls w = -2/3 Quintessence: generic name for dark energy with time-varying w - e.g. supergravity, superstring, branes, Interaction: dark energy interacts with matter or energy - e.g. unifying dark energy and dark matter Modifications to GR: modifying the basic equations Modelling dark energy Most dark energy models can be described with a constant or varying equation of state e.g. constant w w < -1/3 universe accelerates - now required w > -1/3 universe decelerates w < -1 density od dark energy increases with expansion - the big rip 17
Modelling dark energy One case: As a function of time (t) and redshift (z) For dark energy models with a constant equation of state Source: Luke Barnes 2005 Honours Thesis a(t) q(t) 6 5 4 3 2 1 0 X (t) 18