Inflation: Flow, fixed points and observables to arbitrary order in slow roll

I generalize the inflationary flow equations of Hoffman and Turner to arbitrary order in slow roll. This makes it possible to study the predictions of slow roll inflation in the full observable parameter space of tensor/scalar ratio

r

, spectral index

n

, and running

d n / d \ln k

. It also becomes possible to identify exact fixed points in the parameter flow. I numerically evaluate the flow equations to fifth order in slow roll for a set of randomly chosen initial conditions and find that the models cluster strongly in the observable parameter space, indicating a ``generic'' set of predictions for slow roll inflation. I comment briefly on the the interesting proposed correspondence between flow in inflationary parameter space and renormalization group flow in a boundary conformal field theory.

Note:

16 pages, 7 figures. LaTeX. V4: Fixed important error in numerical constant in the second-order slow roll expressions for the observables r, n, and dn/dlog(k). See footnote after Eq. (48). New figures, minor changes to conclusions. Supersedes version published in Phys. Rev. D Report-no: CU-TP-1061 Journal-ref: Phys.Rev. D66 (2002) 083508

98.80.Cq
inflation
Hamilton-Jacobi equation
fluctuation
fixed point
renormalization group
field theory: conformal
perturbation: scalar
perturbation: tensor
numerical calculations

References(48)

Figures(0)

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

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

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

Particle physics models of inflation and the cosmological density perturbation

David H. Lyth
(
- Lancaster U.
)
,
Antonio Riotto
(
- CERN
)

- Phys.Rept. 314 (1999) 1-146
•
e-Print:
- hep-ph/9807278
•
DOI:
- 10.1016/S0370-1573(98)00128-8

New constraints on inflation from the cosmic microwave background

William H. Kinney
(
- Florida U.
)
,
Alessandro Melchiorri
(
- Rome U.
)
,
Antonio Riotto
(
- Pisa, Scuola Normale Superiore
)

- Phys.Rev.D 63 (2001) 023505
•
e-Print:
- astro-ph/0007375
•
DOI:
- 10.1103/PhysRevD.63.023505

Constraints on inflation from CMB and Lyman alpha forest

S. Hannestad
(
- Nordita
)
,
S.H. Hansen
(
- Oxford U.
)
,
F.L. Villante
(
- Ferrara U. and
- INFN, Ferrara
)
,
A.J.S. Hamilton
(
- JILA, Boulder
)

- Astropart.Phys. 17 (2002) 375-382
•
e-Print:
- astro-ph/0103047
•
DOI:
- 10.1016/S0927-6505(01)00160-8

Cosmic microwave background measurements can discriminate among inflation models

Scott Dodelson
(
- Fermilab
)
,
William H. Kinney
(
- Fermilab
)
,
Edward W. Kolb
(
- Fermilab and
- Chicago U., EFI
)

- Phys.Rev.D 56 (1997) 3207-3215
•
e-Print:
- astro-ph/9702166
•
DOI:
- 10.1103/PhysRevD.56.3207

Constraining inflation with cosmic microwave background polarization

William H. Kinney
(
- Fermilab
)

- Phys.Rev.D 58 (1998) 123506
•
e-Print:
- astro-ph/9806259
•
DOI:
- 10.1103/PhysRevD.58.123506

Kinematic constraints to the key inflationary observables

Mark B. Hoffman
(
- Chicago U.
)
,
Michael S. Turner
(
)

- Phys.Rev.D 64 (2001) 023506
•
e-Print:
- astro-ph/0006321
•
DOI:
- 10.1103/PhysRevD.64.023506

Inflation and the dS / CFT correspondence

Andrew Strominger
(
- Harvard U.
)

- JHEP 11 (2001) 049
•
e-Print:
- hep-th/0110087
•
DOI:
- 10.1088/1126-6708/2001/11/049

De Sitter holography and the cosmic microwave background

- JHEP 04 (2002) 047
•
e-Print:
- hep-th/0202127
•
DOI:
- 10.1088/1126-6708/2002/04/047

On the Scalar Field Dynamics in a Spatially Flat Friedman Universe

A.G. Muslimov
(
- Ioffe Phys. Tech. Inst.
)

- Class.Quant.Grav. 7 (1990) 231-237
•
DOI:
- 10.1088/0264-9381/7/2/015

Nonlinear evolution of long wavelength metric fluctuations in inflationary models

D.S. Salopek
(
- Fermilab
)
,
J.R. Bond
(
- Canadian Inst. Theor. Astrophys.
)

- Phys.Rev.D 42 (1990) 3936-3962
•
DOI:
- 10.1103/PhysRevD.42.3936

Reconstructing the inflation potential : An overview

James E. Lidsey
(
- Queen Mary, U. of London
)
,
Andrew R. Liddle
(
- Sussex U.
)
,
Edward W. Kolb
(
)
,
Edmund J. Copeland
(
- Sussex U.
)
,
Tiago Barreiro
(
- Sussex U.
)

et al.

- Rev.Mod.Phys. 69 (1997) 373-410
•
e-Print:
- astro-ph/9508078
•
DOI:
- 10.1103/RevModPhys.69.373

The Development of Irregularities in a Single Bubble Inflationary Universe

S.W. Hawking
(
- Cambridge U.
)

- Phys.Lett.B 115 (1982) 295,
- In *Abbott, L.F. (ed.), Pi, S.Y. (ed.): Inflationary cosmology*, 235-237. (Phys. Lett. B115 (1982) 295-297). (see Book Index)
•
DOI:
- 10.1016/0370-2693(82)90373-2

Dynamics of Phase Transition in the New Inflationary Universe Scenario and Generation of Perturbations

Alexei A. Starobinsky
(
- Landau Inst.
)

- Phys.Lett.B 117 (1982) 175-178,
- Phys. Lett. B117 ( 1982) 175-178
•
DOI:
- 10.1016/0370-2693(82)90541-X

Fluctuations in the New Inflationary Universe

Alan H. Guth
(
- MIT, LNS
)
,
S.Y. Pi
(
- Harvard U. and
- New Hampshire U.
)

- Phys.Rev.Lett. 49 (1982) 1110-1113,
- In *Abbott, L.F. (ed.), Pi, S.Y. (ed.): Inflationary cosmology*, 231-234
•
DOI:
- 10.1103/PhysRevLett.49.1110

Spontaneous Creation of Almost Scale - Free Density Perturbations in an Inflationary Universe

- Phys.Rev.D 28 (1983) 679,
- In *Abbott, L.F. (ed.), Pi, S.Y. (ed.): Inflationary cosmology*, 242-256. (Phys. Rev. D28 (1983) 679-693) and Pennsylvania Univ. Philadelphia - UPR-0202T (rec.May 83) 55 p. (307007) (see Book Index)
•
DOI:
- 10.1103/PhysRevD.28.679