Abstract
Combining previous results, the D3-\( \overline{D}3 \)-brane pair potential U(T, ϕ) is presented here, where the inflaton ϕ measures the separation between the D3-brane and the anti-D3-brane, and the complex scalar mode T becomes tachyonic when the annihilation of the branes happens as they collide. Besides the distinct form of the inflationary potential, this hybrid inflationary model differs from a typical hybrid model in 2 important aspects: (1) U(T, ϕ) becomes complex when T becomes tachyonic, where Im U(T, ϕ) plays an important role in the dynamics towards the end of the inflationary epoch; (2) tunnelling during the inflationary epoch can happen; this is particularly relevant if there are multiple D3-\( \overline{D}3 \)-brane pairs in different warped throats. Besides the production of cosmic superstrings, the model offers the possibility of first order phase transition that may generate large enough density perturbation for the primordial black hole production. Stochastic gravitational wave background from these sources remain to be fully investigated.
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References
A.H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D 23 (1981) 347 [INSPIRE].
A.D. Linde, A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems, Phys. Lett. B 108 (1982) 389 [INSPIRE].
G.R. Dvali and S.H.H. Tye, Brane inflation, Phys. Lett. B 450 (1999) 72 [hep-ph/9812483] [INSPIRE].
G.R. Dvali, Q. Shafi and S. Solganik, D-brane inflation, in the proceedings of the 4th European Meeting From the Planck Scale to the Electroweak Scale, La Londe les Maures, France, May 11–16 (2001) [hep-th/0105203] [INSPIRE].
C.P. Burgess et al., The inflationary brane anti-brane universe, JHEP 07 (2001) 047 [hep-th/0105204] [INSPIRE].
S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].
S. Kachru et al., Towards inflation in string theory, JCAP 10 (2003) 013 [hep-th/0308055] [INSPIRE].
Planck collaboration, Planck 2015 results. XX. Constraints on inflation, Astron. Astrophys. 594 (2016) A20 [arXiv:1502.02114] [INSPIRE].
N.T. Jones and S.H.H. Tye, An improved brane anti-brane action from boundary superstring field theory and multivortex solutions, JHEP 01 (2003) 012 [hep-th/0211180] [INSPIRE].
S. Sarangi and S.H.H. Tye, Interbrane potential and the decay of a nonBPS D-brane to closed strings, Phys. Lett. B 573 (2003) 181 [hep-th/0307078] [INSPIRE].
COBE collaboration, Structure in the COBE differential microwave radiometer first year maps, Astrophys. J. Lett. 396 (1992) L1 [INSPIRE].
A.D. Linde, Hybrid inflation, Phys. Rev. D 49 (1994) 748 [astro-ph/9307002] [INSPIRE].
J. Polchinski, String theory. Volume 1: An Introduction to the Bosonic String, Cambridge University Press (1998) [https://doi.org/10.1017/CBO9780511816079].
J. Polchinski, String theory. Volume 2: Superstring Theory and Beyond, Cambridge University Press (1998) [https://doi.org/10.1017/cbo9780511618123].
R. Maartens, Brane world gravity, Living Rev. Rel. 7 (2004) 7 [gr-qc/0312059] [INSPIRE].
D. Baumann and L. McAllister, Inflation and String Theory, Cambridge University Press (2015) [https://doi.org/10.1017/CBO9781316105733] [INSPIRE].
N.T. Jones, H. Stoica and S.H.H. Tye, Brane interaction as the origin of inflation, JHEP 07 (2002) 051 [hep-th/0203163] [INSPIRE].
S. Sarangi and S.H.H. Tye, Cosmic string production towards the end of brane inflation, Phys. Lett. B 536 (2002) 185 [hep-th/0204074] [INSPIRE].
N.T. Jones, H. Stoica and S.H.H. Tye, The Production, spectrum and evolution of cosmic strings in brane inflation, Phys. Lett. B 563 (2003) 6 [hep-th/0303269] [INSPIRE].
E.J. Copeland, R.C. Myers and J. Polchinski, Cosmic F and D strings, JHEP 06 (2004) 013 [hep-th/0312067] [INSPIRE].
M.G. Jackson, N.T. Jones and J. Polchinski, Collisions of cosmic F and D-strings, JHEP 10 (2005) 013 [hep-th/0405229] [INSPIRE].
L. Randall, M. Soljacic and A.H. Guth, Supernatural inflation: Inflation from supersymmetry with no (very) small parameters, Nucl. Phys. B 472 (1996) 377 [hep-ph/9512439] [INSPIRE].
J. Garcia-Bellido, A.D. Linde and D. Wands, Density perturbations and black hole formation in hybrid inflation, Phys. Rev. D 54 (1996) 6040 [astro-ph/9605094] [INSPIRE].
