# DRF: Thesis subject SL-DRF-20-0660

The Higgs Boson Mass and Cosmology

Context: In our current description of Nature there are two parameters that have the strongest impact on the

phenomenology of the Universe. At the same time they are the most sensitive to the details of the underlying

theory at high energies. These parameters are the cosmological constant and the Higgs boson mass. The

cosmological constant ultimately determines the size of the observable Universe. It was measured about two

decades ago by studying the luminosity of high-redshift supernovae [1, 2]. The Higgs boson mass determines

the vacuum expectation value of the Higgs field which enters the mass of most known particles and determines

the scale of weak interactions. The stability of nuclei, and thus complex chemistry and ultimately life as we

know it, are strongly tied to this parameter. The Higgs boson was discovered, and its mass measured, by the

ATLAS and CMS experiments at the Large Hadron Collider (LHC) [3,4]. Theoretically it is hard to understand

the measured values of the Higgs mass and of the cosmological constant. The difficulty has the same origin for

both parameters and can be traced to quantum corrections and the symmetries of fundamental interactions. As a

consequence the values of these parameters are still unexplained. In this proposal we study a class of ideas that

tie the Higgs boson mass to the evolution of the Universe. This makes the values of the cosmological constant

and of the Higgs mass deeply interconnected and points to the sky as the ultimate laboratory to understand their

origin.

Thesis Project: We develop a class of ideas that ties the origin of the weak scale to the evolution of the

Universe at early times and explore their connections to the cosmological constant. This has experimental

consequences for CMB-Stage4 experiments [5, 6], fifth-force searches [7–14], equivalence principle violation

tests [15–17] and high-luminosity lepton colliders [18, 19]. I will consider models where the Higgs mass

changes via a scalar field that is slowly rolling during inflation and stops at the observed value [20, 21] (Higgs

mass “relaxation”) and models where the Higgs mass is dynamically selected at reheating [22].

Project (1a): Experimental Impact of the Cosmological Origin of the Higgs Mass. The first step of the

project is to work out in detail the experimental implications of existing cosmological explanations of the Higgs

mass. In the case of the reheating solution in [22], explaining the Higgs mass requires introducing dark sectors

with the same particle content as the SM and a new particle that reheats them. We will consider the implications

of fixing neutrinos, electrons or protons in the new sectors to be dark matter and work out the signatures in the

CMB and in small scale structure [23]. We will also study the induced exotic Higgs and Z decays at lepton

colliders and new particles at high-intensity beam-dump experiments. In the case of dynamical effects during

inflation (including the class of ideas in [20, 21, 24]), the most interesting research direction is the study of the

imprint on the CMB of the very unique models of inflation needed to make the mechanisms work.

Project (1b): Model Building Challenges in Cosmological Explanations. The first half of this project

can be enough for a PhD thesis. If the student completes the work ahead of time, there is a second direction of

investigation worth pursuing.

In this second part of the project we try to turn the proof-of-concept ideas in the first papers into more

appealing, complete theoretical models. In the case of [22] one objective is to find dynamical constructions that

require fewer copies of the SM for a fixed fundamental scale in the theory. A second objective is to improve the

reheating mechanism, decoupling the mass of the particle responsible for reheating the Universe from the weak

scale. This requires employing pre-heating and parametric resonance. In the case of [20, 21] and related ideas,

the key open question is what is the model building price to pay to write a complete model that includes an

explanation for their tiny dimensionful couplings and at the same time an inflationary sector that successfully

reheats the SM. In some sense one can reformulate the question by saying that while these models make the

weak scale technically natural they still do not explain its origin. At the end of this effort we will have more

solid models or have conclusively disfavored this class of theories.

References

[1] Supernova Search Team Collaboration, A. G. Riess et al., “Observational evidence from supernovae

for an accelerating universe and a cosmological constant,” Astron. J. 116 (1998) 1009–1038,

arXiv:astro-ph/9805201 [astro-ph].

[2] Supernova Cosmology Project Collaboration, S. Perlmutter et al., “Measurements of O and ? from 42

high redshift supernovae,” Astrophys. J. 517 (1999) 565–586, arXiv:astro-ph/9812133

[astro-ph].

[3] ATLAS Collaboration, G. Aad et al., “Observation of a new particle in the search for the Standard

Model Higgs boson with the ATLAS detector at the LHC,” Phys. Lett. B716 (2012) 1–29,

arXiv:1207.7214 [hep-ex].

[4] CMS Collaboration, S. Chatrchyan et al., “Observation of a New Boson at a Mass of 125 GeV with the

CMS Experiment at the LHC,” Phys. Lett. B716 (2012) 30–61, arXiv:1207.7235 [hep-ex].

[5] CMB-S4 Collaboration, K. N. Abazajian et al., “CMB-S4 Science Book, First Edition,”

arXiv:1610.02743 [astro-ph.CO].

