FURTHER COSMOLOGY Book page T H E M A K E U P O F T H E U N I V E R S E

Transcription

1 FURTHER COSMOLOGY Book page T H E M A K E U P O F T H E U N I V E R S E

2 COSMOLOGICAL PRINCIPLE Is the Universe isotropic or homogeneous? There is no place in the Universe that would be considered as the source of the Big Bang it expanded identical everywhere

3 ISOTROPY Assume Universe looks the same in every direction Not true on small scale Large scale: it looks the same in all direction Imagine: You are standing at the edge of the Universe Looking outward there would be a limited number of galaxies sending photons to us Looking inward, there would be an immense number of galaxies to send photon

4 EDGE OF THE UNIVERSE The two situations would appear different Isotropy says that this isn t the case

5 HOMOGENEITY Matter is uniformly spread in space Not true on small scale On large scale: average density of matter is about the same in all places in the Universe

6 Isotropy and homogeneity only considered in scales of millions of ly

7 EVIDENCE FOR COSMOLOGICAL PRINCIPLE Cosmic microwave background radiation CMB is the image of photons emitted from the early Universe Isotropy and homogeneity are seen in its random appearance APM Galaxy survey image: there is no special region or place that is different from any other

8 EINSTEIN AND SPECIAL RELATIVITY Einstein showed that Matter can only distort space time in one of three ways: 4rth dimension is time complex to visualize use impact of 3 rd dimension on a flat surface

9 POSITIVELY CURVED SPACE Spherical space of finite size Ω 0 > 1 By travelling through the Universe you could return to the original position in space time

10 NEGATIVELY CURVED Shape of a saddle of infinite size Ω 0 < 1 You would never return to the same point in space time

11 SURFACE REMAINS FLAT Shape remains flat of infinite size Ω 0 = 1 You would never return to the same point in space time

12 CRITICAL DENSITY ρ c Critical density is important Needed to determine what will happen to the Universe It is difficult to measure density We don t know how much there is Existence of dark matter

13 FATE OF THE UNIVERSE The critical density is the average density of matter required for the Universe to just halt its expansion, but only after an infinite time The Universe could be open, closed or flat

14 CLOSED UNIVERSE (POSITIVELY CURVED) Density of Universe is such that gravity will stop Universe from expanding It will cause Universe to contract Leads to big crunch Creation process could start again

15 OPEN UNIVERSE (NEGATIVELY SHAPED SADDLE) Gravity is too weak to stop Universe from expanding for ever

16 FLAT UNIVERSE Density is at critical value Universe will only start to contract after an infinite amount of time Ω 0 = 1

17 CRITICAL DENSITY ρ c - appears to be no greater than 10 particles per m 3 Research suggest that the average density is very close to this value ρ c for Universe ~ kgm 3

18 BUT IMPLICATIONS Rate of expansion has been slowing down Data from supernova type1a suggests that Universe may actually be undergoing an accelerated expansion caused by dark energy

19 FINDING A VALUE FOR ρ c Hubble s Law states the Imagine a speed of the galaxy as homogeneous sphere of radius r v = H 0 R and density ρ A galaxy of mass M will be moving away with speed v from the center of an imaginative sphere

20 TE=KE+PE TOTAL ENERGY OF GALAXY TE = 1 2 mv2 GMm R Mass of sphere ρ = M V M = ρv = 4 3 πr3 ρ TE = 1 2 m(h 0R) 2 G m4 3 πr3 ρ TE = 1 2 m H 0 2 R πmgρr2 R Galaxy will continue to move providing it has enough energy TE becomes positive

21 LET THE LIMIT OF TE=0 1 2 m H 0 2 R 2 = 4 3 πmgρr2 H 0 = Hubble constant G = Newton s gravitational constant

22 POSSIBLE DEVELOPMENT OF THE UNIVERSE Flat Universe ρ = ρ c Open Universe ρ < ρ c Closed Universe ρ > ρ c No gravity, ρ = 0 Accelerating Universe

23 DENSITY PARAMETER Ω 0 Open Universe ρ < ρ c Flat Universe ρ = ρ c Closed Universe ρ > ρ c Ratio of actual matter in Universe ρ to critical density ρ c is called the density parameter Ω 0 Ω 0 = ρ ρ c

24 4 th POSSIBILITY An accelerated Universe might be explained by dark energy This is an increasing likely prospect Hypothetical dark energy outweighs the gravitational effect of baryonic and dark matter

25 COSMIC SCALE FACTOR R Wavelength of emitted radiation will always be in accordance with the cosmic scale factor R Z = λ λ = R R 0 1 where z is the ratio b/w λ and R = cosmic scale factor, which would have changed from R 0 to R Assuming Black Body retains its shape during expansion T 1 R and T 1 λ Since λ R Cosmological Redshift λ of the emitted radiation is lengthened due to the expansion of the Universe

