Chapter 18--astro

(A) Has the expansion rate of the Universe always been accelerating? (B) What could cause a change from deceleration to acceleration?

(a) No, the rate of expansion slowed during the first 9 billion years, due to gravity, & has been accelerating for the last 4 or 5 billion years, due to dark energy. (b) The overall expansion rate is a balance between the effects of gravity & dark energy. In earlier times, when galaxies were closer together, gravity dominated over dark energy; later, as the expansion proceeded, dark energy dominated.

(A) Summarize different methods for determining the value of omega M. (B) What are the difficulties in actually implementing these methods?

(a) Sec. 18.4e lists several possible methods for determining ΩM: (i) directly measure the average density of matter, presumably by totaling up the matter in clusters & superclusters of galaxies & estimating the amount in the intergalactic medium & dark matter; (ii) indirectly by measuring the expansion rate of the Universe in the distant past compared to the present, since the average density is one parameter which determines this; (iii) geometrically by measuring the sum of the angles of an enormous triangle, by measuring the angular sizes of galaxies or the apparent brightness of objects as a function of distance, or by measuring the number of galaxies as a function of volume; (iv) finally, by measuring the relative abundances of the lightest isotopes produced in the big bang, which also depends on the average density. (b) Besides the fact that making observations of things at extremely large distances is difficult & uncertain, Sec. 18.4f also mentions possible difficulties related to selecting representative samples, to deviations from uniformity, & to evolutionary changes over time in the objects measured.

(A) What do we mean when we say that the Universe is expanding? (B) Are galaxies moving through some preexisting space? (C) Do humans, planets, stars, and galaxies themselves expand?

(a) The distance between any two points in space, as described in Einstein's general theory of relativity, is increasing with time, which means that the space in the Universe is expanding. (b) No, since space itself is expanding, points in space (as well as galaxies) are not moving through a preexisting space. (c) No, since material objects, including galaxies, are held together by forces which overcome the expansion of the space they occupy. However, the space between material objects, or aggregates like clusters & superclusters of galaxies, is expanding.

Which one of the following distributions is isotropic but is not homogeneous?

(a) The distribution of stars in a globular cluster, as measured from its center

Suppose from the top of your palace you notice a circular patch of land of radius 10 meters that needs landscaping. You hire Edwin, who charges $5 per square meter. Edwin completes the job, and comes back with a bill of $3000. What type of homogeneous, isotropic space can you deduce that you live on?

(b) Hyperbolic

Observations of what kind of objects were the first to strongly imply that the expansion of the Universe is currently accelerating?

(b) Supernovae

Which one of the following statements about Hubble's constant, Ho, if false?

(b) The value of Hubble's constant can be measured accurately

Which one of the following is not a possible homogeneous, isotropic, expanding universe according to Einstein's general theory of relativity?

(c)

Using incomplete data, suppose you find that the value of Hubble's constant in our Universe is about 700 km/s/Mpc instead of about 70 km/s/Mpc. How old would you calculate the Universe to be

(c) 1.37 Billion years

Which one of the following is an assumption made as part of the "cosmological principle"?

(c) The Universe is isotropic on scales of billions of light-years

Which one of the following statements about the big bang theory is false?

(e) There is a unique center within the Universe that coincides with where the big bang happened

In a universe where the Hubble constant is 0.05 Gyr-1 and in which omega M= 0 and there is no dark energy, you can determine that the universe has an age of____

20 billion years. Under these restrictive assumptions, the age of the universe is the Hubble time, which is the reciprocal of the Hubble constant (FIGURE IT OUT 18.1). Then T0 = 1/H0 = 1/(0.05 Gy-1) = (1 Gy)/(0.05) = 20 Gy.

What are two ways of estimating the age of the Universe?

A lower limit on the age of the Universe is provided by the age of the oldest entity that can be measured, e.g. the Universe must be older than the stars in the oldest globular clusters, 12 to 13 billion years old. Another estimate is arrived at by extrapolating the present rate of expansion back in time, e.g. the reciprocal of the Hubble constant, or Hubble time, of about 14 billion years.

Suppose we assume that the recession speed of a given galaxy never changes with time. Why is the derived age of the Universe likely to be an overestimate of its true age?

Astronomers believe the recession speed of galaxies may have been faster in the past, because gravity had been acting to slow the expansion for less time. Thus, the average speeds of recession are greater than the present values, so the actual age of the Universe would be less than the age assuming the present values were constant (t = d/v, grater v, smaller t).

