provides a period/luminosity relationship between Cepheid variable stars, allowing
an inference of the intrinsic brightness—and hence the distance—to any such star
observed. Since Hubble could measure the apparent brightness and then the period
of these Cepheids, a distance could be calculated.
By continuing on to measure Cepheids in a slew of spiral nebulae, Hubble and his
assistant, Humason, derived the distance to a large number of galaxies. Complementary to that data set was Vesto Slipher’s work, which noted the large redshifts of
the spectral lines in a myriad of spiral and elliptical nebulae, corresponding to large
recession velocities. These two data sets were first combined by Georges Lemaître to
derive a redshift-distance relation, and then more robustly and independently by
Hubble himself. This relationship is now known as Hubble’s Law and has an
astounding implication in the context of Einstein’s relativity: that the fabric of
space itself is expanding over time. The reason light gets redshifted is because the
space between the emitting source and us, the observer, is stretching.
The rate of expansion is determined, on the observational side, by the measured
Hubble constant, while on the theoretical side, it’s a combination of the Universe’s
initial conditions along with the ratio of the various energy components present in
the Universe. Although there are many possible cosmologies that admit expanding
space like this, one of the most straightforward was put forth by George Gamow in
what would grow into the idea of the Big Bang. If space was expanding and
stretching, that implied that any gravitationally bound objects within it, like individual, isolated galaxies, would be expanding away from one another. Similarly, any
radiation within this space would be stretched as is traveled through the Universe,
causing its wavelength to lengthen and its energy to decrease. As you moved farther
and farther forward in time, the Universe would become more dilute, and the
temperature of the Universe would become cooler.
But as you extrapolated in the opposite direction—backwards in time—you’d
move towards a hotter, denser, more uniform state. If the Universe becomes cooler,
sparser, and gravitationally clumpier as we move forward in time, then the converse
would be true as we moved backwards. Since the volume of our three-dimensional
space scales is a
3 , where a is the scale factor of the Universe, and the energy of an
individual photon scales is a
À1 , this implies that the matter density will shrink as
a
À3 , while the radiation density will shrink as a
À4 . If we define the scale factor today,
a 0 , to equal 1, then we can extrapolate back to earlier times where the Universe was
denser, hotter, and more uniform, and we can do this in a quantitative fashion, noting
the cosmological implications along the way.
The remainder of these proceedings is laid out as follows. Section 9.2 focuses on
the classical steps that take place as we move through time in the standard hot Big
Bang. Section 9.3 focuses on the puzzles that arise if we extrapolate back to
arbitrarily high temperatures, energies, and densities in such a model. Section 9.4
presents the solution to these puzzles in the form of cosmological inflation and
includes the novel, generic predictions that arise from inflation and the status of
where, whether, and how well they’ve been measured and tested. Finally, Sect. 9.5
presents an in-depth discussion of the implications for what occurred in our Universe
before the Big Bang.
86
E. R. Siegel
an inference of the intrinsic brightness—and hence the distance—to any such star
observed. Since Hubble could measure the apparent brightness and then the period
of these Cepheids, a distance could be calculated.
By continuing on to measure Cepheids in a slew of spiral nebulae, Hubble and his
assistant, Humason, derived the distance to a large number of galaxies. Complementary to that data set was Vesto Slipher’s work, which noted the large redshifts of
the spectral lines in a myriad of spiral and elliptical nebulae, corresponding to large
recession velocities. These two data sets were first combined by Georges Lemaître to
derive a redshift-distance relation, and then more robustly and independently by
Hubble himself. This relationship is now known as Hubble’s Law and has an
astounding implication in the context of Einstein’s relativity: that the fabric of
space itself is expanding over time. The reason light gets redshifted is because the
space between the emitting source and us, the observer, is stretching.
The rate of expansion is determined, on the observational side, by the measured
Hubble constant, while on the theoretical side, it’s a combination of the Universe’s
initial conditions along with the ratio of the various energy components present in
the Universe. Although there are many possible cosmologies that admit expanding
space like this, one of the most straightforward was put forth by George Gamow in
what would grow into the idea of the Big Bang. If space was expanding and
stretching, that implied that any gravitationally bound objects within it, like individual, isolated galaxies, would be expanding away from one another. Similarly, any
radiation within this space would be stretched as is traveled through the Universe,
causing its wavelength to lengthen and its energy to decrease. As you moved farther
and farther forward in time, the Universe would become more dilute, and the
temperature of the Universe would become cooler.
But as you extrapolated in the opposite direction—backwards in time—you’d
move towards a hotter, denser, more uniform state. If the Universe becomes cooler,
sparser, and gravitationally clumpier as we move forward in time, then the converse
would be true as we moved backwards. Since the volume of our three-dimensional
space scales is a
3 , where a is the scale factor of the Universe, and the energy of an
individual photon scales is a
À1 , this implies that the matter density will shrink as
a
À3 , while the radiation density will shrink as a
À4 . If we define the scale factor today,
a 0 , to equal 1, then we can extrapolate back to earlier times where the Universe was
denser, hotter, and more uniform, and we can do this in a quantitative fashion, noting
the cosmological implications along the way.
The remainder of these proceedings is laid out as follows. Section 9.2 focuses on
the classical steps that take place as we move through time in the standard hot Big
Bang. Section 9.3 focuses on the puzzles that arise if we extrapolate back to
arbitrarily high temperatures, energies, and densities in such a model. Section 9.4
presents the solution to these puzzles in the form of cosmological inflation and
includes the novel, generic predictions that arise from inflation and the status of
where, whether, and how well they’ve been measured and tested. Finally, Sect. 9.5
presents an in-depth discussion of the implications for what occurred in our Universe
before the Big Bang.
86
E. R. Siegel