Higgscitement: Cosmological Dynamics of Fine Tuning

The Higgs potential appears to be fine-tuned, hence very sensitive to values of other scalar fields that couple to the Higgs. We show that this feature can lead to a new epoch in the early universe featuring violent dynamics coupling the Higgs to a scalar modulus. The oscillating modulus drives tachyonic Higgs particle production. We find a simple parametric understanding of when this process can lead to rapid modulus fragmentation, resulting in gravitational wave production. A nontrivial equation-of-state arising from the nonlinear dynamics also affects the time elapsed from inflation to the CMB, influencing fits of inflationary models. Supersymmetric theories automatically contain useful ingredients for this picture.

The number of EW-flipping oscillations probes fine tuning.

Tachyonic particle production
As the modulus oscillates, if m is at least a little bit small compared to M, the Higgs has time to respond.
That is, there is a tachyonic particle production process when the Higgs flips to the tachyonic side, converting modulus energy into the Higgs energy.
Tachyonic resonance efficiency parameter: The problem of backreaction As the modulus oscillates, if m is at least a little bit small compared to M, the Higgs has time to respond.
That is, there is a tachyonic particle production process.
This potentially depletes energy from the modulus. But: create too many Standard Model particles, and they backreact.

Parametrics: Can We Get an Effect?
What the numerics are showing is that to get a significant period of coupled, out-of-equilibrium modulus/Higgs dynamics, we need This could be satisfied in:

For a), small quartics can arise along D-flat directions in SUSY.
If we think in the full SUSY 2HDM, the Higgs getting a large VEV can be H u = H d . This is the possibility we'll discuss in the most detail.

IF the universe remains radiation dominated after GW production until the usual matter-radiation equality
where we assume that the universe can be approximated as radiation dominated shortly after begins oscillation. Note that for ⌧ 1, these frequencies are beyond the reach of current interferometric detectors (f . 10 3 Hz).
The fraction of energy density in gravitational waves today (per logarithmic interval in frequency around f 0 ) can be estimated as [11,12] ⌦ where ⌦ r0 is today's fraction of energy density stored in radiation and ⇡ is the fraction of the energy density in anisotropic stresses at the time of gravitational wave production. From the scalar field simulations, [MA: ⇡ ⇠ 0.1 and ⇠ 0.1 (or estimated from linear instability calculations, and energetic arguments)] which yield ⌦ gw ⇠ 10 9 10 10 . This result is consistent with our more detailed lattice simulations which calculate the gravitational wave spectrum using HLattice [13](see The amplitude isn't terrible, and astrophysical backgrounds are low at high frequencies. Numerical GW Spectrum computed with HLattice (Z. Huang '11)

Numerical GW Spectrum
A difficulty is that we do not expect the moduli will instantly decay fully into radiation. From the numerics we expect an extended phase of w ~ 0.3, possibly reverting to standard moduli cosmology at some time.
This means more redshift: smaller f and smaller gw .

This could change our story in interesting ways, as the modulus doesn't redshift inside the oscillon. More mass sign flipping and less backreaction?
No conclusions yet! Need more studies.

One More Ingredient: Oscillons
be testable with future CMB data and galaxy surveys. As we will see below, these conclusions are robust to the current order-unity uncertainty in r.
ln(1/aH) ln a ln a k ln a end ln a re ln a eq ln a 0 1: The evolution of the comoving Hubble scale 1/aH. The reheating phase connects the inflationary phase and the radiation era. Compared to instantaneous reheating (thick dotted curve), a reheating equation-of-state parameter w re < 1/3 implies more post-inflationary e-folds of expansion. Fewer post-inflationary e-folds requires w re > 1/3 (thin dotted curve).
We start by sketching the cosmic expansion history in Fig. 1. At early times, the inflaton field φ drives the quasi-de-Sitter phase for N k e-folds of expansion. The comoving horizon scale decreases as ∼ a −1 . The reheating phase begins once the accelerated expansion comes to an end and the comoving horizon starts to increase. After another N re e-folds of expansion, the energy in the inflaton field has been completely dissipated into a hot plasma with a reheating temperature T re . Beyond that (2 of e-folds from the time that the field value is φ until th end of inflation. Note that the field value at the end o inflation φ end is small compared to that during slow-roll The conventional slow-roll parameters are then given by ϵ = α/(4N ), and η = (α − 1)/(2N ).
(3 For power-law potentials, the scalar spectral tilt n s − and the tensor-to-scalar ratio r are inversely proportiona to the number of e-folds, Simultaneous measurements of n s − 1 and r with high precision in principle pin down both N and α. However given the current uncertainty in r, we treat α as a mode input and use n s − 1 to infer both N and r. As we shal see, the precise value of r does not affect our results. In cosmology we observe perturbation modes on scale that are comparable to that of the horizon. For example the pivot scale at which Planck determines n s lies at k = 0.05 Mpc −1 . The comoving Hubble scale a k H k = k when this mode exited the horizon can be related to that of th present time,

Reminder:
The tree-level MSSM has a Higgs quartic coupling from D-terms, completely fixed by the Higgs' electroweak representations: Notice the D-flat direction: How to achieve small Higgs quartic?
The Higgs quartic coupling a SUSY-breaking contribution to the Higgs quartic comes from loops of stops: In addition to the tree-level potential, Non-vanishing along the D-flat direction. Does it stop us?

EWSB Along the Flat Direction
Suppose there is a tachyonic direction pointing along the flat direction, that is, that we have How large will the Higgs VEV be? At first, you would expect to be stopped by the loop-level quartic coupling: But importantly, the stop mass here is the geometric mean of the physical stop masses, and as we move far out along the flat direction the stop and top become degenerate: Approximate SUSY suppresses the quartic by a factor of M soft 2 /H 2 , allowing Higgs VEVs much larger than soft masses! Flat directions should always be lifted at very large field values.
Kähler corrections are compatible with VEVs of order the cutoff: ◆ Superpotential terms at first glance appear more dangerous. An alternative for what is natural in SUSY: "Standard SUSY" "Flat-Higgs SUSY" The typical SUSY naturalness story is that as we vary input UV parameters, the Higgs VEV should change by O(1) amounts. But in theories where the Higgs has a (badly broken!) shift symmetry, we will find exponential sensitivity of the VEV to UV parameters. The ratio v/M soft is exponentially sensitive to the parameters!