Abstract
I consider the Festina Lente Swampland bound and argue taking thermal effects, as for instance occur during reheating, into account significantly strengthens the implications of this bound. I argue that the confinement scale should be higher than a scale proportional to the vacuum energy, while Festina Lente without thermal effects only bounds the confinement scale to be above the Hubble scale. For Higgsing of nonabelian gauge fields, I find that the magnitude of the Higgs mass should be heavier than a bound proportional to the Electroweak scale (or generally the scale set by the Higgs VEV). The measured values of the Higgs in the SM satisfy the bound. A way to avoid the bound being violated during inflation is to have a large number of species becoming light. If one wants the inflationary scale to lie below the species scale in this case, this bounds the inflationary scale to be ≪ 105 GeV. These bounds have phenomenological implications for BSM physics such as GUTs, suggesting for example a weak or absent gravitational wave signature from the GUT Higgsing phase transition.
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References
M. Montero, T. Van Riet and G. Venken, Festina Lente: EFT Constraints from Charged Black Hole Evaporation in de Sitter, JHEP 01 (2020) 039 [arXiv:1910.01648] [INSPIRE].
M. Montero, C. Vafa, T. Van Riet and G. Venken, The FL bound and its phenomenological implications, JHEP 10 (2021) 009 [arXiv:2106.07650] [INSPIRE].
G. Dall’Agata, M. Emelin, F. Farakos and M. Morittu, The unbearable lightness of charged gravitini, JHEP 10 (2021) 076 [arXiv:2108.04254] [INSPIRE].
E. Gonzalo, L.E. Ibáñez and I. Valenzuela, Swampland constraints on neutrino masses, JHEP 02 (2022) 088 [arXiv:2109.10961] [INSPIRE].
S.M. Lee et al., Festina-Lente bound on Higgs vacuum structure and inflation, JHEP 02 (2022) 100 [arXiv:2111.04010] [INSPIRE].
N. Cribiori, De Sitter, gravitino mass and the swampland, PoS CORFU2021 (2022) 200 [arXiv:2203.15449] [INSPIRE].
K. Ban et al., Phenomenological implications on a hidden sector from the festina lente bound, PTEP 2023 (2023) 013B04 [arXiv:2206.00890] [INSPIRE].
V. Guidetti, N. Righi, G. Venken and A. Westphal, Axionic Festina Lente, JHEP 01 (2023) 114 [arXiv:2206.03494] [INSPIRE].
M. Montero, J.B. Muñoz and G. Obied, Swampland bounds on dark sectors, JHEP 11 (2022) 121 [arXiv:2207.09448] [INSPIRE].
R.K. Mishra, Confinement in de Sitter space and the swampland, JHEP 01 (2023) 002 [arXiv:2207.12364] [INSPIRE].
A. Mohseni and M. Torabian, Higgs in nilpotent supergravity: Vacuum energy and Festina Lente, Phys. Lett. B 844 (2023) 138102 [arXiv:2207.13593] [INSPIRE].
I. Dalianis, F. Farakos and A. Kehagias, Is gauge mediation in the swampland?, Phys. Lett. B 844 (2023) 138077 [arXiv:2305.17089] [INSPIRE].
A. Mohseni and M. Torabian, Confinement from Distance in Metric Space and its Relation to Cosmological Constant, arXiv:2310.17000 [INSPIRE].
M. Graña and A. Herráez, The Swampland Conjectures: A Bridge from Quantum Gravity to Particle Physics, Universe 7 (2021) 273 [arXiv:2107.00087] [INSPIRE].
H. Nariai, On some static solutions of Einstein’s gravitational field equations in a spherically symmetric case, Sci. Rep. Tohoku Univ. Eighth Ser. 34 (1950) 160.
L.J. Romans, Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory, Nucl. Phys. B 383 (1992) 395 [hep-th/9203018] [INSPIRE].
G. Dvali, Black Holes and Large N Species Solution to the Hierarchy Problem, Fortsch. Phys. 58 (2010) 528 [arXiv:0706.2050] [INSPIRE].
G. Dvali and D. Lüst, Evaporation of Microscopic Black Holes in String Theory and the Bound on Species, Fortsch. Phys. 58 (2010) 505 [arXiv:0912.3167] [INSPIRE].
