Higgs chameleon

The existing constraints from particle colliders reveal a suspicious but nonlethal metastability for our current electroweak vacuum of Higgs potential in the standard model of particle physics, which is, however, disfavored in the early Universe if the inflationary Hubble scale is larger than the instability scale when Higgs quartic self-coupling runs into negative value. Alternative to previous trials of acquiring a positive effective mass-squared from Higgs quadratic couplings to Ricci scalar or inflaton field, we propose a third approach to stabilize the Higgs potential in the early Universe by regarding Higgs as chameleon coupled to inflaton alone without conflicting to the present constraints on either Higgs or chameleon.

Figure 1

Upper left: the original unstable Higgs potential $V_0$ (red) is stabilized by the Higgs chameleon coupling to inflaton with appearance of a second minimum (blue curves around degeneracy case ${\xi }_{\mathrm{deg}}$) until its disappearance at the inflection case ${\xi }_{\inf }$ (green) with increasing dimensionless chameleon coupling $\alpha \equiv \xi /4$ and fixed amplitude of chameleon coupling $c$. Upper right: the cases of degeneracy ${\xi }_{\mathrm{deg}}$ (red) and inflection ${\xi }_{\inf }$ (blue) with respect to $c$ approach asymptotically to ${\xi }_{\infty }=4c^{-1/4}$ (green dashed) at large $c$ limit. The built-in panel in the lower left corner exhibits an asymptotically vanishing difference between ${\xi }_{\mathrm{deg}}$ and ${\xi }_{\inf }$ at large $c$ limit. The built-in panel in the upper right corner exhibits similar asymptotic behavior of Higgs field values at degenerated minimum $h_{\mathrm{deg}}$ (red) and inflection point $h_{\inf }$ (blue) approaches to $h_{\mathrm{deg}}^{\infty }=c^{1/4}{h}_c$ (green dashed) at large $c$ limit. Lower left: the region for an absolutely stable Higgs effective potential without presence of a second minimum (green shaded) is shown above the blue lines computed from $\xi >{\xi }_{\inf }$ for some illustrative values of the amplitude of Higgs chameleon coupling ${\mathrm{\Omega }}_{\varphi }(0)={10}^{-1},{10}^{-2},{10}^{-3},{10}^{-4}$ from top to below. The gray shaded regions are ruled out by current constraint on the tensor-to-scalar ratio $r<0.06$ and the UV effectiveness $H_{\inf }<{\mathrm{\Lambda }}_n$. The stability analysis in the red shaded region below the blue lines with presence of a second minimum is presented in the next panel. Lower right: for given amplitude of Higgs chameleon coupling ${\mathrm{\Omega }}_{\varphi }(0)$ (black numbers), the directions of arrows point to larger position, higher height, and broader width of Higgs potential barrier with respect to Higgs quantum fluctuation scale, $h_{\max }/H_{\inf }$ (red), $V_{\mathrm{bar}}^{1/4}/H_{\inf }$ (blue), and $|V_{\mathrm{bar}}^{\prime \prime }|/(4H_{\inf }^2)$ (green) as well as larger position of Higgs potential barrier at finite temperature with respect to the position of the second minimum at zero temperature $h_{\max }^T/h_{\min }$ (purple).