### [1008.5157] Higgs inflation: consistency and generalisation

Posted:

**September 17 2010**This is the most recent analysis of the validity of effective field theory and stability under quantum corrections in the very interesting proposal by Bezrukov and Shaposhnikov (0710.3755) of using the Standard Model Higgs as the inflaton.

The model relies on a large non-minimal coupling of the Higgs field to gravity, [tex]\xi\sim10^4[/tex]. It has been argued that this means that the cut-off scale of the model is below the Planck scale by the factor [tex]1/\xi[/tex], and that the model is therefore not valid at the high energy scales where inflation occurs. Similarly, since the model involves gravity, it is non-renormalisable, and it has been argued that this spoils the predictivity of the model (0902.4465, 0903.0355, 1002.2730).

Bezrukov et al analyse the situation by identifying a lower limit on the breakdown scale from the suppression coefficients of non-renormalisable operators, and do the analysis both in the Einstein and Jordan frames. The key feature is that the cutoff scale depends on the field value, since the background is time-dependent. They conclude that the cutoff scale remains above the scales of interest. However, they find that the connection between the inflationary parameters and the low-energy parameters accessible to collider experiments is sensitive to the quantum corrections, so connecting cosmological measurements and LHC measurements requires extra assumptions.

This model brings home the fact that while conformal transformations don't change the content of a classical scalar theory in curved space, quantising and changing conformal frame do not commute. This is of course also true for inflationary models which are written in the Einstein frame to begin with: how do you know which is the correct frame?

One question is that the motivation for the SM Higgs potential plus a non-minimal coupling comes from arguments about renormalisation, but since the model is non-renormalisable anyway, I'm not sure about the strength of that starting assumption.

The model relies on a large non-minimal coupling of the Higgs field to gravity, [tex]\xi\sim10^4[/tex]. It has been argued that this means that the cut-off scale of the model is below the Planck scale by the factor [tex]1/\xi[/tex], and that the model is therefore not valid at the high energy scales where inflation occurs. Similarly, since the model involves gravity, it is non-renormalisable, and it has been argued that this spoils the predictivity of the model (0902.4465, 0903.0355, 1002.2730).

Bezrukov et al analyse the situation by identifying a lower limit on the breakdown scale from the suppression coefficients of non-renormalisable operators, and do the analysis both in the Einstein and Jordan frames. The key feature is that the cutoff scale depends on the field value, since the background is time-dependent. They conclude that the cutoff scale remains above the scales of interest. However, they find that the connection between the inflationary parameters and the low-energy parameters accessible to collider experiments is sensitive to the quantum corrections, so connecting cosmological measurements and LHC measurements requires extra assumptions.

This model brings home the fact that while conformal transformations don't change the content of a classical scalar theory in curved space, quantising and changing conformal frame do not commute. This is of course also true for inflationary models which are written in the Einstein frame to begin with: how do you know which is the correct frame?

One question is that the motivation for the SM Higgs potential plus a non-minimal coupling comes from arguments about renormalisation, but since the model is non-renormalisable anyway, I'm not sure about the strength of that starting assumption.