Recovering the inflationary potential

Michael S. Turner

doi:10.1103/PhysRevD.48.5539

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Recovering the inflationary potential

Michael S. Turner

Departments of Physics and of Astronomy and Astrophysics, Enrico Fermi Institute, The University of Chicago, Chicago, Illinois 60637-1433 and NASA/Fermilab Astrophysics Center, Fermi National Accelerator Laboratory, Batavia, Illinois 60510-0500

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Phys. Rev. D 48, 5539 – Published 15 December, 1993

DOI: https://doi.org/10.1103/PhysRevD.48.5539

Abstract

A procedure is developed for the recovery of the inflationary potential over the interval that affects astrophysical scales (≈1 Mpc to $10^{4}$ Mpc). The amplitudes of the scalar and tensor metric perturbations and their power-spectrum indices, which in principle can be inferred from large-angle CBR anisotropy and other cosmological data, determine the value of the inflationary potential and its first two derivatives. From these, the inflationary potential can be reconstructed in a Taylor series and the consistency of the inflationary hypothesis tested. Examples are presented, and the effect of observational uncertainties is discussed.

References (17)

G. Smoot et al., Astrophys. J. 396, L1 (1992) E. L. Wright et al., ibid.396 L13 (1992)
K. Ganga, E. S. Cheng, S. S. Meyer, and L. A. Page, Astrophys. J. 410, L57 (1993)
N. Turok, Phys. Rev. Lett. 63, 2652 (1989) N. Turok and D. Spergel, ibid. 64, 2736 (1990) A. Albrecht and A. Stebbins, ibid. 69, 2615 (1992) D. Bennett, A. Stebbins, and F. Bouchet, Astrophys. J. 399, L5 (1992) U. Pen, D. Spergel, and N. Turok, Princeton Univ. report, 1993 (unpublished)
P. J. E. Peebles, Nature (London) 327, 210 (1987) Astrophys. J. 315, L73 (1987) R. Cen, J. P. Ostriker, and P. J. E. Peebles, ibid. 415, 423 (1993)
J. P. Ostriker, Annu. Rev. Astron. Astrophys. 31, 689 (1993) M. S. Turner, in Proceedings of TASI-92, edited by J. A. Harvey and J. Polchinski (World Scientific, Singapore, 1993), p. 165
(a) H. M. Hodges and G. R. Blumenthal, Phys. Rev. D 42, 3329 (1990) (b) R. Davis et al., Phys. Rev. Lett. 69, 1856 (1992) D. Salopek, ibid. 69, 3602 (1992) F. Lucchin et al., Astrophys. J. 401, L49 (1992) A. Liddle and D. Lyth, Phys. Lett. B 291, 391 (1992) J. E. Lidsey and P. Coles, Mon. Not. R. Astron. Soc. 358, 57 (1992) T. Souradeep and V. Sahni, Mod. Phys. Lett. A 7, 3541 (1992) (c) E. Copeland et al., Phys. Rev. Lett. 71, 219 (1993) Phys. Rev. D 48, 2529 (1993)
M. S. Turner, Phys. Rev. D 48, 3502 (1993) Liddle and Lyth [[6]]
R. Davis et al., Phys. Rev. Lett. 69, 1856 (1992)
R. Crittenden et al., Phys. Rev. Lett. 71, 324 (1993) R. Crittenden, R. Davis, and P. J. Steinhardt, Astrophys. J. 417, L13 (1993)
D. Salopek, J. R. Bond, and J. M. Bardeen, Phys. Rev. D 40, 1753 (1989) H. M. Hodges, G. R. Blumenthal, J. R. Primack, and L. Kofman, Nucl. Phys. B335, 197 (1990)
P. J. Steinhardt and M. S. Turner, Phys. Rev. D 29, 2162 (1984)
A. D. Linde, Phys. Lett. 129B, 177 (1983) V. Belinsky, L. Grishchuk, I. Khalatanikov, and Ya. B. Zel'dovich, ibid. 155B, 232 (1985)
M. S. Turner, M. White, and J. Lidsey, Phys. Rev. D 48, 4613 (1993)
D. La and P. J. Steinhardt, Phys. Rev. Lett. 62, 376 (1989) E. W. Kolb, D. Salopek, and M. S. Turner, Phys. Rev. D 42, 3925 (1990)
F. Adams et al., Phys. Rev. D 47, 426 (1993) J. Gelb et al., Astrophys. J. 403, L5 (1993) R. Cen et al., ibid. 399, L11 (1992)
K. Freese, J. Frieman, and A. Olinto, Phys. Rev. Lett. 65, 3233 (1990)
J. D. Barrow and A. R. Liddle, Phys. Rev. D 47, R5219 (1993)