What is the overall shape of the Universe, as implied by the total amount of luminous matter, dark matter, and dark energy?

At present, the overall shape of the Universe appears to be nearly flat.

Two types of stars that have played central roles as cosmological yardsticks are ____ variables and ____ supernovae

Cepheid; Type Ia

The expansion of the Universe appears to be accelerating, driven by the repulsive effect of the cosmological constant or, more generally, _____

Dark energy

What do we mean by "dark energy"? How might it affect the expansion of the Universe?

Dark energy is the term applied to whatever is causing the repulsive effect resulting in the observed acceleration of the expansion rate of the Universe

A time far in the future of the Universe, when the density of photons and elementary particles will be very low, is known as the ____

Dark era.

A value of omega total that is greater than 1 indicates that the Universe has a positive curvature, while a value less than 1 indicates that the Universe has negative curvature.

False.

According to Einstein's equation, E-mc^2, dark energy and dark matter are essentially the same thing.

False.

Current observational evidence suggests that the Universe will eventually collapse; the expansion rate is decelerating rapidly.

False.

The curvature of three-dimensional space cannot be detected because we live within the three spatial dimensions.

False.

Summarize the first observational evidence found for the expansion of the Universe and a possible beginning of time.

Hubble determined, from the redshifts of Cepheids in other galaxies, that the recessional speed of a galaxy was proportional to its distance (Hubble's law), which is explained by the expansion of space. Reasoning backward from the present expansion, all of space must have been in the same location at the beginning of time.

Why does the recession of galaxies not necessarily imply that the Milky Way Galaxy is at the center of the Universe?

If space itself were expanding, every distant galaxy would be receding, as seen from any particular galaxy

If the expansion rate of the Universe were increasing with time, would the true expansion age be less than or greater than that derived by assuming a constant expansion rate?

If the recession speed of galaxies was slower in the past (contrary to the supposition in the previous question), the average recession speed, up till now, would be less than present value, & the true age of the Universe, calculated from d/vave, would be greater than the age calculated assuming the present value had remained constant, d/v0

Describe Olbers's paradox- the darkness of the night sky- and several possible resolutions

If the universe were infinite, with galaxies & stars everywhere, then any line-of-sight you looked at in the sky would terminate on a star, so the whole sky would have the surface brightness of a star & it would not be dark at night! Known as Olbers's paradox, it could be resolved if either of the two assumptions on which it's based were false, i.e. the universe is finite in size, or there aren't any stars beyond a certain distance (neither of which is presently supported by observational evidence). A better resolution arises if the universe is not infinitely old, but began at a certain time (the big bang, which is supported by observations). Then no light could reach us from anything with a lookback time greater than the age of the universe.

Why can relatively nearby galaxies give erroneous values for Hubble's constant?

Nearby galaxies are gravitationally affected by other galaxies in the clusters to which they belong, or other adjacent clusters. This induces peculiar motions which contribute to their observed recession speeds & give rise to errors in the derived value of Hubble's constant

A universe with ____ curvature is said to be "hyperbolic," shaped somewhat like a potato chip.

Negative.

If the expansion of the Universe is currently accelerating, can we conclude that the Universe will necessarily expand forever? Why?

Since little is currently known about the source of the dark energy which is causing the present accelerated expansion of the Universe, it cannot be concluded that it will continue unchanged in the future. Thus, the Universe might, or might not expand forever

Calculate the Hubble time if Hubble's constant is 71 km/s/Mpc.

T0 = 1/H0 = 1/(71 km/s/Mpc) = 1.41 x 10-2 Mpc-s/km. You only need to convert the units, 1 Mpc = 3.09 x 1019 km & 1 y = 3.16 x 107 s, to get the result in years: T0 = (1.41 x 10-2)(3.09 x 1019)(1 y/3.16 x 107) = 1.38 x 1010 y, or about 14 billion years.

What are some of the processes that will eventually occur if the Universe expands forever?

The Universe will go, from the present stelliferous era, through a degenerate era, a black-hole era, & eventually into a dark era, the details of which are described in Sec. 18.6.

Explain how Einstein's cosmological constant is relevant to the conclusion in question 22

The acceleration found by the distant supernovae studies is attributed to a long-range repulsion, similar to that produced by Einstein's cosmological constant

Define what we mean by the cosmological constant

The cosmological constant is a term, in Einstein's relativistic equations for the Universe that represents a long-range repulsive force, which can counteract gravity & make a static universe possible, or cause an accelerated expansion.

State the cosmological principle. Why is it a reasonable assumption?

