Warped radion inflation
Tóm tắt
We show that the radion in a warped geometry bounded by two branes can have a potential suitable for inflation. Our construction is based upon a solution known in string theory as the linear dilaton, in which the back-reaction from a bulk scalar Φ is exactly accounted for. The radion, stabilized by Φ, is much heavier than the TeV scale and its couplings to the standard model are much more suppressed than in the usual Randall-Sundrum solution. We present a new formalism for obtaining approximate time-dependent solutions, based on perturbing the exact solution to the coupled Einstein and scalar field equations in the bulk. It allows the radion potential to be computed directly in terms of the brane potentials for Φ. We show that simple exponential potentials on the branes can lead to a 4D radion potential with a flattened hilltop form, yielding inflation with a spectral index of typically n
s = 0.96 and no higher than 0.99. With more complicated brane potentials, the descent from the hilltop can be a linear potential, giving a tensor-to-scalar ratio as large as r = 0.07 with n
s = 0.974. The couplings of the radion to the standard model particles are dictated by general covariance, so the details of reheating are explicitly calculable, leading to a reheat temperature of at least 107 GeV. The quantum corrections to the inflaton potential from its couplings to matter are also calculable and are shown to be small, so that the prediction for the shape of the potential is under theoretical control, even with superPlanckian field excursions.
Tài liệu tham khảo
P. Hořava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B 475 (1996) 94 [hep-th/9603142] [INSPIRE].
P. Hořava and E. Witten, Heterotic and type-I string dynamics from eleven-dimensions, Nucl. Phys. B 460 (1996) 506 [hep-th/9510209] [INSPIRE].
L. Randall and R. Sundrum, A Large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].
W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447] [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos, N. Kaloper and J. March-Russell, Rapid asymmetric inflation and early cosmology in theories with submillimeter dimensions, Nucl. Phys. B 567 (2000) 189 [hep-ph/9903224] [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos and G. Dvali, The Hierarchy problem and new dimensions at a millimeter, Phys. Lett. B 429 (1998) 263 [hep-ph/9803315] [INSPIRE].
I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G. Dvali, New dimensions at a millimeter to a Fermi and superstrings at a TeV, Phys. Lett. B 436 (1998) 257 [hep-ph/9804398] [INSPIRE].
J.M. Cline, Inflation from extra dimensions, Phys. Rev. D 61 (2000) 023513 [hep-ph/9904495] [INSPIRE].
R. Sundrum and C.M. Wells, Warped Hybrid Inflation, JHEP 02 (2010) 097 [arXiv:0909.3254] [INSPIRE].
A. Vilenkin, Topological inflation, Phys. Rev. Lett. 72 (1994) 3137 [hep-th/9402085] [INSPIRE].
A.D. Linde and D.A. Linde, Topological defects as seeds for eternal inflation, Phys. Rev. D 50 (1994) 2456 [hep-th/9402115] [INSPIRE].
R.C. Myers, New Dimensions for Old Strings, Phys. Lett. B 199 (1987) 371 [INSPIRE].
E. Kiritsis, C. Kounnas and D. Lüst, A Large class of new gravitational and axionic backgrounds for four-dimensional superstrings, Int. J. Mod. Phys. A 9 (1994) 1361 [hep-th/9308124] [INSPIRE].
J. Polchinski, String Theory, Vol. 1, An Introduction to the Bosonic String, Cambridge University Press (2000).
O. DeWolfe, D. Freedman, S. Gubser and A. Karch, Modeling the fifth-dimension with scalars and gravity, Phys. Rev. D 62 (2000) 046008 [hep-th/9909134] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-de Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].
P. Kanti, S.-c. Lee and K.A. Olive, Stable, time dependent, exact solutions for brane models with a bulk scalar field, Phys. Rev. D 67 (2003) 024037 [hep-ph/0209036] [INSPIRE].
N. Kaloper, Bent domain walls as brane worlds, Phys. Rev. D 60 (1999) 123506 [hep-th/9905210] [INSPIRE].
J.M. Cline and H. Firouzjahi, Brane world cosmology of modulus stabilization with a bulk scalar field, Phys. Rev. D 64 (2001) 023505 [hep-ph/0005235] [INSPIRE].
D. Langlois and M. Rodriguez-Martinez, Brane cosmology with a bulk scalar field, Phys. Rev. D 64 (2001) 123507 [hep-th/0106245] [INSPIRE].
K. Koyama and K. Takahashi, Primordial fluctuations in bulk inflaton model, Phys. Rev. D 67 (2003) 103503 [hep-th/0301165] [INSPIRE].
K. Koyama and K. Takahashi, Exactly solvable model for cosmological perturbations in dilatonic brane worlds, Phys. Rev. D 68 (2003) 103512 [hep-th/0307073] [INSPIRE].
C. Csáki, M.L. Graesser and G.D. Kribs, Radion dynamics and electroweak physics, Phys. Rev. D 63 (2001) 065002 [hep-th/0008151] [INSPIRE].
J.M. Cline and H. Firouzjahi, Five-dimensional warped cosmological solutions with radius stabilization by a bulk scalar, Phys. Lett. B 495 (2000) 271 [hep-th/0008185] [INSPIRE].
