Cosmology Evidences PDF

 Contents   Introduction.  Observational Evidences  Matter distribution  Hubble Law.  The Cosmic Microwave Background.  Cosmic Curvature  What is the universe made of ?  Mass.  Radiation  Dark energy.  Li...

 Contents   Introduction.  Observational Evidences  Matter distribution  Hubble Law.  The Cosmic Microwave Background.  Cosmic Curvature  What is the universe made of ?  Mass.  Radiation  Dark energy.  Limits and evolution of density  Summary of the session.  Introduction   The term cosmology comes from the greek kosmos (world) and logia (study of)]  Branch of the physics that deals with the study of the origin, evolution and eventual fate of the universe.  It gathers knowledge from astrophysics, observational astronomy, General Relativity and particle physics.  There are several cosmological models  The FLRW (Friedmann-Lemaitre-Robertson-Walker) model, called the Standad Model of Modern cosmoloy: Big-Bang + isotropic and homogeneous universe  Main questions   How old is the universe ?  What is the universe made of ?  What is the shape of the universe ?  What is the size of the universe ?  Where does the matter come from ?  What did trigger the formation of galaxies and how do large structures originate?  How many star populations did/does exist ?  What is the fate of the universe ? Distribution of matter  Visible light   Stars (example the Sun). Mass in the order of 1030 kg and distance among nearest stars around 1 pc.  Galaxies (example the Milky way). Made of around 1011 stars. Typical length tens of kpc.  Cluster of galaxies (example Local Group with around 30 galaxies). Typical distance among galaxies is around hundreds of kpc. The volume of a cluster is in the order of a few cubic Mpc.  Visible light   Cluster are grouped into Supercluster of galaxies (example Coma cluster with around 10000 galaxies). Length in the order of tens of Mpc:  Supercluster are joined by filament and walls of galaxies.  Supercluster are separated by huge voids.  Foam-like structure  At scales of hundreds of Mpc or more, the Universe begin to appear smooth. Visible light  Sloan Digital Sky Survey The positions of the galaxies were obtained by measuring the redshift (spectral lines). Radius is 600Mpc  Other wavelength   Microwave: Cosmic Microwave Background (see next slides)  X-rays reveals that there is hot gas (tens of millions of Kelvin) between the galaxies. It is so hot that emits X-rays and it is probably remmant material from the formation of the galaxies (that failed to create stars).  Radio waves: the 21-cm emission line (splin-flip of the electron in Hydrogen atom) enable to map the neutral hydrogen gas in the distance universe (no blocked by dust) The Hubble Law  Spectral lines   Photometry vs spectroscopy.  When radiation interacts with matter, a set of bright or dark lines appear in the continuous spectrum.  They result from emission or absorption of light in a narrow frequency range.  Each chemical element produces its own unique set of spectral lines.  Spectral line shift   The measured wavelength depend on the relative velocity between the emitter and the receptor.  Such effect could come from Doppler effect (intrinsic motion) or expansion of the space itself  Methodology   Hubble and Humason photographed the spectra of many galaxies and computed the redshift. 𝜆 − 𝜆0 𝑧= 𝜆0 and the velocities 𝑣 𝑧+1 2−1 = 𝑐 𝑧+1 2+1  In parallel, they computed the distance to the galaxies by observing the apparent brightnesses and pulsation periods of Cepheid variables in these galaxies Image from “Universe” Freedman-Geller-Kaufmann. The red arrow show how much H and K lines of single ionized calcium are redshifted in each galaxy.  (b) (c) (a) Images from “Universe” Freedman-Geller-Kaufmann. (a) Hertzsprung-Russell diagram, (b) Apparent magnitude versus time (light curve) for δ Cepheid, (c) Period Luminosity of δ Cepheid  The Hubble law  𝑣 = 𝐻0 𝑑 V = recesional velocity H0=Hubble constant (Hubble Parameter) d = distance to the galaxy Image from “Universe” Freedman-Geller- Kaufmann. Distances and recesional velocities for a sample of galaxies  Comments about the Hubble law   The redshift of distance galaxies are not Doppler shift but cosmological redshift (caused by the expansion of space)  Are we at the center of the universe (center of expansion) ? ….. We do not think so !  