Large scale structure of the Universe Hot Big Bang Theory Concepts of General Re
Gerard, Alexis, Founder and President has reference to this Academic Journal, PHwiki organized this Journal Large scale structure of the Universe Hot Big Bang Theory Concepts of General Relativity Geometry of Space/Time The Friedmann Model Dark Matter (Cosmological Constant) Cosmology The large scale structure of the Universe Age of the Universe: 15 billion years. Evidence from dynamics of universe expansion (model) AND age of oldest stars. Size of the Universe: more complicated question. Cosmology is an evolutionary science (at least in principle) which does not allow controlled repetition of the system. (We cannot build a universe in a laboratory). Analogy with archaeology, geology, paleo-biology. Units in astronomy: Astronomical Unit AU = 150 millions km (Earth/Sun distance) Parsec = 3.26 light years (ly) Light Year = 9.46 x 10^15 m Size of Solar System (Plutos orbit) : about 6 light hours. Size of Milky Way: 10^5 ly x 10^3 ly Galaxies: bunches of stars (in evolution), with typically 10^11 stars. Galaxies agglomerate in clusters with size of a few Mpc (e.g. Local Group) Galaxy Clusters agglomerate in Superclusters with size: 200 Mpc Dominant interaction in the Universe: Gravitation
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How distances are measured The Cosmic distance ladder Parallax methods Main-sequence fitting (HR plot) Variable (Cepheid) stars Supernovae, cosmological methods The Universe as seen by us is strongly dishomogeneus in addition to anisotropic. This statement holds true also on the galactic scales (kpc distances) . in addition to remains true also on the scale of galaxy clusters (Mpc distances) However, if seen from distances of 100 Mpc or more, the universe gets homogeneus in addition to isotropic. This is homogeneity in addition to isotropy at large scales! The Hot Big Bang Model Model as long as the large scale structure in addition to evolution of the Universe. Based on important experimental observations. Cosmological Red Shift Radiation is emitted from stars in addition to other celestial bodies This radiation has the same physical origin of the radiation we study in terrestrial laboratories (e.g. atom absorption in addition to emission). Stellar evolution in addition to many other branches of astrophysics are based on such evidence. E.g. chemical composition of star surfaces are well known. The radiation emitted by any source can be affected by the Doppler effect if there is a relative motion between the source in addition to the receiver
Red shift In laboratory From a distant galaxy 1929: Hubble discovered the empirical relation Birth of Modern Cosmology! From the nonrelativistic Doppler as long as mula: A relation between the Galaxy velocity (away from us) in addition to its distance Since our position in the Universe is hardly a privileged one, galaxy superclusters recede from each other with the cosmological Hubble law. Universe is exp in addition to ing! Two immediate consequences: In the far past all matter was lumped in very little space (the Big Bang) The timescale as long as this is roughly 1/H (assuming the expansion law was the same all over, which is not really the case) The Universe is exp in addition to ing into what It is the space itself that is exp in addition to ing Yes. Are rulers exp in addition to ing No, only gravitationally independent systems participate in the expansion! The Hubble law is a linear expansion law which generates an homologous expansion (it is the same as seen from every Galaxy) H = 70 ± 7 km/sec Mpc The expansion looks the same as seen from A or from B
Naïve expansion model (assuming H = const) = Patch of size 100 Mpc What we see in our Patch is consistent with isotropic in addition to homogeneous expansion plus the Cosmological Principle (no privileged place in Universe!) 1 1 2 3 Homogeneous in addition to isotropic expansion: the shape of the triangle must be preserved. There as long as e Seen from patch 1: Seen from patch 2: In any universe undertaking homogeneous in addition to isotropic expansion, the velocity/distance relation must have the as long as m Now we see that: a(t): scale parameter Elements of a naïve thermal history of the Universe Going backward in time means: No structures (No stars, galaxies ) Only Matter in addition to Radiation Higher densities in addition to higher temperatures Matter Radiation e p When E() > 13.6 eV radiation in addition to matter are coupled. This took place at cosmic time 400,000 yrs. Radiations is in equilibrium with atoms. Be as long as e this era, let us imagine: nuclei, electrons in addition to radiation, at some T. Energy ~ kT. Electrons streaming freely at this point. (photodissociation) (radiative recombination)
