248
Inflation in supergravity
8.7 Exercises
I. Derive the effective potential of (8.3) from (8.1) using the superpotential
(8.2).
2. Derive the effective potential (8.10) for the superpotential (8.9) with minimal
kinetic terms.
3. Derive the effective potential (8.50) for a model of D-term inflation.
4. Check that the D-term inflation model effective potential (8.50) has a
minimum at 4>+ = 4>- = 0 when the inequality (8.51) is satisfied.
5. Estimate the minimum of the effective potential for the Polonyi field in the
presence of the inflaton field.
8.8 General references
The books and review articles that we have found most useful in preparing this
chapter are:
• Bailin D and Love A 1994 Super symmetric Gauge Field Theory and String
Theory (Bristol: lOP)
Bibliography
[1] Nanopoulos D V, Olive K A, Srednicki M and Tamvakis K 1983 Phys. Len. B 123 41
[2] Ho1mam H, Ramond P and Ross G G 1984 Phys. Len. B 137 343
[3] Steinhardt P I and Turner MS 1984 Phys. Rev. D 29 2162
[4] Ovrut B A and Steinhardt P I 1983 Phys. Len. B 133 161
[5] Golwirth D Sand Piran T 1992 Phys. Rep. 214223 and references therein
[6] Binetruy P and DvaIi G 1996 Phys. Lett. B 388 241, arXiv:hep-ph/9606342
[7] Linde A and Riotto A 1997 Phys. Rev. D 56 1841. arXiv:hep-ph/9703209
[8] Ellis I, Kim I E and Nanopoulos D V 1984 Phys. Len. B 145 181
[9] Ellis I, Gelmini G B and Sarkar S 1992 Nucl. Phys. B 373 399
[10] Ross G G and Sarkar S 1996 Nucl. Phys. B 461597, arXiv:hep-ph/9506283
[1 I] CoughJan G D et al 1983 Phys. Len. B 131 59
[12] Bailin D and Love A 1994 Supersymmetric Gauge Field Theory and String Theory
(Bristol: lOP)
[13] CoughJan G D. Holman R. Ramond P and Ross G G 1984 Phys. Len. B 140 44
[14] de Carlos B. Casas J A. Quevedo F and Roulet E 1993 Phys. Len. B 318447
Inflation in supergravity
8.7 Exercises
I. Derive the effective potential of (8.3) from (8.1) using the superpotential
(8.2).
2. Derive the effective potential (8.10) for the superpotential (8.9) with minimal
kinetic terms.
3. Derive the effective potential (8.50) for a model of D-term inflation.
4. Check that the D-term inflation model effective potential (8.50) has a
minimum at 4>+ = 4>- = 0 when the inequality (8.51) is satisfied.
5. Estimate the minimum of the effective potential for the Polonyi field in the
presence of the inflaton field.
8.8 General references
The books and review articles that we have found most useful in preparing this
chapter are:
• Bailin D and Love A 1994 Super symmetric Gauge Field Theory and String
Theory (Bristol: lOP)
Bibliography
[1] Nanopoulos D V, Olive K A, Srednicki M and Tamvakis K 1983 Phys. Len. B 123 41
[2] Ho1mam H, Ramond P and Ross G G 1984 Phys. Len. B 137 343
[3] Steinhardt P I and Turner MS 1984 Phys. Rev. D 29 2162
[4] Ovrut B A and Steinhardt P I 1983 Phys. Len. B 133 161
[5] Golwirth D Sand Piran T 1992 Phys. Rep. 214223 and references therein
[6] Binetruy P and DvaIi G 1996 Phys. Lett. B 388 241, arXiv:hep-ph/9606342
[7] Linde A and Riotto A 1997 Phys. Rev. D 56 1841. arXiv:hep-ph/9703209
[8] Ellis I, Kim I E and Nanopoulos D V 1984 Phys. Len. B 145 181
[9] Ellis I, Gelmini G B and Sarkar S 1992 Nucl. Phys. B 373 399
[10] Ross G G and Sarkar S 1996 Nucl. Phys. B 461597, arXiv:hep-ph/9506283
[1 I] CoughJan G D et al 1983 Phys. Len. B 131 59
[12] Bailin D and Love A 1994 Supersymmetric Gauge Field Theory and String Theory
(Bristol: lOP)
[13] CoughJan G D. Holman R. Ramond P and Ross G G 1984 Phys. Len. B 140 44
[14] de Carlos B. Casas J A. Quevedo F and Roulet E 1993 Phys. Len. B 318447