Exercises
273
branes) goes through zero when the branes collide. Since the separation of the
boundary branes is related to the dilaton in the dual description, the dilaton
dynamics discussed in the previous section may be employed taking (the number
of uncompactified spatial dimensions to be) N = 4 (and ignoring the six
compactified dimensions.) As before, we require the universe to be expanding
after the big bang but now we choose the alternative solution in which the universe
is contracting before the big bang. Thus, the solution corresponds to the choice
}., = +(1/..{ii) In \t\ on both branches. For N = 4, this gives
1
2t;(t) - 2t/Jo = In \t\ a(t) Q( \tI 1 / 2 so that H = -.
(9.124)
2t
This choice is qualitatively different from the one made in pre-big-bang
cosmology. There, before the big bang, l/J(t) is positive and diverges as t -+ 0, so
that the gauge and gravitational interactions, whose strength is controlled by e~,
become strong and the vicinity of t = 0 is in a strongly-coupled regime. Here,
l/J(t) is negative near t = 0 and diverges as t -+ O. Instead of strong coupling,
the vicinity of t = 0 is in a weakly-coupled regime. When the branes collide,
radiation modes are excited by the kinetic energy of the collision and a hot big
bang is triggered.
The ekpyrotic universe allows a new solution to the horizon problem. The
collision of the two boundary branes is a non-local event over a region much larger
than the Hubble radius. It is this collision that generates the temperature of the hot
big-bang universe. Thus, a large degree of homogeneity in the cosmic microwave
background radiation is to be expected. However, a number of difficulties in
trying to get the ekpyrotic universe to explain things normally explained by
inflation has been pointed out. (See [20] and references therein.)
9.9 Exercises
1. Derive the curvature scalar of (9.66).
2. Derive the action (9.69).
3. Obtain the field equations (9.72H9.44) from the action (9.69).
4. Derive the finite-temperature equations (9.80) and (9.81).
5. Derive the solutions of the cosmological field equations for pre-big-bang
cosmology (9.113).
9.10 General references
The books and review articles that we have found most useful in preparing this
chapter are:
• Bailin D and Love A 1994 Supersymmetric Gauge Field Theory and String
Theory (Bristol: lOP)
273
branes) goes through zero when the branes collide. Since the separation of the
boundary branes is related to the dilaton in the dual description, the dilaton
dynamics discussed in the previous section may be employed taking (the number
of uncompactified spatial dimensions to be) N = 4 (and ignoring the six
compactified dimensions.) As before, we require the universe to be expanding
after the big bang but now we choose the alternative solution in which the universe
is contracting before the big bang. Thus, the solution corresponds to the choice
}., = +(1/..{ii) In \t\ on both branches. For N = 4, this gives
1
2t;(t) - 2t/Jo = In \t\ a(t) Q( \tI 1 / 2 so that H = -.
(9.124)
2t
This choice is qualitatively different from the one made in pre-big-bang
cosmology. There, before the big bang, l/J(t) is positive and diverges as t -+ 0, so
that the gauge and gravitational interactions, whose strength is controlled by e~,
become strong and the vicinity of t = 0 is in a strongly-coupled regime. Here,
l/J(t) is negative near t = 0 and diverges as t -+ O. Instead of strong coupling,
the vicinity of t = 0 is in a weakly-coupled regime. When the branes collide,
radiation modes are excited by the kinetic energy of the collision and a hot big
bang is triggered.
The ekpyrotic universe allows a new solution to the horizon problem. The
collision of the two boundary branes is a non-local event over a region much larger
than the Hubble radius. It is this collision that generates the temperature of the hot
big-bang universe. Thus, a large degree of homogeneity in the cosmic microwave
background radiation is to be expected. However, a number of difficulties in
trying to get the ekpyrotic universe to explain things normally explained by
inflation has been pointed out. (See [20] and references therein.)
9.9 Exercises
1. Derive the curvature scalar of (9.66).
2. Derive the action (9.69).
3. Obtain the field equations (9.72H9.44) from the action (9.69).
4. Derive the finite-temperature equations (9.80) and (9.81).
5. Derive the solutions of the cosmological field equations for pre-big-bang
cosmology (9.113).
9.10 General references
The books and review articles that we have found most useful in preparing this
chapter are:
• Bailin D and Love A 1994 Supersymmetric Gauge Field Theory and String
Theory (Bristol: lOP)