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 the 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.