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If the electroweak Higgs vacuum expectation value $v$ in early universe is $sim 1 %$ higher than its present value $v_0=246$ GeV, the $^7$Li puzzle in BBN and the CMB/$Lambda$CDM tension with late-universe measurements on Hubble parameter are mitigated. We propose a model of an axion coupled to the Higgs field, named ``axi-Higgs, with its mass $m_a sim 10^{-30} - 10^{-29},{rm eV}$ and decay constant $f_a sim 10^{17} - 10^{18},{rm GeV}$, to achieve this goal. The axion initial value $a_{rm ini}$ yields an initial $Delta v_{rm ini}/v_0 sim 0.01$ throughout the BBN-recombination epoch and a percent level contribution to the total matter density today. Because of its very large de Broglie wavelength, this axion matter density $omega_a$ suppresses the matter power spectrum, alleviating the CMB/$Lambda$CDM $S_8/sigma_8$ tension with the weak-lensing data. It also explains the recently reported isotropic cosmic birefringence by its coupling with photons. Adding the axion ($m sim 10^{-22},$eV) in the fuzzy dark matter model to the axi-Higgs model allows bigger $Delta v_{rm rec}$ and $omega_a$ to address the Hubble and $S_8/sigma_8$ tensions simultaneously. The model predicts that $Delta v$ may be detected by the spectral measurements of quasars, while its oscillation may be observed in the atomic clock measurements.
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We discuss the cosmology of models in which the standard model Yukawa couplings depend on scalar field(s), often referred to as flavons. We find that thermal corrections of the flavon potential tend to decrease the Yukawa couplings, providing an important input to model-building. Working in the specific framework of Froggatt-Nielsen models, we compute the abundance of flavons in the early universe generated both via freeze-in and from coherent oscillations induced by thermal corrections to their potential, and discuss constraints on flavon models from cosmology. We find that cosmology places important constraints on theories containing flavons even for regions of parameter space inaccessible to collider searches.
We propose a mechanism to solve the Higgs naturalness problem through a cosmological selection process. The discharging of excited field configurations through membrane nucleation leads to discrete jumps of the cosmological constant and the Higgs mass, which vary in a correlated way. The resulting multitude of universes are all empty, except for those in which the cosmological constant and the Higgs mass are both nearly vanishing. Only under these critical conditions can inflation be activated and create a non-empty universe.
Recent measurements at the LHC suggest that the current Higgs vacuum could be metastable with a modest barrier (height 10^{10-12}{GeV})^{4}) separating it from a ground state with negative vacuum density of order the Planck scale. We note that metastability is problematic for big bang to end one cycle, bounce, and begin the next. In this paper, motivated by the approximate scaling symmetry of the standard model of particle physics and the primordial large-scale structure of the universe, we use our recent formulation of the Weyl-invariant version of the standard model coupled to gravity to track the evolution of the Higgs in a regularly bouncing cosmology. We find a band of solutions in which the Higgs field escapes from the metastable phase during each big crunch, passes through the bang into an expanding phase, and returns to the metastable vacuum, cycle after cycle after cycle. We show that, due to the effect of the Higgs, the infinitely cycling universe is geodesically complete, in contrast to inflation.
Light scalar fields that couple to matter through the Higgs portal mediate long range fifth forces. We show how the mixing of a light scalar with the Higgs field can lead to this fifth force being screened around macroscopic objects. This behaviour can only be seen by considering both scalar fields as dynamical, and is missed if the mixing between the Higgs field and the scalar field is not taken into account. We explain under which conditions the naive integrating out procedure fails, i.e. when the mass matrix of the Higgs-scalars system has a nearly vanishing mass eigenvalue. The resulting flat direction in field space can be lifted at the quadratic order in the presence of matter and the resulting fifth force mediated by the Higgs portal can be screened either when the gravitating objects are large enough or their surface Newton potential exceeds a threshold. Finally we discuss the implications of these results for nearly massless relaxion models.
We make an estimate of the likelihood function for the Higgs vacuum expectation value by imposing anthropic constraints on the existence of atoms while allowing the other parameters of the Standard Model to also be variable. We argue that the most important extra ingredients are the Yukawa couplings, and for the intrinsic distribution of Yukawa couplings we use the scale invariant distribution which is favored phenomenologically. The result is successful phenomenologically, favoring values close to the observed vev. We also discuss modifications that could change these conclusions. Our work supports the hypothesis that the anthropic constraints could be the origin of the small value of the Higgs vev.
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