Models has proven the Cosmologial Principle: the universe is homogeneous and isotropic on large scales, as proposed by Einstein.  Therefore, we interpret Hubble’s law as a expansion of the universe, and the same law may hold if distance and velocities are measured from a different place of the universe  Comments about the Hubble law   3 Important facts  Galaxies do not move away from each other through empty space - > The space itself expands while carrying the galaxies along with it.  Redshift of light is not produced because the galaxy is moving away from us rapidly-> Redshift is produced because the wavelength of the photons expands while travelling (space is expanding).  The distance between galaxies in a cluster does not change -> Gravitational attraction stabilizes the cluster at a certain size.  Comments about the Hubble law   Hubble law gives the age of the universe 𝑑 1 1 𝑇 = = ~ 73𝑘𝑚 = 13400 Millions of years 𝑣 𝐻0 /𝑀𝑝𝑐 𝑠  Note that the age of the solar system is about 4500 Millions of years, homo sapiens is about 200000 years old, and agriculture arrived 15000 years ago.  Previous calculations assumed an expansion at constant rate.  We can only observe objects inside our cosmic light horizon, a sphere with radius equal to the distance travelled by the light in 13.4 billions of years  Comments about the Hubble law   According to Hubble law’s picture, we can conclude that, in the past, the universe was denser.  There are evidences that a tremendous event (Big Bang) caused high-density matter to begin the expansion that we observe today. The universe, which has a finite age, was originated at a violent event and it is expanding  Comments on the meaning of the expasion   Hubble’s law only applies for the motion of objects governed by cumulative gravitational effect of a homogeneous distribution of matter. (see next session).  It does not apply to the atoms of your body (governed by chemical bonds), the motion of the Earth (basically governed by the attraction to a single object: the Sun ), and the Stars of a galaxies (orbiting according to the force dictates by their collective gravitational potential).  In previous example there is an exceed of mass (and not a uniform and isotropic distribution of mass).  Cosmological principles applies at large scales: above tens- hundreds of Mpc. The meaning of the expansion   Since velocity is proportional to the distance, it can appear that v>c.  Since this is a consequence of the space-expansion, causality principle is not violated.  The expansion is fully compatible with special relativity. The Cosmic Microwave Background (CMB)  Prediction before observation   We observe an amount of He in the Universe that does not fit with the one produced by the stars.  Alpher and Hermann proposed that the universe immediately following the Big Bang was very hot, and thermonuclear reactions occurred.  The amount of He predicted by this model has been confirmed by observations.  Dicke and Peebles, calculated that thermonuclear reactions involve many high-energy photons.  Planck’s blackbody law, which depends on the temperature, governs the properties of the photons.  Prediction before observation   Due to the universe expansion, such a high-energy (short wavelength) photons are now low energy (long wavelength) photons.  Dicke and co-worker, computed that the peak intensity is now at microwave wavelength (1 mm) and designed and antenna to detect the photons (early 1960s).  In parallel, Penzias and Wilson, from Bell Telephone Laboratory, were working in a new microwave antenna.  They measured the radiation and were advised about Dicke and Peeble’s work.  Penzias and Wilson claimed that they measured the CMB and received the Nobel Prize in 1978.  CMB fitting to a blackbody is excellent Earth moves at 371 km/s towards LEO (a) (b) Non-uniformities in the CMB are very relevant because they can explain concentrations of mass in our present-day universe, such us super-clusters of galaxies (c) Images from “Universe” Freedman-Geller-Kaufmann. (a) The spectrum of the CMB, (b) small temperature variations (COBE data) produced by Earth’s motion through the CMB, and (c) Temperature variation after subtracting the Earth Motion (WMAP data)  Around 380,000 years after the Big Bang, the early Universe was a high-density fluid made of photons, electrons and ions. Particle collisions triggered random sound waves with compressions and rarefactions. Photons emerging from regions with compression (more mass) and rarefactions (less mass) have Black body spectrum with slightly lower and higher temperatures. The pattern we see in the CMB is a signature of the sound waves just before the Universe became transparent. From cold compression arose the present-day population of galaxies. Cosmic Curvature  How can we measure space curvature?   