Chapter Chapter 1 1
The The standard standard model model of of cosmology cosmology
1.1 1.1 Introduction Introduction
The The principal principal concern concern of of this this book book is is the the way way in in which which recent recent particle particle physics, physics,
including including electroweak electroweak theory, theory, quantum quantum chromodynamics, chromodynamics, grand grand unified unified theory, theory,
supersymmetry, supersymmetry, supergravity supergravity and and superstring superstring theory, theory, has has changed changed our our standpoint standpoint
on on the the history history of of the the universe universe when when its its temperature temperature was was greater greater than than 10 10 15 15 K. K. This This
will will be be studied studied in in the the context context of of the the Friedman-Robertson-Walker Friedman-Robertson-Walker solution solution of of the the
Einstein Einstein equations equations of of general general relativity. relativity. In In this this chapter, chapter, therefore, therefore, our our first first task task
is is the the derivation derivation of of the the field field equations equations relating relating the the scale scale factor factor R(t) R(t) that that appears appears
in in the the metric metric to to the the energy energy density density p p and and the the pressure pressure p p that that characterize characterize the the
(assumed (assumed homogeneous homogeneous and and isotropic) isotropic) energy-momentum energy-momentum tensor. tensor. This This is is done done
in in the the following following two two sections. sections. In In section section 1.4 1.4 we we show show how, how, for for a a given given equation equation
of of state, state, energy-momentum energy-momentum conservation conservation determines determines the the scale scale dependence dependence of of the the
energy energy density density and and pressure. pressure. The The standard standard solutions solutions for for the the time time dependence dependence of of
the the scale scale factor factor in in a a radiation-dominated radiation-dominated universe, universe, in in a a matter-dominated matter-dominated universe, universe,
and and in in a a cosmological cosmological constant-dominated constant-dominated universe universe are are presented presented in in section section I.S; I.S;
we we give give an an estimate estimate of of the the age age of of the the universe universe in in the the matter-dominated matter-dominated case case in in
section section 1.6. 1.6. In In section section 1.7, 1.7, we we present present the the evidence evidence that that there there is, is, in in fact, fact, a a non- nonzero zero cosmological cosmological constant constant and and discuss discuss why why its its size size is is so so difficult difficult to to explain. explain. The The
discussion discussion of of phase phase transitions transitions and and of of relics relics that that is is given given in in later later chapters chapters also also
requires requires a a description description of of the the thermodynamics thermodynamics of of the the universe. universe. So So in in the the following following
two two sections sections we we describe describe the the equilibrium equilibrium thermodynamics thermodynamics of of the the expanding expanding
universe universe and and derive derive the the time time dependence dependence of of the the temperature temperature in in the the various various epochs. epochs.
In In section section l.lO, l.lO, we we discuss discuss briefly briefly the the 'recombination' 'recombination' of of protons protons and and electrons electrons
that that left left the the presently presently observed observed cosmic cosmic microwave microwave background background radiation. radiation. Finally, Finally,
the the synthesis synthesis of of the the light light elements elements that that commenced commenced towards towards the the end end of of the the first first
three three minutes minutes is is discussed discussed in in section section 1.11. 1.11. The The consistency consistency of of the the predicted predicted
abundances abundances with with those those inferred inferred from from the the measured measured abundances abundances determines determines the the
so-called so-called baryon baryon asymmetry asymmetry of of the the universe, universe, whose whose origin origin is is discussed discussed at at length length
in in chapter chapter 4. 4.
DOl: DOl: 10.1201/9780367806637-1 10.1201/9780367806637-1
1
The The standard standard model model of of cosmology cosmology
1.1 1.1 Introduction Introduction
The The principal principal concern concern of of this this book book is is the the way way in in which which recent recent particle particle physics, physics,
including including electroweak electroweak theory, theory, quantum quantum chromodynamics, chromodynamics, grand grand unified unified theory, theory,
supersymmetry, supersymmetry, supergravity supergravity and and superstring superstring theory, theory, has has changed changed our our standpoint standpoint
on on the the history history of of the the universe universe when when its its temperature temperature was was greater greater than than 10 10 15 15 K. K. This This
will will be be studied studied in in the the context context of of the the Friedman-Robertson-Walker Friedman-Robertson-Walker solution solution of of the the
Einstein Einstein equations equations of of general general relativity. relativity. In In this this chapter, chapter, therefore, therefore, our our first first task task
is is the the derivation derivation of of the the field field equations equations relating relating the the scale scale factor factor R(t) R(t) that that appears appears
in in the the metric metric to to the the energy energy density density p p and and the the pressure pressure p p that that characterize characterize the the
(assumed (assumed homogeneous homogeneous and and isotropic) isotropic) energy-momentum energy-momentum tensor. tensor. This This is is done done
in in the the following following two two sections. sections. In In section section 1.4 1.4 we we show show how, how, for for a a given given equation equation
of of state, state, energy-momentum energy-momentum conservation conservation determines determines the the scale scale dependence dependence of of the the
energy energy density density and and pressure. pressure. The The standard standard solutions solutions for for the the time time dependence dependence of of
the the scale scale factor factor in in a a radiation-dominated radiation-dominated universe, universe, in in a a matter-dominated matter-dominated universe, universe,
and and in in a a cosmological cosmological constant-dominated constant-dominated universe universe are are presented presented in in section section I.S; I.S;
we we give give an an estimate estimate of of the the age age of of the the universe universe in in the the matter-dominated matter-dominated case case in in
section section 1.6. 1.6. In In section section 1.7, 1.7, we we present present the the evidence evidence that that there there is, is, in in fact, fact, a a non- nonzero zero cosmological cosmological constant constant and and discuss discuss why why its its size size is is so so difficult difficult to to explain. explain. The The
discussion discussion of of phase phase transitions transitions and and of of relics relics that that is is given given in in later later chapters chapters also also
requires requires a a description description of of the the thermodynamics thermodynamics of of the the universe. universe. So So in in the the following following
two two sections sections we we describe describe the the equilibrium equilibrium thermodynamics thermodynamics of of the the expanding expanding
universe universe and and derive derive the the time time dependence dependence of of the the temperature temperature in in the the various various epochs. epochs.
In In section section l.lO, l.lO, we we discuss discuss briefly briefly the the 'recombination' 'recombination' of of protons protons and and electrons electrons
that that left left the the presently presently observed observed cosmic cosmic microwave microwave background background radiation. radiation. Finally, Finally,
the the synthesis synthesis of of the the light light elements elements that that commenced commenced towards towards the the end end of of the the first first
three three minutes minutes is is discussed discussed in in section section 1.11. 1.11. The The consistency consistency of of the the predicted predicted
abundances abundances with with those those inferred inferred from from the the measured measured abundances abundances determines determines the the
so-called so-called baryon baryon asymmetry asymmetry of of the the universe, universe, whose whose origin origin is is discussed discussed at at length length
in in chapter chapter 4. 4.
DOl: DOl: 10.1201/9780367806637-1 10.1201/9780367806637-1
1