M. Kawasaki, N. Sugiyama and T. Yanagida, Primordial black hole formation in a double inflation model in supergravity, Phys. Rev. D 57 (1998) 6050 [hep-ph/9710259] [INSPIRE].
A.A. Abolhasani and H. Firouzjahi, No Large Scale Curvature Perturbations during Waterfall of Hybrid Inflation, Phys. Rev. D 83 (2011) 063513 [arXiv:1005.2934] [INSPIRE].
D.H. Lyth, Primordial black hole formation and hybrid inflation, arXiv:1107.1681 [INSPIRE].
D.H. Lyth, The hybrid inflation waterfall and the primordial curvature perturbation, JCAP 05 (2012) 022 [arXiv:1201.4312] [INSPIRE].
M. Sasaki, T. Suyama, T. Tanaka and S. Yokoyama, Primordial black holes — perspectives in gravitational wave astronomy, Class. Quant. Grav. 35 (2018) 063001 [arXiv:1801.05235] [INSPIRE].
O. Özsoy and G. Tasinato, Inflation and Primordial Black Holes, Universe 9 (2023) 203 [arXiv:2301.03600] [INSPIRE].
S. Hawking, Gravitationally collapsed objects of very low mass, Mon. Not. Roy. Astron. Soc. 152 (1971) 75 [INSPIRE].
D. Kutasov, M. Marino and G.W. Moore, Remarks on tachyon condensation in superstring field theory, hep-th/0010108 [INSPIRE].
P. Kraus and F. Larsen, Boundary string field theory of the \( D\overline{D} \) system, Phys. Rev. D 63 (2001) 106004 [hep-th/0012198] [INSPIRE].
T. Takayanagi, S. Terashima and T. Uesugi, Brane-anti-brane action from boundary string field theory, JHEP 03 (2001) 019 [hep-th/0012210] [INSPIRE].
E. Witten, On background independent open string field theory, Phys. Rev. D 46 (1992) 5467 [hep-th/9208027] [INSPIRE].
E. Witten, Some computations in background independent off-shell string theory, Phys. Rev. D 47 (1993) 3405 [hep-th/9210065] [INSPIRE].
S.L. Shatashvili, Comment on the background independent open string theory, Phys. Lett. B 311 (1993) 83 [hep-th/9303143] [INSPIRE].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
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. Garcia-Bellido, R. Rabadan and F. Zamora, Inflationary scenarios from branes at angles, JHEP 01 (2002) 036 [hep-th/0112147] [INSPIRE].
T. Banks and L.J. Dixon, Constraints on String Vacua with Space-Time Supersymmetry, Nucl. Phys. B 307 (1988) 93 [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, De Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
O. DeWolfe and S.B. Giddings, Scales and hierarchies in warped compactifications and brane worlds, Phys. Rev. D 67 (2003) 066008 [hep-th/0208123] [INSPIRE].
M. Berg, M. Haack and B. Kors, Loop corrections to volume moduli and inflation in string theory, Phys. Rev. D 71 (2005) 026005 [hep-th/0404087] [INSPIRE].
D. Baumann et al., D3-brane Potentials from Fluxes in AdS/CFT, JHEP 06 (2010) 072 [arXiv:1001.5028] [INSPIRE].
H. Firouzjahi and S.-H.H. Tye, Brane inflation and cosmic string tension in superstring theory, JCAP 03 (2005) 009 [hep-th/0501099] [INSPIRE].
N. Barnaby, C.P. Burgess and J.M. Cline, Warped reheating in brane-antibrane inflation, JCAP 04 (2005) 007 [hep-th/0412040] [INSPIRE].
L. Kofman and P. Yi, Reheating the universe after string theory inflation, Phys. Rev. D 72 (2005) 106001 [hep-th/0507257] [INSPIRE].
D. Chialva, G. Shiu and B. Underwood, Warped reheating in multi-throat brane inflation, JHEP 01 (2006) 014 [hep-th/0508229] [INSPIRE].
A.R. Frey, A. Mazumdar and R.C. Myers, Stringy effects during inflation and reheating, Phys. Rev. D 73 (2006) 026003 [hep-th/0508139] [INSPIRE].
X. Chen and S.-H.H. Tye, Heating in brane inflation and hidden dark matter, JCAP 06 (2006) 011 [hep-th/0602136] [INSPIRE].
A. Villenkin and E.P.S. Shellard, Cosmic strings and other topological defects, Cambridge University Press (2000).
H. Firouzjahi, L. Leblond and S.-H. Henry Tye, The (p, q) string tension in a warped deformed conifold, JHEP 05 (2006) 047 [hep-th/0603161] [INSPIRE].
M. Sakellariadou, A note on the evolution of cosmic string/superstring networks, JCAP 04 (2005) 003 [hep-th/0410234] [INSPIRE].