Take three powerful light sources and detectors and place them at the vertices of a triangle with side lengths equal to billion light-years.  If the sum of the three angles of the triangle are less, equal or greater than 180º, then space is hyperbolic, flat, and spherical, respectively. Image from “Universe” Freedman- Geller-Kaufmann. Space curvature  How can we measure space curvature?   We cannot do the previous experiment but astronomer can measure the bending of the oldest radiation (CMB)  The CMB is not isotropic but exhibit “hot” and “cold” spots.  We can count the number of hot and cold spots of Image from “Universe” Freedman-Geller- Kaufmann. Hot and cold spots with angular different angular sizes. size about 1º are more common than other  By using models, it is found that the dominant “hot-spots” should have an angular size of about 1º if the universe is flat.  Therefore, the curvature should be very close to zero and the universe must either be flat or very nearly so.  Contents   Introduction.  Observational Evidences  Hubble Law.  The Cosmic Microwave Background.  Cosmic Curvature  What is the universe made of ?  Mass.  Radiation  Dark energy.  Limits and evolution of density  Summary of the session. Mass Density  Mass density   By counting galaxies and other measurements, astronomers determine that the average density of luminous matter is about 4.2 × 10−28 𝑘𝑔/𝑚3  However, Rotation curves indicate the presence of extended halos of dark matter that we cannot see.  Dark matter lies within and immediately surrounding galaxies (not in the vast space between Image from “Universe” Freedman-Geller- Kaufmann. Rotation curves of four spiral galaxies) Galaxies  Dark matter candidates include a large number of faint, red, low-mass stars ( 𝜌𝑚 +𝜌𝑟𝑎𝑑 ~ 𝜌𝑚 = 2.4 × 10−27 8𝜋𝐺 𝑚3 𝑚3  Dark Energy   Astronomers prefer to use the density 𝜌𝑚 Ω𝑚 = = 0.24 𝜌𝑐  There is a problem: we observe a flat universe (k=0) but we only observe a matter/energy density to make it hyperbolic (k=-1).  Conclusion: there is matter or energy that we do not observe.  Since the missing energy density does not appear to emit detectable radiation and has evaded detection of the gravitational effects, we refer to this energy as dark energy.  The dark energy density should be 𝜌Λ ΩΛ = = 0.76 𝜌𝑐  Candidates for dark energy: a constant energy filling the space homogeneously (cosmological constant) and scalar fields.  Evidence 2: accelerated expansion of the universe   Observations of distant supernovae reveal that the expansion of the universe is accelerated Images from “Universe” Freedman-Geller-Kaufmann. Left: types of universes, and right: Hubble diagram for distant supernovae Limits and evolution of density:  Limits and evolution of density  Images from “Universe” Freedman-Geller-Kaufmann. Left: Limits on the Nature of the Universe, and right: evolution of Density  Contents   Introduction.  Observational Evidences  Hubble Law.  The Cosmic Microwave Background.  Cosmic Curvature  What is the universe made of ?  Mass.  Radiation  Dark energy.  Limits and evolution of density  Summary of the session.  Main questions   How old is the universe ? 13400 Millions of years  What is the universe made of ? Radiation, Matter and dark energy  What is the shape of the universe ? Flat  What is the size of the universe ? The universe is infinite (flat) Read Chapter 27 in “Universe” to find response to the following questions Where does the matter come from ? What did trigger the formation of galaxies and how do large structures originate? How many star populations did/does exist ? What is the fate of the universe ?  Exercise  For a galaxy, the observed wavelength of the H Alpha line is 𝝀 = 6970Å. The wavelength at rest is 𝝀𝟎 = 𝟔𝟓𝟔𝟑Å. Compute the redshift, the velocity of recession and the distance to the galaxy 𝜆−𝜆0 𝑧= =0.062 𝜆0 𝑣 𝑧+1 2 −1 = 2 +1 = 0.06 -> v=18030km/s 𝑐 𝑧+1 D = v/H0 = 247Mpc