[6] K. Abazajian et al., “CMB-S4 Science Case, Reference Design, and Project Plan,” arXiv:1907.04473

[astro-ph.IM].

[7] R. Spero, J. K. Hoskins, R. Newman, J. Pellam, and J. Schultz, “Test of the Gravitational Inverse-Square

Law at Laboratory Distances,” Phys. Rev. Lett. 44 (1980) 1645–1648.

[8] J. K. Hoskins, R. D. Newman, R. Spero, and J. Schultz, “Experimental tests of the gravitational inverse

square law for mass separations from 2-cm to 105-cm,” Phys. Rev. D32 (1985) 3084–3095.

[9] J. Chiaverini, S. J. Smullin, A. A. Geraci, D. M. Weld, and A. Kapitulnik, “New experimental constraints

on nonNewtonian forces below 100 microns,” Phys. Rev. Lett. 90 (2003) 151101,

arXiv:hep-ph/0209325 [hep-ph].

[10] C. D. Hoyle, D. J. Kapner, B. R. Heckel, E. G. Adelberger, J. H. Gundlach, U. Schmidt, and H. E.

Swanson, “Sub-millimeter tests of the gravitational inverse-square law,” Phys. Rev. D70 (2004) 042004,

arXiv:hep-ph/0405262 [hep-ph].

[11] S. J. Smullin, A. A. Geraci, D. M. Weld, J. Chiaverini, S. P. Holmes, and A. Kapitulnik, “New

constraints on Yukawa-type deviations from Newtonian gravity at 20 microns,” Phys. Rev. D72 (2005)

122001, arXiv:hep-ph/0508204 [hep-ph]. [Erratum: Phys. Rev.D72,129901(2005)].

[12] D. J. Kapner, T. S. Cook, E. G. Adelberger, J. H. Gundlach, B. R. Heckel, C. D. Hoyle, and H. E.

Swanson, “Tests of the gravitational inverse-square law below the dark-energy length scale,” Phys. Rev.

Lett. 98 (2007) 021101, arXiv:hep-ph/0611184 [hep-ph].

[13] M. Bordag, U. Mohideen, and V. M. Mostepanenko, “New developments in the Casimir effect,” Phys.

Rept. 353 (2001) 1–205, arXiv:quant-ph/0106045 [quant-ph].

[14] M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, “Advances in the Casimir

effect,” Int. Ser. Monogr. Phys. 145 (2009) 1–768.

[15] G. L. Smith, C. D. Hoyle, J. H. Gundlach, E. G. Adelberger, B. R. Heckel, and H. E. Swanson, “Short

range tests of the equivalence principle,” Phys. Rev. D61 (2000) 022001.

[16] S. Schlamminger, K. Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, “Test of the

equivalence principle using a rotating torsion balance,” Phys. Rev. Lett. 100 (2008) 041101,

arXiv:0712.0607 [gr-qc].

[17] J. Bergé, P. Brax, G. Métris, M. Pernot-Borràs, P. Touboul, and J.-P. Uzan, “MICROSCOPE Mission:

First Constraints on the Violation of the Weak Equivalence Principle by a Light Scalar Dilaton,” Phys.

Rev. Lett. 120 (2018) no. 14, 141101, arXiv:1712.00483 [gr-qc].

[18] FCC Collaboration, A. Abada et al., “FCC-ee: The Lepton Collider,” Eur. Phys. J. ST 228 (2019) no. 2,

261–623.

[19] CEPC Study Group Collaboration, M. Dong et al., “CEPC Conceptual Design Report: Volume 2 -

Physics & Detector,” arXiv:1811.10545 [hep-ex].

[20] P. W. Graham, D. E. Kaplan, and S. Rajendran, “Cosmological Relaxation of the Electroweak Scale,”

Phys. Rev. Lett. 115 (2015) no. 22, 221801, arXiv:1504.07551 [hep-ph].

[21] M. Geller, Y. Hochberg, and E. Kuflik, “Inflating to the Weak Scale,” Phys. Rev. Lett. 122 (2019) no. 19,

191802, arXiv:1809.07338 [hep-ph].

[22] N. Arkani-Hamed, R. T. D’Agnolo, M. Low, and D. Pinner, “Unification and New Particles at the LHC,”

JHEP 11 (2016) 082, arXiv:1608.01675 [hep-ph].

[23] GAIA Collaboration, “The Gaia mission,” 595 (Nov, 2016) A1, arXiv:1609.04153 [astro-ph.IM].

[24] G. F. Giudice, A. Kehagias, and A. Riotto, “The Selfish Higgs,” arXiv:1907.05370 [hep-ph].

Service de Physique Théorique

Place: Saclay

Start date of the thesis: 01/10/2020

Physique en Île-de-France (EDPIF)