Search Results (6)

For the deconfinement phase of an SU(2) Yang–Mills theory, we compute the axion mass $m_A$ by appealing to the Veneziano–Witten formula. The topological susceptibility $\chi$ arises (i) from a precisely computable thermal ground-state contribution due to a center of a relevant (anti)caloron, and (ii) from contributions due to free thermal quasi-particles in the effective theory. Both (i) and (ii) are derived by using standard Euclidean thermal field theory techniques. While contribution (i) is positive and $\propto T^4$, contribution (ii) is negative, as demanded by reflection positivity, but negligible compared to contribution (i). As a consequence, practically from the critical temperature $T_c$ onward, a real-valued axion mass $m_A\left(T\right)=\sqrt{{\displaystyle \frac{2}{3}}}\pi {\displaystyle \frac{T^2}{M_P}}$ emerges when the Peccei–Quinn scale is assumed to be the Planck mass $M_P$, independently of the Yang–Mills scale that the axion associates with. We discuss why our results deviate from those found in the dilute instanton gas and interacting instanton liquid approximations, and from results obtained in lattice simulations. Assuming the universe is dark sector to be based on such ultralight axion species, which are nonrelativistic for $T\ll M_P$, we investigate the cosmological conditions for their global Bose condensation as the very early universe cooled to temperatures of the order of ${10}^9$eV. Full article

An alternative formulation of the no-boundary initial state of the universe in the Euclidean quantum theory of gravity is proposed. Unlike the no-boundary Hartle–Hawking wave function, in which time appears together with macroscopic space–time in the semiclassical approximation, in the proposed formalism, time is present from the very beginning on an equal footing with spatial coordinates. The main element of the formalism is the wave functional, which is defined based on the world histories of the universe. This ensures formal 4D covariance of the theory. The wave functional is defined independently of the wave function as an eigenvector of the action operator. The shape of the Origin region, together with the boundary conditions, is determined by the structure of the total energy of the universe, which includes a 3D-invariant contribution of the expansion energy. The own mass of the universe arises as a non-zero value of the expansion energy in the Origin. Full article

The exact solution of the Hamiltonian constraint in canonical gravity and the resultant reduction of Einstein’s theory reveal the synergy between gravitation and the intrinsic cosmic clock of our expanding universe. Intrinsic Time Geometrodynamics advocates a paradigm shift from four covariance to just spatial diffeomorphism invariance. Consequently, causal time-ordering and quantum Schrödinger–Heisenberg evolution in cosmic time become meaningful. The natural addition of a Cotton–York term to the physical Hamiltonian changes the initial data problem radically. In the classical context, this is studied with the Lichnerowicz–York equation; quantum mechanically, it lends weight to the origin of the universe as an exact Chern–Simons Hartle–Hawking state, which features Euclidean–Lorentzian instanton tunneling. At the level of expectation values, this quantum state yields a low-entropy hot smooth Robertson–Walker beginning in accord with Penrose’s Weyl Curvature Hypothesis. The Chern–Simons Hartle–Hawking state also manifests transverse traceless quantum metric fluctuations, with, at the lowest approximation, scale-invariant two-point correlations as one of its defining characteristics. Full article

The Euclidean path integral is well approximated by instantons. If instantons are dynamical, they will necessarily be complexified. Fuzzy instantons can have multiple physical applications. In slow-roll inflation models, fuzzy instantons can explain the probability distribution of the initial conditions of the universe. Although the potential shape does not satisfy the slow-roll conditions due to the swampland criteria, the fuzzy instantons can still explain the origin of the universe. If we extend the Euclidean path integral beyond the Hartle–Hawking no-boundary proposal, it becomes possible to examine fuzzy Euclidean wormholes that have multiple physical applications in cosmology and black hole physics. Full article

We study the geometry of Euclidean instantons in loop quantum cosmology (LQC) such as those relevant for the no-boundary proposal. Confining ourselves to the simplest case of a cosmological constant in minisuperspace cosmologies, we analyze solutions of the semiclassical (Euclidean) path integral in LQC. We find that the geometry of LQC instantons have the peculiar feature of an infinite tail which distinguishes them from Einstein gravity. Moreover, due to quantum-geometry corrections, the small-a behaviour of these instantons seem to naturally favor a closing-off of the geometry in a regular fashion, as was originally proposed for the no-boundary wavefunction. Full article

In this seven-part paper, we show that gravitational waves (classical and quantum) produce the accelerated de Sitter expansion at the start and at the end of the cosmological evolution of the Universe. In these periods, the Universe contains no matter fields but contains classical and quantum metric fluctuations, i.e., it is filled with classical and quantum gravitational waves. In such evolution of the Universe, dominated by gravitational waves, the de Sitter state is the exact solution to the self-consistent equations for classical and quantum gravitational waves and background geometry for the empty space-time with FLRW metric. In both classical and quantum cases, this solution is of the instanton origin since it is obtained in the Euclidean space of imaginary time with the subsequent analytic continuation to real time. The cosmological acceleration from gravitational waves provides a transparent physical explanation to the coincidence, threshold and “old cosmological constant” paradoxes of dark energy avoiding recourse to the anthropic principle. The cosmological acceleration from virtual gravitons at the start of the Universe evolution produces inflation, which is consistent with the observational data on CMB anisotropy. Section 1 is devoted to cosmological acceleration from classical gravitational waves. Section 2 is devoted to the theory of virtual gravitons in the Universe. Section 3 is devoted to cosmological acceleration from virtual gravitons. Section 4 discusses the consistency of the theory with observational data on dark energy and inflation. The discussion of mechanism of acceleration and cosmological scenario are contained in Sections 5 and 6. Appendix contains the theory of stochastic nonlinear gravitational waves of arbitrary wavelength and amplitude in an isotropic Universe. Full article