Standard Model Higgs inflation: CMB, Higgs mass and quantum cosmology

We consider the inflation model generated by the Standard Model (SM) Higgs boson having a strong non-minimal curvature coupling. This model suggests the range of the Higgs mass $135.6\; {\rm GeV} \lesssim M_H\lesssim 184.5\;{\rm GeV}$ entirely determined by the lower WMAP bound on the CMB spectral index. This result is based on the renormalization group analysis of quantum effects which make the SM phenomenology sensitive to the current cosmological data and thus suggest CMB measurements as a SM test complementary to the LHC program. We show naturalness of the gradient and curvature expansion in this model in a conventional perturbation theory range of SM. The origin of initial conditions for inflation within the quantum cosmology concept of the tunneling state of the Universe is also considered. In this way a complete cosmological scenario is obtained, which embraces the formation of initial conditions for the inflationary background in the form of a sharp probability peak in the distribution of the inflaton field and the ongoing generation of the CMB spectrum on this background.Comment: 19 pages, 5 figures, talk given at the Yukawa Institute for Theoretical Physics Symposium "Cosmology-the Next Generation", Kyoto, 2010, to appear in Prog. Theor. Phy

Unimodular Gravity in Restricted Gauge Theory Setup

We develop Lagrangian quantization formalism for a class of theories obtained by the restriction of the configuration space of gauge fields from a wider (parental) gauge theory. This formalism is based on application of Batalin-Vilkovisky technique for quantization of theories with linearly dependent generators, their linear dependence originating from a special type of projection from the originally irreducible gauge generators of the parental theory. The algebra of these projected generators is shown to be closed for parental gauge algebras closed off shell. We demonstrate that new physics of the restricted theory as compared to its parental theory is associated with the rank deficiency of a special gauge restriction operator reflecting the gauge transformation properties of the restriction constraints functions -- this distinguishes restriction of the theory from its partial gauge fixing. As a byproduct of this technique a workable algorithm for one-loop effective action in generic first-stage reducible theory was constructed, along with the explicit set of tree-level Ward identities for gauge field, ghost and ghosts-for-ghosts propagators, which guarantee on-shell gauge independence of this effective action. The restricted theory formalism with reducible set of projected gauge generators is applied to unimodular gravity theory by using background-covariant gauge-fixing procedure. Its one-loop effective action is obtained in terms of functional determinants of minimal second order differential operators calculable on generic backgrounds by Schwinger-DeWitt technique of local curvature expansion. The result is shown to be equivalent to Einstein gravity theory with a cosmological term up to a special contribution of the global degree of freedom associated with the variable value of the cosmological constant. The role of this degree of freedom is briefly discussed.Comment: 47 page

Nonminimal Higgs Inflation and Initial Conditions in Cosmology

We discuss applications of perturbative quantum gravity in the theory of very early quantum Universe and quantum cosmology. Consistency of the theoretical formalism for quantum effects of matter and correspondence with observational status of modern precision cosmology impose stringent bounds on and establish strong links with high energy particle phenomenology. Within this line of reasoning we study various aspects of one-loop approximation for the cosmological wave function, review Higgs inflation model intertwining the physics of electroweak sector of the Standard Model with the characteristics of the observable cosmic microwave background and, finally, consider the problem of quantum initial conditions for inflationary Universe. We formulate a cosmological quantum state in the form of the microcanonical density matrix -- a universal equipartition of eigenstates of the Wheeler-DeWitt equations. We demonstrate elimination of the inalienable infrared catastrophe of vanishing cosmological constant for the no-boundary quantum state of the Universe and derive initial conditions for inflation in the form of a special garland-type cosmological instanton -- the saddle point of quantum gravity path integral. Applied to the cosmological model of the Universe with a hidden sector of numerous conformally invariant higher spin fields, this setup suggests a solution to the problem of hierarchy between the Planck and the inflation energy scales and, thus, admits applicability of perturbative semiclassical expansion methods.Comment: 42 pages, 7 figures, to be published in the section on Perturbative Quantum Gravity (Ed. I. Shapiro) in the Handbook of Quantum Gravity (Eds. C. Bambi, L. Modesto and I. Shapiro), Springer, 2023. arXiv admin note: text overlap with arXiv:0910.1041, arXiv:1012.452

Wheeler-DeWitt equation and Feynman diagrams

We present a systematic expansion of all constraint equations in canonical quantum gravity up to the order of the inverse Planck mass squared. It is demonstrated that this method generates the conventional Feynman diagrammatic technique involving graviton loops and vertices. It also reveals explicitly the back reaction effects of quantized matter and graviton vacuum polarization. This provides an explicit correspondence between the frameworks of canonical and covariant quantum gravity in the semiclassical limit.Comment: 35 pages, LATEX, 1 figur

Comment about the vanishing of the vacuum energy in the Wess-Zumino model

We check the cancellation of the vacuum energy in the Wess-Zumino model at the two-loop order in the component field formalisms with and without auxiliary fields. We show that in both cases the vacuum energy is equal to zero. However, in the formalism where the auxiliary fields are excluded, the vanishing of the vacuum energy arises due to the cancellation between the potential and kinetic energies, while in the formalism with the auxiliary fields, both terms vanish separately.Comment: 13 page