Higgs Starobinsky inflation

Abstract

In this paper we point out that Starobinsky inflation could be induced by quantum effects due to a large nonminimal coupling of the Higgs boson to the Ricci scalar. The Higgs Starobinsky mechanism provides a solution to issues attached to large Higgs field values in the early universe which in a metastable universe would not be a viable option. We verify explicitly that these large quantum corrections do not destabilize Starobinsky's potential.The idea that inflation may be due to degrees of freedom already present in the standard model of particle physics or quantum general relativity is extremely attractive and has received much attention in the recent years. In particular two models stand out by their simplicity and elegance. Higgs inflation [1][2][3] with a large non-minimal coupling of the Higgs boson H to the Ricci scalar (ξ H † H R) and Starobinsky's inflation model [4] based on R 2 gravity are both minimalistic and perfectly compatible with the latest Planck data.These two models should not be considered as physics beyond the standard model but rather both operators ξ H † H R and R 2 are expected to be generated when general relativity is coupled to the standard model of particle physics. We will come back to that point shortly. The aim of this paper is to point out an intriguing distinct possibility, namely that Starobinsky inflation is generated by quantum effects due to a large non-minimal coupling of the Higgs boson to the Ricci scalar. In that framework, we do not need to posit that the Higgs boson starts at a high field value in the early universe which would alleviate constraints coming from the requirement of having a stable Higgs potential even for large Higgs field values [5][6][7].We shall now argue that both terms necessary for Higgs inflation or Starobinsky's model are naturally present when the standard model of particle physics is coupled to general relativity. While the quantization of general relativity remains one of the outstanding challenges of theoretical a e-mail: x.calmet@sussex.ac.uk b e-mail: ibere.kuntz@sussex.ac.uk physics, it is possible to use effective field theory methods below the energy scale M at which quantum gravitational effects are expected to become large. The energy scale M is usually assumed to be of the order of the Planck scale where we have restricted our considerations to dimension four operators which are expected to dominate at least at low energies. Note that we are using the Weyl basis and the following notations: R stands for the Ricci scalar, R μν for the Ricci tensor, E = R μνρσ R μνρσ − 4R μν R μν + R 2 , C 2 = E + 2R μν R μν − 2/3R 2 , the dimensionless ξ is the non-minimal coupling of the Higgs boson H to the Ricci scalar, the coefficients c i are dimensionless free parameters, the cosmological constant C is of order of 10 −3 eV, the Higgs boson vacuum expectation value, v = 246 GeV contributes to the value of the Planck scale,L SM contains all the usual standard model interactions (including mass terms for neutrinos), and finally L DM descr...

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