Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
  • Open Access

Cosmological dynamics of Higgs potential fine tuning

Mustafa A. Amin, JiJi Fan, Kaloian D. Lozanov, and Matthew Reece
Phys. Rev. D 99, 035008 – Published 12 February 2019

Abstract

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
3 More
  • Received 19 February 2018
  • Revised 28 November 2018

DOI:https://doi.org/10.1103/PhysRevD.99.035008

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & AstrophysicsParticles & Fields

Authors & Affiliations

Mustafa A. Amin1, JiJi Fan2, Kaloian D. Lozanov3, and Matthew Reece4

  • 1Physics & Astronomy Department, Rice University, Houston, Texas 77005, USA
  • 2Department of Physics, Brown University, Providence, Rhode Island 02912, USA
  • 3Max Planck Institute for Astrophysics, Karl-Schwarzschild-Straße 1, 85748 Garching, Germany
  • 4Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

Article Text

Click to Expand

References

Click to Expand
Issue

Vol. 99, Iss. 3 — 1 February 2019

Reuse & Permissions
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×

Images

  • Figure 1
    Figure 1

    The shape of the Higgs-moduli potential. The global minimum of the potential is at (ϕ=ϕm, h0), whereas ϕ0 is the point of symmetry breaking.

    Reuse & Permissions
  • Figure 2
    Figure 2

    The ratio of the spatially averaged energy density in the Higgs and modulus fields as a function of time, from our lattice simulations. This dynamics is representative of the energy transfer between the modulus and Higgs fields when bM4/2λf2mϕ2O[1]. For this plot we have chosen Δ=106, M2/mϕ2=102, M/f=1013 and λ1024, which corresponds to b=0.9. We have confirmed that changing the parameters (for example, increasing λ by 6 orders of magnitude), while keeping b1 fixed, does not qualitatively change our results.

    Reuse & Permissions
  • Figure 3
    Figure 3

    The evolution of the normalized fields power spectra for the model with Δ=106, b=0.9, q=102, f=mpl. The normalized power spectrum of a field F(x) is PF(k)ϕosc2(d/dlnk)F2(x)¯, where ϕosc is the amplitude of the background modulus oscillations. For this normalization, when Pϕ(k)=O(1), the modulus becomes inhomogeneous. Initially, the tachyonic instability in the Higgs is closely followed by excitations in the modulus (due to rescattering). Comoving modes k<mϕq1/2 grow exponentially. At the third oscillation of the modulus, backreaction takes place. The spectra then settle down and power slowly propagates towards higher comoving modes.

    Reuse & Permissions
  • Figure 4
    Figure 4

    Snapshots of the values of the modulus (first row) and Higgs (second row) fields on an arbitrary two-dimensional slice through the three-dimensional simulation box at four different times (the spatial coordinates are comoving). Around the time of backreaction, t23mϕ1 (second column), the Higgs field forms domains (“bubbles”) with h=±2|ϕ|f/q. They disappear within Δt10m1, due to collisions, as well as oscillations of the remnant ϕ condensate. The parameters we use are Δ=106, b=0.9, with q=102, M=1013mpl, f=mpl.

    Reuse & Permissions
  • Figure 5
    Figure 5

    Left panel: Evolution of w for the Higgs-modulus system for different values of the fragmentation efficiency parameter bM4/2λf2mϕ2 with tuning Δ=106. For bO[1], 1/4w1/3 is attained after fragmentation (orange curve). Smaller b yields smaller late time w, with continued adiabatic evolution. In the untuned case (ΔO[1], not shown above) and b1, we get w0. Right panel: For fixed b=0.9, varying q=M2/mϕ2 affects when 1/4w1/3 is attained. For all curves, we have averaged energy densities and pressures spatially over the simulation box and temporally over fast oscillations.

    Reuse & Permissions
  • Figure 6
    Figure 6

    Dashed orange curve with Nmod=0: The gravitational waves (GWs) power spectrum today, generated by the nonlinear dynamics at t70mϕ1 (assuming Δ=106, b=0.9, q=102, M/f=1013). The GWs on intermediate frequencies are generated by the slow propagation of power towards smaller comoving scales after backreaction; see Fig. 3. Two paler dashed orange curves with Nmod>0: Rescaled versions of the top one, assuming wmod=0. Solid black curve: Planned sensitivity of the fifth observational run of the aLIGO-AdVirgo Collaboration [17].

    Reuse & Permissions
  • Figure 7
    Figure 7

    The instability chart featuring the real part of the Floquet exponent normalized by the modulus mass (left) and the Hubble rate (right), characterizing the Higgs particle production rate. When ϕinf, Higgs particle production is expected for q>1. In FRW space-time kphys=k/a(t), implying that a given comoving mode flows towards the bottom left corner of the chart as the universe expands, as indicated with the white lines in the second chart. Note that particle production is efficient if |(μk)|/Hqmpl/f1.

    Reuse & Permissions
  • Figure 8
    Figure 8

    The evolution of the equation of state, w, and the ratio of the mean Higgs and modulus densities, ρh/ρϕ. After backreaction, for qmpl/f>102, there is a short-lived oscillatory phase. Despite this curious behavior, w settles to a constant value around 0.3. We have chosen parameters such that b=0.9, Δ=106 in all cases. The grey and orange curves are obtained by averaging over space, with additional averaging over fast oscillations for the orange curves.

    Reuse & Permissions
  • Figure 9
    Figure 9

    The growth in the amplitude of the GW power spectrum from the end of inflation to t70mϕ1 (with b=0.9, q=102, f=mpl). The curves are output at time intervals Δt=6mϕ1.

    Reuse & Permissions
  • Figure 10
    Figure 10

    The lower bound on mϕ as a function of ns (left) and r (right) with the inflation model in Eq. (c17) and α=1. The red solid and green dotted lines correspond to wmod=0 and 0.1, respectively. In the left panel, the light blue shaded region corresponds to the current 1σ bounds on ns from Planck TT+lowP+lensing. The narrower darker blue shaded region corresponds to the 1σ bounds of a future CMB experiment of ns with sensitivity ±2×103 [30], assuming the same central value as Planck. In the right panel, the blue shaded region corresponds to the 1σ bounds of a future CMB experiment of r with sensitivity ±5×104 [30], assuming a measured central value of r being 0.085.

    Reuse & Permissions
×

Sign up to receive regular email alerts from Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

×

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×