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Cosmology

Cosmology. part 2. Topics. Models of the Universe: Recap How Far is Far? The Accelerating Universe Summary. Models of the Universe. Alexander Friedman 1888 - 1925. Density parameters at present epoch W M = r M / r c Matter W L = r L / r c Dark energy W M = W N + W D

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Cosmology

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  1. Cosmology part 2

  2. Topics • Models of the Universe: Recap • How Far is Far? • The Accelerating Universe • Summary

  3. Models of the Universe Alexander Friedman 1888 - 1925 Density parameters at present epoch WM = rM / rc Matter WL = rL / rc Dark energy WM = WN + WD WNNormal matter WDDark matter Friedman Equation Assuming flat geometry and no radiation

  4. Models of the Universe Georges Lemâitre 1927 Assume WL= 0 a(0) = 0 a(t0) = 1 Solution

  5. d0, t0 L = c (t0 – t1) d1, t1 How Far Is Far ? t0 – t1is the look-back time d0 = d(t0) proper distance between galaxies now d1 = d(t1) proper distance between galaxies then

  6. How Far is Far ? – II The Cartwheel Galaxy is said to be 500 million light years away. This, however, is not the distance to the Cartwheel now! It is merely the distance traveled by the light we are now receiving. So how far away is the Cartwheel now? t = t0 d0 a = 1

  7. t = t1 t = t0 a < 1 d1 a = 1 How Far is Far ? – III We know t0 – t1 and t0 and we know that d(t) = a(t) d0. d0 Therefore, if we knew d0, we could compute the proper distance d(t) for any cosmic time t. By convention, the proper distances now define a reference frame called the comoving frame. This reference frame expands with the Universe, so comoving distances do not change. But the comoving distance coincides with the proper distance d(t) for our epoch t0.

  8. t = t1 t = t0 a < 1 d1 a = 1 How Far is Far ? – IV For light ds = 0, therefore d0 To compute d0 we must add up the proper distances R(t0) ds. But, this is exactly the same as c dt / a(t). Therefore, using a(t) = (t/t0)2/3

  9. t = t1 a < 1 d1 How Far is Far ? – V Light from the Cartwheel Galaxy has taken 500 million years to reach us, so, using t0 = 14 Gyr, t1 = 14 Gyr - 0.5 Gyr = 13.5 Gyr one finds d0 = 506 Mly But at time t1, the Cartwheel was at a distance of d1 = a(t1) d0 = (t1 / t0)2/3 x 506 Mly = 494 Mly t = t0 d0 a = 1

  10. The Accelerating Universe - I Measuring Distances Using Standard Candles Type 1a supernovae occur a few times per minute somewhere in the known Universe Each is thought to be the detonation of a 1.4 solar mass white dwarf orbiting a red giant The constant mass, suggests that Type 1a supernovae are standard candles. They can therefore be used to measure distancesusing the inverse square law

  11. The Accelerating Universe - II 1998 Breakthrough of the Year Two teams – one led by Saul Perlmutter, the other by Brian Schmidt – announced that the supernovae were fainter and therefore further away than expected for a decelerating Universe.

  12. distance red shift The Accelerating Universe - III

  13. The Accelerating Universe - IV The Universe appears to be undergoing an acceleration by an energy field such as that postulated by Einstein, but considered by him to be his biggest mistake The mysterious energy is called dark energy

  14. Results Assuming Flat Geometry Matter Density WM = 0.25 ± 0.08 Dark Energy Density WL = 0.75 ± 0.08 Scale factor for constant dark energy density Lifetime for constant dark energy density

  15. Summary Distances In an Expanding Universe There are at least two: 1) the distance that light has traveled, which depends on two times t1 and t0 or 2) the proper distance, which depends on a single time. Accelerating Expansion Distant Type 1a supernovae seem to be further away than expected. If this is confirmed, the implication is that the Universe is not slowing down as quickly as expected – and that some unknown energy field is countering the breaking effect of gravity.

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