Reconstruction of the Scalar Field Potential in Inflationary Models with a Gauss-Bonnet term

We consider inflationary models with a Gauss-Bonnet term to reconstruct the scalar-field potentials and the Gauss-Bonnet coupling functions. Both expressions are derived from the observationally favored configurations of ns and r. Our result implies that, for the reconstructed potentials and coupling functions, the blue tilt of inflationary tensor fluctuations can be realized. To achieve a blue tilt for the inflationary tensor fluctuations, a scalar field must climb up its potential before rolling down. We further investigate the properties of propagation of the perturbation modes in Friedmann-Robertson-Walker spacetime. For the reconstructed configurations that give rise to the blue tilt for the inflationary tensor fluctuations, we show that the ghosts and instabilities are absent with the superluminal propagation speeds for the scalar perturbation modes, whereas the propagation speeds of the tensor perturbations are subluminal.

Note:

13 pages, 6 figures

field theory: scalar
potential: scalar
perturbation: scalar
perturbation: tensor
power spectrum: scalar
power spectrum: tensor
inflation
gravitation: model
Gauss-Bonnet term

References(31)

Figures(12)

[1]

Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results

WMAP

Collaboration

•

G. Hinshaw
(
- British Columbia U.
)

et al.

- Astrophys.J.Suppl. 208 (2013) 19
•
e-Print:
- 1212.5226
•
DOI:
- 10.1088/0067-0049/208/2/19

[1]

Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation

WMAP

Collaboration

•

E. Komatsu
(
- Texas U.
)

et al.

- Astrophys.J.Suppl. 192 (2011) 18
•
e-Print:
- 1001.4538
•
DOI:
- 10.1088/0067-0049/192/2/18

[1]

Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation

WMAP

Collaboration

•

E. Komatsu
(
- Texas U.
)

et al.

- Astrophys.J.Suppl. 180 (2009) 330-376
•
e-Print:
- 0803.0547
•
DOI:
- 10.1088/0067-0049/180/2/330

[2]

Planck 2013 results. XVI. Cosmological parameters

Planck

Collaboration

•

P.A.R. Ade
(
- Cardiff U.
)

et al.

- Astron.Astrophys. 571 (2014) A16
•
e-Print:
- 1303.5076
•
DOI:
- 10.1051/0004-6361/201321591

[2]

Planck 2013 results. XXII. Constraints on inflation

Planck

Collaboration

•

P.A.R. Ade
(
- Cardiff U.
)

et al.

- Astron.Astrophys. 571 (2014) A22
•
e-Print:
- 1303.5082
•
DOI:
- 10.1051/0004-6361/201321569

[3]

Planck 2015 results. XIII. Cosmological parameters

Planck

Collaboration

•

P.A.R. Ade
(
- Cardiff U.
)

et al.

- Astron.Astrophys. 594 (2016) A13
•
e-Print:
- 1502.01589
•
DOI:
- 10.1051/0004-6361/201525830

[3]

Planck 2015 results. XX. Constraints on inflation

Planck

Collaboration

•

P.A.R. Ade
(
- Cardiff U.
)

et al.

- Astron.Astrophys. 594 (2016) A20
•
e-Print:
- 1502.02114
•
DOI:
- 10.1051/0004-6361/201525898

[4]

The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems

Alan H. Guth
(
- SLAC
)

- Phys.Rev.D 23 (1981) 347-356,
- Adv.Ser.Astrophys.Cosmol. 3 (1987) 139-148 (reprint)
•
DOI:
- 10.1103/PhysRevD.23.347

[4]

Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking

- Phys.Rev.Lett. 48 (1982) 1220-1223,
- Adv.Ser.Astrophys.Cosmol. 3 (1987) 158-161 (reprint)
•
DOI:
- 10.1103/PhysRevLett.48.1220

[4]

A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems

Andrei D. Linde
(
- Lebedev Inst.
)

- Phys.Lett.B 108 (1982) 389-393,
- In *Moscow 1981, Proceedings, Quantum Gravity*, 185-195 and Moscow Inst. Phys. Acad. Sci. - 81-229 (81,REC.DEC.) 15p,
- Adv.Ser.Astrophys.Cosmol. 3 (1987) 149-153 (reprint)
•
DOI:
- 10.1016/0370-2693(82)91219-9