A. Avgoustidis and E.P.S. Shellard, Effect of reconnection probability on cosmic (super)string network density, Phys. Rev. D 73 (2006) 041301 [astro-ph/0512582] [INSPIRE].
S.-H.H. Tye, I. Wasserman and M. Wyman, Scaling of multi-tension cosmic superstring networks, Phys. Rev. D 71 (2005) 103508 [Erratum ibid. 71 (2005) 129906] [astro-ph/0503506] [INSPIRE].
A. Vilenkin, Gravitational radiation from cosmic strings, Phys. Lett. B 107 (1981) 47 [INSPIRE].
C.J. Hogan and M.J. Rees, Gravitational interactions of cosmic strings, Nature 311 (1984) 109.
J.J. Blanco-Pillado, K.D. Olum and B. Shlaer, The number of cosmic string loops, Phys. Rev. D 89 (2014) 023512 [arXiv:1309.6637] [INSPIRE].
J.J. Blanco-Pillado, K.D. Olum and X. Siemens, New limits on cosmic strings from gravitational wave observation, Phys. Lett. B 778 (2018) 392 [arXiv:1709.02434] [INSPIRE].
J. Ellis, M. Lewicki, C. Lin and V. Vaskonen, Cosmic superstrings revisited in light of NANOGrav 15-year data, Phys. Rev. D 108 (2023) 103511 [arXiv:2306.17147] [INSPIRE].
T. Damour and A. Vilenkin, Gravitational wave bursts from cusps and kinks on cosmic strings, Phys. Rev. D 64 (2001) 064008 [gr-qc/0104026] [INSPIRE].
T. Damour and A. Vilenkin, Gravitational radiation from cosmic (super)strings: Bursts, stochastic background, and observational windows, Phys. Rev. D 71 (2005) 063510 [hep-th/0410222] [INSPIRE].
N. Suresh and D.F. Chernoff, Modeling the Beam of Gravitational Radiation from a Cosmic String Loop, arXiv:2310.00825 [INSPIRE].
L. Leblond, B. Shlaer and X. Siemens, Gravitational Waves from Broken Cosmic Strings: The Bursts and the Beads, Phys. Rev. D 79 (2009) 123519 [arXiv:0903.4686] [INSPIRE].
D.F. Chernoff and S.H.H. Tye, Cosmic String Detection via Microlensing of Stars, arXiv:0709.1139 [INSPIRE].
W. Hu, R. Barkana and A. Gruzinov, Cold and fuzzy dark matter, Phys. Rev. Lett. 85 (2000) 1158 [astro-ph/0003365] [INSPIRE].
H.-Y. Schive, T. Chiueh and T. Broadhurst, Cosmic Structure as the Quantum Interference of a Coherent Dark Wave, Nature Phys. 10 (2014) 496 [arXiv:1406.6586] [INSPIRE].
L. Hui, J.P. Ostriker, S. Tremaine and E. Witten, Ultralight scalars as cosmological dark matter, Phys. Rev. D 95 (2017) 043541 [arXiv:1610.08297] [INSPIRE].
H.N. Luu, S.-H.H. Tye and T. Broadhurst, Multiple Ultralight Axionic Wave Dark Matter and Astronomical Structures, Phys. Dark Univ. 30 (2020) 100636 [arXiv:1811.03771] [INSPIRE].
L.W.H. Fung et al., Axi-Higgs cosmology, JCAP 08 (2021) 057 [arXiv:2102.11257] [INSPIRE].
A. Sen, Tachyon condensation on the brane anti-brane system, JHEP 08 (1998) 012 [hep-th/9805170] [INSPIRE].
G. Shiu, S.H.H. Tye and I. Wasserman, Rolling tachyon in brane world cosmology from superstring field theory, Phys. Rev. D 67 (2003) 083517 [hep-th/0207119] [INSPIRE].
N.D. Lambert, H. Liu and J.M. Maldacena, Closed strings from decaying D-branes, JHEP 03 (2007) 014 [hep-th/0303139] [INSPIRE].
X. Chen, One loop evolution in rolling tachyon, Phys. Rev. D 70 (2004) 086001 [hep-th/0311179] [INSPIRE].
A. Sen, Tachyon dynamics in open string theory, Int. J. Mod. Phys. A 20 (2005) 5513 [hep-th/0410103] [INSPIRE].
L. Leblond and S. Shandera, Cosmology of the Tachyon in Brane Inflation, JCAP 01 (2007) 009 [hep-th/0610321] [INSPIRE].
R.H. Brandenberger, A.R. Frey and L.C. Lorenz, Entropy fluctuations in brane inflation models, Int. J. Mod. Phys. A 24 (2009) 4327 [arXiv:0712.2178] [INSPIRE].
D. Battefeld, T. Battefeld, H. Firouzjahi and N. Khosravi, Brane Annihilations during Inflation, JCAP 07 (2010) 009 [arXiv:1004.1417] [INSPIRE].