The cosmological principle states that the Universe is uniform, i.e. isotropic & homogeneous, on the largest of scales, from our point of view.

Explain what we mean by the critical density of the Universe.

The critical value for the average density of matter in the Universe would allow the expansion of space to just barely continue forever, assuming no cosmological constant or dark energy. In other words, gravity would just be sufficient to slow the recessional speeds of galaxies to zero as time approaches infinity.

Describe how the current value of Hubble's constant is measured.

The current value of Hubble's constant, adopted in this text, combines the results of two methods (Sec. 18.2a). One relies on using Cepheid variables & Type Ia supernovae as "standard candles" (Sec.'s 18.3b & e) to estimate distances (from the inverse-square law & the apparent & intrinsic brightness) to galaxies with measured spectral redshifts. The other involves measurements of the properties of radiation left over from after the big bang, by WMAP

Does the average matter density appear to be large enough to close the Universe?

The currently accepted value for ΩM of about 0.27, given at the end of Sec. 18.4f, is not large enough, by itself, to close the Universe.

Discuss the main conclusion of the distant supernova studies, and its implications.

The two teams of astronomers, that measured high-redshift Type Ia supernovae, found the surprising result that the expansion of the Universe is accelerating. This Nobel prize-winning conclusion was based on observations that these very-distant supernovae were fainter & therefore even more distant than expected.

Discuss why omega M,, the ratio of the average matter density to the critical density of the Universe, is such an important parameter.

The value of ΩM, together with the contribution from dark energy (since Ωtotal = ΩX + ΩM), determines the geometry of space & the ultimate fate of the Universe.

Why might high-redshift supernovae appear fainter than expected, other than an acceleration of the expansion rate of the Universe?

They might have been intrinsically less bright early on, or they may have been dimmed by intervening dust, etc. However, neither of these possible explanations is supported by observations, whereas the greater distance to high-redshift supernovae, due to an accelerated expansion, is supported.

Summarize the possible types of overall geometry for a homogeneous, isotropic universe with a cosmological constant equal to zero.

Three Friedmann universes are allowed by the equations of general relativity & the stated assumptions (the cosmological principle with no cosmological constant): (i) a closed, finite universe, with positive curvature & average density greater than the critical density, which will eventually stop expanding & collapse to a big crunch; (ii) an open, infinite universe, with negative curvature & average density less than the critical density, which will expand forever; (iii) a flat universe with zero curvature & average density equal to the critical density, which will just barely expand forever.

According to the "cosmological principle," the Universe is homogeneous and isotropic on the largest size scales, but its properties can change with time.

True.

Most astronomers believe that "Olbers's paradox," the darkness of the night sky, is resolved by the fact that the Universe has a finite age.

True.

The cosmological constant was a concept introduced by Albert Einstein to support a static universe, one that is neither expanding nor contracting

True.

Explain how the effective center of expansion can be in an unobservable spatial dimension.

We can mathematically describe the shape of a space only if it is embedded in a space of higher dimensionality & the effective center of the lower-dimensional space can be outside it, at a point in the higher-dimensional space. For example, the two-dimensional space of the surface of a balloon has a center in three-dimensional space which is not on the balloon

What is the "age crisis" that rocked cosmology until the late 1900s? Discuss two developments that helped alleviate this crisis.

When earlier attempts were made to measure Hubble's constant, the values found often yielded an age of the Universe (the Hubble time, 1/H0) which was younger than the oldest globular clusters, leading to what was called the "age crisis". Better determinations of stellar distances, by the Hipparcos satellite, & more precise measurements of Hubble's constant, by HST's Key Project & WMAP, have dispelled the crisis.

Why are exploding white dwarf stars so useful for measuring the distances of galaxies?

White dwarfs, which capture too much matter from a companion, & explode as Type Ia supernovae, are all assumed to have the same mass (the Chandrasekhar limit) & the same luminosity. Therefore, they are useful as standard candles, for measuring the distance to galaxies, needed for determining Hubble's constant.

Describe how the geometry of the Universe is intimately connected to the ultimate fate of the Universe, assuming the cosmological constant is zero.

With no cosmological constant or dark energy, the types of Friedmann universes (Sec. 18.4c) possible with general relativity are: (i) closed & spherical (positive curvature); (ii) open & hyperbolic (negative curvature); (iii) critical & flat (no curvature). The ultimate fate of (i) is a big crunch, of (ii) is expansion forever, & of (iii) is recession speeds approaching zero as time becomes infinite.