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The Fate of the Universe

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The cosmological principle The simplest universes is: Homogenous – the same everywhere you go Isotropic – the same in all directions

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Discussion Do you think one can have a universe (or any situation) that is homogeneous, the same everywhere, but anisotropic, not the same in all directions?

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Discussion Do you think one can have a universe that is isotropic, the same in every direction, but not homogenous, not the same everywhere?

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Discussion Is it possible to prove the universe we live in is homogeneous?

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Discussion Is it possible to prove the universe we live in is isotropic?

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The Location Principle It is very unlikely that we occupy a special place in the universe.

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Isotropic and Homogeneous If the universe is isotropic (from observations) and it is inhomogeneous, then we occupy a special location in the universe. If a special location is improbable, then inhomogeneity is also improbable

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The perfect cosmological principle The simplest of all possible universes is: Homogenous – the same everywhere you go Isotropic – the same in all directions The same at all times

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Discussion How do we know the perfect cosmological principle does not hold?

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Discussion If all the galaxies in the universe are attracted to all the other galaxies in the universe, would you expect the expansion of the universe to be constant over time?

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The non-constant Hubble constant H 0 – refers to the present-day expansion rate. H(t) – the Hubble parameter, varies with time.

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The fate of the universe Will the universe expand forever or will the expansion stop someday and start contracting?

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The fate depends on the rate of expansion and the density Density greater than critical value – gravity will halt expansion Density less than or equal to the critical value – gravity will not stop expansion

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Critical density 1 to 2 × g/cm 3 Anything with a density above the critical value will stop the expansion of spacetime.

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Discussion Which type of universe would you rather live in, one that will expand forever, or one that re-collapses in on itself? Why?

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How could we determine the fate of the universe? Discussion

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How would a different expansion rate change Hubble’s plot? That is, how would the distance vs. the recessional velocity graph change if the universe were expanding at twice or ½ the measured value of 70 km/sec/Mpc?

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Discussion If the expansion of the universe is constant with time, the Hubble plot will be a straight line out to the highest redshifts. What does the Hubble plot look like if the expansion of the universe slows with time? How about if it speeds up over time.

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Supernova type Ia All have about the same peak luminosity Make good standard candles

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Discussion If the expansion of the universe is slowing, the expansion rate was greater in the past (at high redshift) than it is today. Will high-redshift galaxies be closer or farther away than we think if we assume a constant expansion rate.

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With a greater expansion rate in the past, we will think that a given redshift is farther away from us than it actually is.

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Discussion If the expansion of the universe is slowing, the expansion rate was greater in the past (at high redshift) than it is today. Will high-redshift supernovae be brighter or fainter than we would expect using the present day Hubble constant?

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We think high redshift supernovae are farther away than they actually are they will appear brighter than we expect

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Accelerating Supernovae data at high redshift are fainter than we expect the expansion rate of the universe was slower in the past. The expansion rate is increasing with time.

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Discussion Maybe the rate of expansion is not increasing with time. What else might make supernovae at large redshift dimmer than low redshift supernovae?

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Discussion Perhaps this is just the effect of dust between us and the distant supernovae, the dust would make them appear dimmer even though they aren’t really farther away. What observations could you do to eliminate this possible explanation?

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No reddening They do not appear to be reddened by dust.

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Cosmological constant is back! The cosmological constant introduced by Einstein can be thought of as anti-gravity or a repulsive force pushing the galaxies apart. Some researchers are now referring to this as “dark energy.”

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Discussion Because mass and energy are the same, this means that dark matter and dark energy are the same right? What is the difference?

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Universe may not expand forever We know nothing about what dark energy is or how it works Right now, it appears the dark energy is due to a cosmological constant, i.e. constant acceleration over the observable universe

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Discussion If all the galaxies are getting farther away, what does this tell you about the universe in the past?

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Discussion What happens when you compress something?

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Discussion What do you expect to observe from a hot dense gas?

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Discussion What happens to this blackbody radiation as the universe expands?

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The cosmic microwave background radiation (CMBR) The universe is filled with microwave radiation that matches a blackbody curve with a temperature of K.

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The universe started from an extremely dense, hot phase from which it expanded in an event termed the “Big Bang.” The Big Bang is an explosion of space and time, not an explosion in space at a time. The hot Big Bang

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Discussion Where did the Big Bang take place?

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Discussion What happened before the Big Bang?

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The isotropy of the CMBR The temperature of the CMBR is the same in all directions. Although is does vary by K in opposite directions, this is interpreted as the Earth’s motion relative to the Universe.

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If we remove our motion of 620 km/sec in the direction of the local supercluster of galaxies, we find the CMBR temperature varies by less than 1 part in 10,000. In order to be the same temperature, each part of the sky must have been in thermal contact with every other part of the sky.

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The horizon problem We can see about 14 billion light years in every direction.

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Inflation An early phase of exponential expansion lasted only sec – Universe expanded by a factor of The space between bits of matter expanded faster than the speed of light.

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The curvature of spacetime Matter and energy warp spacetime

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Geometry of Spacetime Two parallel lines remain parallel, never getting farther apart of closer together. The sum of the angles in a triangle is 180 degrees.

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Types of curvature Positive curvature – a closed universe – one the will collapse Negative curvature – an open universe – one that will expand forever Flat – an open universe with density equal to the critical density

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Positively curved spacetime

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Negatively curved spacetime

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Flat spacetime

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Boundaries and Infinities An open Universe is infinite in space or has no edge A closed Universe in finite but need not be bounded by an edge – think surface of a sphere

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