T. Banks and L. Susskind, Brane-anti-brane forces, hep-th/9511194 [INSPIRE].
A.H. Guth and E.J. Weinberg, Could the Universe Have Recovered from a Slow First Order Phase Transition?, Nucl. Phys. B 212 (1983) 321 [INSPIRE].
S.R. Coleman, The Fate of the False Vacuum. I. Semiclassical Theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. 16 (1977) 1248] [INSPIRE].
S.R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay, Phys. Rev. D 21 (1980) 3305 [INSPIRE].
Q.-G. Huang and S.-H.H. Tye, The Cosmological Constant Problem and Inflation in the String Landscape, Int. J. Mod. Phys. A 24 (2009) 1925 [arXiv:0803.0663] [INSPIRE].
J. Silk and M.S. Turner, Double Inflation, Phys. Rev. D 35 (1987) 419 [INSPIRE].
S.W. Hawking and I.G. Moss, Supercooled Phase Transitions in the Very Early Universe, Phys. Lett. B 110 (1982) 35 [INSPIRE].
N.T. Jones, L. Leblond and S.H.H. Tye, Adding a brane to the brane anti-brane action in BSFT, JHEP 10 (2003) 002 [hep-th/0307086] [INSPIRE].
NANOGrav collaboration, The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background, Astrophys. J. Lett. 951 (2023) L8 [arXiv:2306.16213] [INSPIRE].
NANOGrav collaboration, The NANOGrav 15 yr Data Set: Observations and Timing of 68 Millisecond Pulsars, Astrophys. J. Lett. 951 (2023) L9 [arXiv:2306.16217] [INSPIRE].
H. Xu et al., Searching for the Nano-Hertz Stochastic Gravitational Wave Background with the Chinese Pulsar Timing Array Data Release I, Res. Astron. Astrophys. 23 (2023) 075024 [arXiv:2306.16216] [INSPIRE].
EPTA collaboration, The second data release from the European Pulsar Timing Array — I. The dataset and timing analysis, Astron. Astrophys. 678 (2023) A48 [arXiv:2306.16224] [INSPIRE].
A. Zic et al., The Parkes Pulsar Timing Array third data release, Publ. Astron. Soc. Austral. 40 (2023) e049 [arXiv:2306.16230] [INSPIRE].
J. Ellis et al., What is the source of the PTA GW signal?, arXiv:2308.08546 [INSPIRE].
E. Witten, Cosmic Separation of Phases, Phys. Rev. D 30 (1984) 272 [INSPIRE].
C.J. Hogan, Gravitational radiation from cosmological phase transitions, Mon. Not. Roy. Astron. Soc. 218 (1986) 629.
M.S. Turner and F. Wilczek, Relic gravitational waves and extended inflation, Phys. Rev. Lett. 65 (1990) 3080 [INSPIRE].
M. Kamionkowski, A. Kosowsky and M.S. Turner, Gravitational radiation from first order phase transitions, Phys. Rev. D 49 (1994) 2837 [astro-ph/9310044] [INSPIRE].
D. Chialva, Gravitational waves from first order phase transitions during inflation, Phys. Rev. D 83 (2011) 023512 [arXiv:1004.2051] [INSPIRE].
M. Hindmarsh, S.J. Huber, K. Rummukainen and D.J. Weir, Numerical simulations of acoustically generated gravitational waves at a first order phase transition, Phys. Rev. D 92 (2015) 123009 [arXiv:1504.03291] [INSPIRE].
H. Jiang, T. Liu, S. Sun and Y. Wang, Echoes of Inflationary First-Order Phase Transitions in the CMB, Phys. Lett. B 765 (2017) 339 [arXiv:1512.07538] [INSPIRE].
H. An, K.-F. Lyu, L.-T. Wang and S. Zhou, A unique gravitational wave signal from phase transition during inflation, Chin. Phys. C 46 (2022) 101001 [arXiv:2009.12381] [INSPIRE].
M. Alishahiha, E. Silverstein and D. Tong, DBI in the sky, Phys. Rev. D 70 (2004) 123505 [hep-th/0404084] [INSPIRE].
S.E. Shandera and S.-H.H. Tye, Observing brane inflation, JCAP 05 (2006) 007 [hep-th/0601099] [INSPIRE].
Acknowledgments
This work is based on early collaborations with Sash Sarangi and Nick Jones, to whom I am grateful. I thank Xingang Chen, Hassan Firouzjahi, Tao Liu and especially Liam McAllister for valuable comments.
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Tye, SH.H. The D3-\( \overline{D}3 \)-brane inflation model revisited. J. High Energ. Phys. 2024, 171 (2024). https://doi.org/10.1007/JHEP01(2024)171
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DOI: https://doi.org/10.1007/JHEP01(2024)171