G. Dvali and C. Gomez, Species and Strings, arXiv:1004.3744 [INSPIRE].
G. Dvali, C. Gomez and D. Lüst, Black Hole Quantum Mechanics in the Presence of Species, Fortsch. Phys. 61 (2013) 768 [arXiv:1206.2365] [INSPIRE].
V. Mukhanov, Physical Foundations of Cosmology, Cambridge University Press, Oxford (2005) [https://doi.org/10.1017/CBO9780511790553] [INSPIRE].
D.A. Kirzhnits and A.D. Linde, Macroscopic Consequences of the Weinberg Model, Phys. Lett. B 42 (1972) 471 [INSPIRE].
L. Dolan and R. Jackiw, Symmetry Behavior at Finite Temperature, Phys. Rev. D 9 (1974) 3320 [INSPIRE].
S. Weinberg, Gauge and Global Symmetries at High Temperature, Phys. Rev. D 9 (1974) 3357 [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2022 (2022) 083C01 [INSPIRE].
M. D’Onofrio and K. Rummukainen, Standard model cross-over on the lattice, Phys. Rev. D 93 (2016) 025003 [arXiv:1508.07161] [INSPIRE].
S.K. Garg and C. Krishnan, Bounds on Slow Roll and the de Sitter Swampland, JHEP 11 (2019) 075 [arXiv:1807.05193] [INSPIRE].
H. Ooguri, E. Palti, G. Shiu and C. Vafa, Distance and de Sitter Conjectures on the Swampland, Phys. Lett. B 788 (2019) 180 [arXiv:1810.05506] [INSPIRE].
H. Ooguri and C. Vafa, On the Geometry of the String Landscape and the Swampland, Nucl. Phys. B 766 (2007) 21 [hep-th/0605264] [INSPIRE].
D. Lüst, E. Palti and C. Vafa, AdS and the Swampland, Phys. Lett. B 797 (2019) 134867 [arXiv:1906.05225] [INSPIRE].
G. German, G.G. Ross and S. Sarkar, Low scale inflation, Nucl. Phys. B 608 (2001) 423 [hep-ph/0103243] [INSPIRE].
J. Rubio, Higgs inflation, Front. Astron. Space Sci. 5 (2019) 50 [arXiv:1807.02376] [INSPIRE].
I.R. Klebanov and A.A. Tseytlin, Gravity duals of supersymmetric SU(N) × SU(N + M) gauge theories, Nucl. Phys. B 578 (2000) 123 [hep-th/0002159] [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].
S. Kachru, J. Pearson and H.L. Verlinde, Brane / flux annihilation and the string dual of a nonsupersymmetric field theory, JHEP 06 (2002) 021 [hep-th/0112197] [INSPIRE].
B. Michel et al., Remarks on brane and antibrane dynamics, JHEP 09 (2015) 021 [arXiv:1412.5702] [INSPIRE].
J. Polchinski, Brane/antibrane dynamics and KKLT stability, arXiv:1509.05710 [INSPIRE].
I. Bena, M. Graña, S. Kuperstein and S. Massai, Giant Tachyons in the Landscape, JHEP 02 (2015) 146 [arXiv:1410.7776] [INSPIRE].
D. Cohen-Maldonado, J. Diaz, T. van Riet and B. Vercnocke, Observations on fluxes near anti-branes, JHEP 01 (2016) 126 [arXiv:1507.01022] [INSPIRE].
I. Bena, J. Blåbäck and D. Turton, Loop corrections to the antibrane potential, JHEP 07 (2016) 132 [arXiv:1602.05959] [INSPIRE].
D. Cohen-Maldonado, J. Diaz and F.F. Gautason, Polarised antibranes from Smarr relations, JHEP 05 (2016) 175 [arXiv:1603.05678] [INSPIRE].
J. Armas et al., Meta-stable non-extremal anti-branes, Phys. Rev. Lett. 122 (2019) 181601 [arXiv:1812.01067] [INSPIRE].
J. Armas, N. Nguyen, V. Niarchos and N.A. Obers, Thermal transitions of metastable M-branes, JHEP 08 (2019) 128 [arXiv:1904.13283] [INSPIRE].
J. Blåbäck, F.F. Gautason, A. Ruipérez and T. Van Riet, Anti-brane singularities as red herrings, JHEP 12 (2019) 125 [arXiv:1907.05295] [INSPIRE].
