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Register a new userHiggs inflation and quantum gravity: An exact renormalisation group approach
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Ippocratis Saltas Dr
Publication date
2015
fields
Physics
and research's language is
English
Authors
Ippocratis D. Saltas
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We use the Wilsonian functional Renormalisation Group (RG) to study quantum corrections for the Higgs inflationary action including the effect of gravitons, and analyse the leading-order quantum gravitational corrections to the Higgs quartic coupling, as well as its non-minimal coupling to gravity and Newtons constant, at the inflationary regime and beyond. We explain how within this framework the effect of Higgs and graviton loops can be sufficiently suppressed during inflation, and we also place a bound on the corresponding value of the infrared RG cut-off scale during inflation. Finally, we briefly discuss the potential embedding of the model within the scenario of Asymptotic Safety, while all main equations are explicitly presented.
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We study inflation driven by the Higgs field in the Einstein-Cartan formulation of gravity. In this theory, the presence of the Holst and Nieh-Yan terms with the Higgs field non-minimally coupled to them leads to three additional coupling constants. For a broad range of parameters, we find that inflation is both possible and consistent with observations. In most cases, the spectral index is given by $n_s=1-2/N_star$ (with $N_star$ the number of e-foldings) whereas the tensor-to-scalar ratio $r$ can vary between about $10^{-10}$ and $1$. Thus, there are scenarios of Higgs inflation in the Einstein-Cartan framework for which the detection of gravitational waves from inflation is possible in the near future. In certain limits, the known models of Higgs inflation in the metric and Palatini formulations of gravity are reproduced. Finally, we discuss the robustness of inflationary dynamics against quantum corrections due to the scalar and fermion fields.
The application of the exact renormalisation group to a many-fermion system with a short-range attractive force is studied. We assume a simple ansatz for the effective action with effective bosons, describing pairing effects and derive a set of approximate flow equations for the effective coupling including boson and fermionic fluctuations. The phase transition to a phase with broken symmetry is found at a critical value of the running scale. The mean-field results are recovered if boson-loop effects are omitted. The calculations with two different forms of the regulator was shown to lead to similar results.
We study quantum effects in Higgs inflation in the Palatini formulation of gravity, in which the metric and connection are treated as independent variables. We exploit the fact that the cutoff, above which perturbation theory breaks down, is higher than the scale of inflation. Unless new physics above the cutoff leads to unnaturally large corrections, we can directly connect low-energy physics and inflation. On the one hand, the lower bound on the top Yukawa coupling due to collider experiments leads to an upper bound on the non-minimal coupling of the Higgs field to gravity: $xi lesssim 10^8$. On the other hand, the Higgs potential can only support successful inflation if $xi gtrsim 10^6$. This leads to a fairly strict upper bound on the top Yukawa coupling of $0.925$ (defined in the $overline{text{MS}}$-scheme at the energy scale $173.2,text{GeV}$) and constrains the inflationary prediction for the tensor-to-scalar ratio. Additionally, we compare our findings to metric Higgs inflation.
We present a comparative study of inflation in two theories of quadratic gravity with {it gauged} scale symmetry: 1) the original Weyl quadratic gravity and 2) the theory defined by a similar action but in the Palatini approach obtained by replacing the Weyl connection by its Palatini counterpart. These theories have different vectorial non-metricity induced by the gauge field ($w_mu$) of this symmetry. Both theories have a novel spontaneous breaking of gauged scale symmetry, in the absence of matter, where the necessary scalar field is not added ad-hoc to this purpose but is of geometric origin and part of the quadratic action. The Einstein-Proca action (of $w_mu$), Planck scale and metricity emerge in the broken phase after $w_mu$ acquires mass (Stueckelberg mechanism), then decouples. In the presence of matter ($phi_1$), non-minimally coupled, the scalar potential is similar in both theories up to couplings and field rescaling. For small field values the potential is Higgs-like while for large fields inflation is possible. Due to their $R^2$ term, both theories have a small tensor-to-scalar ratio ($rsim 10^{-3}$), larger in Palatini case. For a fixed spectral index $n_s$, reducing the non-minimal coupling ($xi_1$) increases $r$ which in Weyl theory is bounded from above by that of Starobinsky inflation. For a small enough $xi_1leq 10^{-3}$, unlike the Palatini version, Weyl theory gives a dependence $r(n_s)$ similar to that in Starobinsky inflation, while also protecting $r$ against higher dimensional operators corrections.
We study quadratic gravity $R^2+R_{[mu u]}^2$ in the Palatini formalism where the connection and the metric are independent. This action has a {it gauged} scale symmetry (also known as Weyl gauge symmetry) of Weyl gauge field $v_mu= (tildeGamma_mu-Gamma_mu)/2$, with $tildeGamma_mu$ ($Gamma_mu$) the trace of the Palatini (Levi-Civita) connection, respectively. The underlying geometry is non-metric due to the $R_{[mu u]}^2$ term acting as a gauge kinetic term for $v_mu$. We show that this theory has an elegant spontaneous breaking of gauged scale symmetry and mass generation in the absence of matter, where the necessary scalar field ($phi$) is not added ad-hoc to this purpose but is extracted from the $R^2$ term. The gauge field becomes massive by absorbing the derivative term $partial_mulnphi$ of the Stueckelberg field (dilaton). In the broken phase one finds the Einstein-Proca action of $v_mu$ of mass proportional to the Planck scale $Msim langlephirangle$, and a positive cosmological constant. Below this scale $v_mu$ decouples, the connection becomes Levi-Civita and metricity and Einstein gravity are recovered. These results remain valid in the presence of non-minimally coupled scalar field (Higgs-like) with Palatini connection and the potential is computed. In this case the theory gives successful inflation and a specific prediction for the tensor-to-scalar ratio $0.007leq r leq 0.01$ for current spectral index $n_s$ (at $95%$CL) and N=60 efolds. This value of $r$ is mildly larger than in inflation in Weyl quadratic gravity of similar symmetry, due to different non-metricity. This establishes a connection between non-metricity and inflation predictions and enables us to test such theories by future CMB experiments.
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