26 EVIDENCE FOR DARK MATTER fg

27 SUPPOSE v 2 = GM R a star of mass m is near the center of a spiral galaxy of total mass M The average density of the galaxy is ρ Star moves in circular orbit with orbital velocity v and radius R

28 CENTRAL BULB Assume the central bulb is spherical v 2 = GM R = G 4 3 πr3 ρ v 2 = 4 3 GρπR2 R v = 4 3 Gρπ R Hence v = constant R

29 ASSUME STAR IN ARMS OF GALAXY If the star is in the less populated areas of the arms of a galaxy, the galaxy would behave as if the total mass was concentrated at its center Stars would be free to move with nothing impede their orbits v 2 = GM R and v 1 R

30 SPEED OF STARS IN ARM: v 1 R When plotting rotational velocity against the distance from center of galaxy, we would expect to see rapidly increasing line that changes to decaying at the edge of the hub

31 EXPECTATION VS OBSERVATION By increasing speed from redshifts a different, much higher curve is observed Stars far out into the region beyond the arms move at same speeds as stars inside the galaxy

32 EXPLANATION Dark matter forms a halo around the outer rim of a galaxy Matter is not luminous or baryonic and emits no radiation

33 DARK MATTER HALO When the halo with dark matter is added to the curve, it almost fits the observed data

34 OTHER EVIDENCE Velocity of galaxies orbiting each other in clusters They emit far less light than suggested by their velocities WRT their mass

35 GRAVITATIONAL LENSING Radiation passing through a cluster of galaxies becomes much more distorted than expected due to the luminous mass of the cluster This is observable from Quasars

36 X-RAY IMAGES X-ray images of elliptical galaxies show halos of hot gas extending well outside the galaxy To be bound to the galaxy, galaxy must have mass far greater than observed Up to 90% of galaxies is assumed to be dark matter

37 WHAT IS DARK MATTER? Nobody knows

38 CANDIDATES FOR DARK MATTER MACHO s Massive compact halo objects - black holes - neutron stars - small stars such as brown dwarfs Compact stars at the end of their lives with high density Detected by gravitational lensing Not sufficient to provide amount of dark matter in cgrahamphysics.com Universe 2016

39 WIMP S Weakly interacting massive particles They are subatomic particles - non baryonic - they pass through baryonic matter with very little effect - massive does not mean big, but rather they have mass, also very small mass To make up dark matter, there would need to be an cgrahamphysics.com unimaginable 2016 amount of them

40 MORE WIMP S 1998 neutrinos with very little mass were discovered other hypothetical particles are called axions and neutralinos They have not been discovered experimentally Dark matter research in CERN

41 DARK ENERGY Unknown force causing galaxies to move further apart and stretching the fabric of space faster

42 ESA S PLANCK MISSION 68% of the Universe consists of dark energy 26.8% is dark matter 4.9% is ordinary matter

43 DATA FROM SUPERNOVA Supernova dimmer than Suggested expected explanation: They are further away than expected They must be speeding Dark energy is a up rather than slowing down property of space As universe expands so does dark energy Dark energy comes into existence with more space

44 ANISTROPIES IN CMB According to Big Bang Theory First ~300000years of Universe atoms could not exist Matter distributed as ionized plasma Photons trapped in fog that hid early times of Universe s history Universe expanded Density and temperature dropped Nucleus and electrons could combine to form atoms Epoch of recombination Now photon could escape CMB is the record of these at the moment of their escape

45 BLACK BODY SPECTRUM Multiple scattering of photons resulted in BB spectrum Had temperature ~ 3000K They were undergoing cosmological redshift to longer λ during their ~ 13 billion journey Now detected in microwave region at temperature of 2.725K In agreement with Big Bang prediction

46 DEFINITION ANISOTROPY Although radiation is almost perfectly isotropic, observations show slightly variations in temperature Temperature fluctuations with direction are called anisotropies

47 FLUCTUATIONS.. Fluctuations in temperature correspond to regions of slightly different densities Slightly shorter λ in direction of constellation Leo (hotter) In opposite direction radiation is slightly cooler Fluctuations in density developed later into galaxies and galaxy clusters

48 EVIDENCE FROM CMB ANISOTROPIES.. may require to rethink the theory Lack of symmetry in average temperatures in opposite hemispheres in sky suggest Universe may not be isotropic There is also a cold spot extending over a patch of sky

49 HUBBLE CONSTANT The Hubble constant is now ~ 67.15kms 1 Mpc 1 Significantly less Age of Universe billion of years New orbiting telescopes will provide new additional data NASA/ESA Euclid mission James Webb space telescope