N. Nguyen, Comments on the stability of the KPV state, JHEP 11 (2020) 055 [arXiv:1912.04646] [INSPIRE].
N. Nguyen and V. Niarchos, On matched asymptotic expansions of backreacting metastable anti-branes, JHEP 06 (2022) 055 [arXiv:2112.04514] [INSPIRE].
T. Van Riet and G. Zoccarato, Beginners lectures on flux compactifications and related Swampland topics, Phys. Rept. 1049 (2024) 1 [arXiv:2305.01722] [INSPIRE].
D.J. Weir, Gravitational waves from a first order electroweak phase transition: a brief review, Phil. Trans. Roy. Soc. Lond. A 376 (2018) 20170126 [Erratum ibid. 381 (2023) 20230212] [arXiv:1705.01783] [INSPIRE].
C. Caprini and D.G. Figueroa, Cosmological Backgrounds of Gravitational Waves, Class. Quant. Grav. 35 (2018) 163001 [arXiv:1801.04268] [INSPIRE].
A. Mazumdar and G. White, Review of cosmic phase transitions: their significance and experimental signatures, Rept. Prog. Phys. 82 (2019) 076901 [arXiv:1811.01948] [INSPIRE].
D. Croon et al., GUT Physics in the era of the LHC, Front. in Phys. 7 (2019) 76 [arXiv:1903.04977] [INSPIRE].
P. Agrawal, G. Obied, P.J. Steinhardt and C. Vafa, On the Cosmological Implications of the String Swampland, Phys. Lett. B 784 (2018) 271 [arXiv:1806.09718] [INSPIRE].
A. Hebecker and T. Wrase, The Asymptotic dS Swampland Conjecture — a Simplified Derivation and a Potential Loophole, Fortsch. Phys. 67 (2019) 1800097 [arXiv:1810.08182] [INSPIRE].
A. Bedroya and C. Vafa, Trans-Planckian Censorship and the Swampland, JHEP 09 (2020) 123 [arXiv:1909.11063] [INSPIRE].
A. Bedroya, R. Brandenberger, M. Loverde and C. Vafa, Trans-Planckian Censorship and Inflationary Cosmology, Phys. Rev. D 101 (2020) 103502 [arXiv:1909.11106] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff, Eur. Phys. J. C 78 (2018) 337 [arXiv:1712.01868] [INSPIRE].
D. Harlow, Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture, JHEP 01 (2016) 122 [arXiv:1510.07911] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Emergence of Weak Coupling at Large Distance in Quantum Gravity, Phys. Rev. Lett. 121 (2018) 051601 [arXiv:1802.08698] [INSPIRE].
T.W. Grimm, E. Palti and I. Valenzuela, Infinite Distances in Field Space and Massless Towers of States, JHEP 08 (2018) 143 [arXiv:1802.08264] [INSPIRE].
P. Agrawal, S. Gukov, G. Obied and C. Vafa, Topological Gravity as the Early Phase of Our Universe, arXiv:2009.10077 [INSPIRE].
R.H. Brandenberger and C. Vafa, Superstrings in the Early Universe, Nucl. Phys. B 316 (1989) 391 [INSPIRE].
R. Brustein and P.J. Steinhardt, Challenges for superstring cosmology, Phys. Lett. B 302 (1993) 196 [hep-th/9212049] [INSPIRE].
J.P. Conlon and F. Revello, Catch-me-if-you-can: the overshoot problem and the weak/inflation hierarchy, JHEP 11 (2022) 155 [arXiv:2207.00567] [INSPIRE].
V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP 03 (2005) 007 [hep-th/0502058] [INSPIRE].
J.P. Conlon, F. Quevedo and K. Suruliz, Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 08 (2005) 007 [hep-th/0505076] [INSPIRE].
Acknowledgments
I thank Arthur Hebecker for valuable feedback on an early draft. I thank Arthur Hebecker, Miguel Montero, Georges Obied, and Thomas Van Riet for valuable discussion. This work was supported by funding from an STFC consolidated grant, grant reference ST/X000761/1.
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Venken, G. Cosmological phase transitions and the swampland. J. High Energ. Phys. 2024, 114 (2024). https://doi.org/10.1007/JHEP02(2024)114
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DOI: https://doi.org/10.1007/JHEP02(2024)114