Nucleosynthesis already taking place at that time (from 1 sec to 300 sec). Electrons cannot free stream. Then by going backward some more in time energy increases to: Then by going backward some more in time energy increases to give a mean energy 10 MeV. There as long as e the reactions became possible. These reactions mix p in addition to n together making nucleosynthesis impossible. This is T around 10^10 K ( in addition to cosmic time 0.1 sec). This took place at about T=10^10 K in addition to cosmic time 100 sec To summarize, a timeline of important events: T>10^10 K, E>10 MeV, t<0.1 sec . Neutrons in addition to protons kept into equilibrium by weak interactions. Neutrinos in addition to photons in equilibrium. t = 1 sec. No more p/n equilibrium. Beginning of nucleosyntesis. Neutrinos decoupling from matter. T=10^9 K ,E =1 MeV, t= 100 sec. Positrons in addition to electrons annihilate into photons t = 300 sec nucleosysnthesis finished because of low energy available in addition to no more free neutrons around Low mass nuclei abundance fixed Protons, photons, electrons, neutrinos (decoupled) T=5000 K, E=10 eV, t=400,000 years. No more radiation,e,p equilibrium. Atoms as long as mation (hydrogen, helium). Photons decouple CMB Primordial Nucleosynthesis Gamow, Alpher in addition to Herman proposed that in the very early Universe, temperature was so hot as to allow fusion of nuclei, the production of light elements (up to Li), through a chain of reactions that took place during the first 3 min after the Big Bang. The elemental abundances of light elements predicted by the theory agree with observations. Y ~ 24% Helium mass abundance in the Universe Cosmic Microwave Background Probably the most striking evidence that something like the Big Bang really happened is the all pervading Cosmic Background predicted by G. Gamow in 1948 in addition to discovered by Penzias in addition to Wilson in 1965. This blackbody gamma radiation originated in the hot early Universe. As the Universe exp in addition to ed in addition to cooled the radiation cooled down. CMB temperature fluctuations (COBE) By way of summary, the 3 experimental evidences as long as Big Bang: Red shift (Cosmic Expansion) Primordial Nucleosynthesis Cosmic Microwave Background Key concepts of the Hot Big Bang Model: General Relativity as a theory of Gravitation (Inflation) Concepts of General Relativity General Relativity: a theory of Gravitation in agreement with the Equivalence Principle Classical Physics concepts Special Relativity concepts Spacetime of Classical Physics in addition to Special Relativity Spacetime must be curved !! Classical Physics Existence of Inertial Reference Frames (IRF) Relativity Principle (Hey man, physics gotta be the same in any IRF!) Invariance of length in addition to time intervals Special Relativity Existence of Inertial Reference Frames (IRF) Relativity Principle (Hey man, physics gotta be the same in any IRF!) Invariance of c Gravitation, a peculiar as long as ce field Gravity field P = m(g) g P = m(i) a m(g)g = m(i)a a = g m(g)/m(i) a = g One as long as all bodies Electric field F = qE F = m(i)a qE = m(i)a a = E q/m(i) Depending on particle charge If gravitation does not depend on the characteristics of a body then it can be ascribed to spacetime. It is a spacetime property. Equivalence between inertial mass in addition to gravitational mass Free fall in gravitational field (apple from a tree) cannot be distinguished from acceleration (the rocket) Free fall the same as long as every body geometric theory of gravitation Gravitation equivalent to non-inertial frames (EP)
Einstein replaced the idea of as long as ce with the idea of geometry. To him the space through which objects move has an inherent shape to it in addition to the objects are just travelling along the straightest lines that are possible given this shape (J. Allday). Underst in addition to ing gravitation requires underst in addition to ing space-time geometry. The concept of elementary interaction Newton Faraday Maxwell Action at a distance Field concept Quantum Fields (field quanta exchange) Gravity (spacetime curvature) Spacetime geometry Geometry: study of the properties of space. Euclidean geometry: based on postulates – example: given an infinitely long line L in addition to a point P, which is not on the line, there is only one infinitely long line that can be drawn through P that is not crossing L at any other point. L P Some consequences: The angles in a triangle when added together sum up to 180° The circumference of a circle divided by its diameter is a fixed number : In a right angled triangle the lengths of the sides are related by (Pythagoras Theorem)
Euclid geometry is a description of our common sense (= classical physics) three-dimensional space However there are spaces that do not obey Euclid axioms. Spaces having a non-Euclidean geometry. We will consider the (2-dimensional) example of the surface of a sphere. What are the straight lines on the sphere surface They are the great cirlces! (the shortest path between two point is an element of a great circle). Now, suppose we choose A as a point in addition to we draw from B the parallel to A. They meet at the North Pole! (Euclid axiom does not hold) Another consequence: the sum of the angles of a triangle is higher than 180° With the example of a bidimensional space (the sphere surface) we have shown the existence of non-Euclidean (Riemannian) spaces. In this case parallel axiom does no hold true! Einsteins theory replaced gravity as a as long as ce with the notion that space can have a different geometry from the Euclidean. It is a curved space. The sphere surface is 2-d in addition to is a curved space when seen from outside (3-d) We live in a 4-d curved (by gravity) spacetime Three kind of geometry are in general possible (depending on energy content of Universe) Newtonian, Minkowski, General Relativity geometries Newtonian physics spacetime. Length of a rules is invariant (as well as time interval dt) Special Relativity spacetime: the 4-interval is invariant g Matrix (spacetime metric) General Relativity Spacetime: similar in structure to Special Relativity spacetime but now the gravity field makes the metric spacetime dependent.
Two suggestions as long as further reading B. F. Schutz, A first course in general relativity, Cambridge University press. B. Ryden, Introduction to cosmology, Addison Wesley
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