C. Csáki, M. Graesser, L. Randall and J. Terning, Cosmology of brane models with radion stabilization, Phys. Rev. D 62 (2000) 045015 [hep-ph/9911406] [INSPIRE].
L. Kofman, J. Martin and M. Peloso, Exact identification of the radion and its coupling to the observable sector, Phys. Rev. D 70 (2004) 085015 [hep-ph/0401189] [INSPIRE].
V.F. Mukhanov, Gravitational Instability of the Universe Filled with a Scalar Field, JETP Lett. 41 (1985) 493 [Pisma Zh. Eksp. Teor. Fiz. 41 (1985) 402]. [INSPIRE].
M. Sasaki, Large Scale Quantum Fluctuations in the Inflationary Universe, Prog. Theor. Phys. 76 (1986) 1036 [INSPIRE].
P. Brax, C. van de Bruck, A. Davis and C. Rhodes, Cosmological evolution of brane world moduli, Phys. Rev. D 67 (2003) 023512 [hep-th/0209158] [INSPIRE].
J. Lesgourgues and L. Sorbo, Goldberger-Wise variations: Stabilizing brane models with a bulk scalar, Phys. Rev. D 69 (2004) 084010 [hep-th/0310007] [INSPIRE].
J. Blanco-Pillado et al., Racetrack inflation, JHEP 11 (2004) 063 [hep-th/0406230] [INSPIRE].
L. Boubekeur and D. Lyth, Hilltop inflation, JCAP 07 (2005) 010 [hep-ph/0502047] [INSPIRE].
J. Blanco-Pillado et al., Inflating in a better racetrack, JHEP 09 (2006) 002 [hep-th/0603129] [INSPIRE].
P. Brax, S.C. Davis and M. Postma, The Robustness of n s < 0.95 in racetrack inflation, JCAP 02 (2008) 020 [arXiv:0712.0535] [INSPIRE].
K. Kohri, C.-M. Lin and D.H. Lyth, More hilltop inflation models, JCAP 12 (2007) 004 [arXiv:0707.3826] [INSPIRE].
C. Burgess, J.M. Cline and M. Postma, Axionic D3-D7 Inflation, JHEP 03 (2009) 058 [arXiv:0811.1503] [INSPIRE].
D.H. Lyth and A. Riotto, Particle physics models of inflation and the cosmological density perturbation, Phys. Rept. 314 (1999) 1 [hep-ph/9807278] [INSPIRE].
D.H. Lyth, What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?, Phys. Rev. Lett. 78 (1997) 1861 [hep-ph/9606387] [INSPIRE].
G. Efstathiou and K.J. Mack, The Lyth bound revisited, JCAP 05 (2005) 008 [astro-ph/0503360] [INSPIRE].
S. Hotchkiss, A. Mazumdar and S. Nadathur, Observable gravitational waves from inflation with small field excursions, JCAP 2 (2012) 8 [arXiv:1110.5389] [INSPIRE].
L. McAllister, E. Silverstein and A. Westphal, Gravity Waves and Linear Inflation from Axion Monodromy, Phys. Rev. D 82 (2010) 046003 [arXiv:0808.0706] [INSPIRE].
M. Cicoli, C. Burgess and F. Quevedo, Fibre Inflation: Observable Gravity Waves from IIB String Compactifications, JCAP 03 (2009) 013 [arXiv:0808.0691] [INSPIRE].
Planck collaboration, The Planck Blue Book, www.rssd.esa.int/SA/PLANCK/docs/Bluebook-ESA-SCI(2005)1 V2.pdf.
N. Barnaby, J. Bond, Z. Huang and L. Kofman, Preheating After Modular Inflation, JCAP 12 (2009) 021 [arXiv:0909.0503] [INSPIRE].
C.G. Callan Jr., J.A. Harvey and A. Strominger, Supersymmetric string solitons, hep-th/9112030 [INSPIRE].
J. Polchinski, String Theory, Vol. 2, Superstring Theory and Beyond, Cambridge University Press (2000).
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and χSB-resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
J.M. Maldacena and C. Núñez, Towards the large-N limit of pure N = 1 super Yang-Mills, Phys. Rev. Lett. 86 (2001) 588 [hep-th/0008001] [INSPIRE].
A.H. Chamseddine and M.S. Volkov, NonAbelian solitons in N = 4 gauged supergravity and leading order string theory, Phys. Rev. D 57 (1998) 6242 [hep-th/9711181] [INSPIRE].
A.H. Chamseddine and M.S. Volkov, NonAbelian BPS monopoles in N = 4 gauged supergravity, Phys. Rev. Lett. 79 (1997) 3343 [hep-th/9707176] [INSPIRE].
B. Greene, K. Hinterbichler, S. Judes and M.K. Parikh, Smooth Initial Conditions from Weak Gravity, Phys. Lett. B 697 (2011) 178 [arXiv:0911.0693] [INSPIRE].
A.R. Liddle, A. Mazumdar and F.E. Schunck, Assisted inflation, Phys. Rev. D 58 (1998) 061301 [astro-ph/9804177] [INSPIRE].
J.M. Cline and J. Trudeau, Analytic results in N-flation, in preparation.