[c1] G. Smoot et al., Astrophys. J. 396, L1 (1992) E. L. Wright et al., ibid.396 L13 (1992)

[c2] K. Ganga, E. S. Cheng, S. S. Meyer, and L. A. Page, Astrophys. J. 410, L57 (1993)

[c3] N. Turok, Phys. Rev. Lett. 63, 2652 (1989) N. Turok and D. Spergel, ibid. 64, 2736 (1990) A. Albrecht and A. Stebbins, ibid. 69, 2615 (1992) D. Bennett, A. Stebbins, and F. Bouchet, Astrophys. J. 399, L5 (1992) U. Pen, D. Spergel, and N. Turok, Princeton Univ. report, 1993 (unpublished)

[c4] P. J. E. Peebles, Nature (London) 327, 210 (1987) Astrophys. J. 315, L73 (1987) R. Cen, J. P. Ostriker, and P. J. E. Peebles, ibid. 415, 423 (1993)

[c5] J. P. Ostriker, Annu. Rev. Astron. Astrophys. 31, 689 (1993) M. S. Turner, in Proceedings of TASI-92, edited by J. A. Harvey and J. Polchinski (World Scientific, Singapore, 1993), p. 165

[c6] (a) H. M. Hodges and G. R. Blumenthal, Phys. Rev. D 42, 3329 (1990) (b) R. Davis et al., Phys. Rev. Lett. 69, 1856 (1992) D. Salopek, ibid. 69, 3602 (1992) F. Lucchin et al., Astrophys. J. 401, L49 (1992) A. Liddle and D. Lyth, Phys. Lett. B 291, 391 (1992) J. E. Lidsey and P. Coles, Mon. Not. R. Astron. Soc. 358, 57 (1992) T. Souradeep and V. Sahni, Mod. Phys. Lett. A 7, 3541 (1992) (c) E. Copeland et al., Phys. Rev. Lett. 71, 219 (1993) Phys. Rev. D 48, 2529 (1993)

[c7] M. S. Turner, Phys. Rev. D 48, 3502 (1993) Liddle and Lyth [[6]]

[c8] R. Davis et al., Phys. Rev. Lett. 69, 1856 (1992)

[c9] R. Crittenden et al., Phys. Rev. Lett. 71, 324 (1993) R. Crittenden, R. Davis, and P. J. Steinhardt, Astrophys. J. 417, L13 (1993)

[c10] D. Salopek, J. R. Bond, and J. M. Bardeen, Phys. Rev. D 40, 1753 (1989) H. M. Hodges, G. R. Blumenthal, J. R. Primack, and L. Kofman, Nucl. Phys. B335, 197 (1990)

[c11] P. J. Steinhardt and M. S. Turner, Phys. Rev. D 29, 2162 (1984)

[c12] A. D. Linde, Phys. Lett. 129B, 177 (1983) V. Belinsky, L. Grishchuk, I. Khalatanikov, and Ya. B. Zel'dovich, ibid. 155B, 232 (1985)

[c13] M. S. Turner, M. White, and J. Lidsey, Phys. Rev. D 48, 4613 (1993)

[c14] D. La and P. J. Steinhardt, Phys. Rev. Lett. 62, 376 (1989) E. W. Kolb, D. Salopek, and M. S. Turner, Phys. Rev. D 42, 3925 (1990)

[c15] F. Adams et al., Phys. Rev. D 47, 426 (1993) J. Gelb et al., Astrophys. J. 403, L5 (1993) R. Cen et al., ibid. 399, L11 (1992)

[c16] K. Freese, J. Frieman, and A. Olinto, Phys. Rev. Lett. 65, 3233 (1990)

[c17] J. D. Barrow and A. R. Liddle, Phys. Rev. D 47, R5219 (1993)

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Recovering the inflationary potential

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