Scalar Field and Particle Dynamics in Conformal Frame

This is the first of three papers on Conformal General Relativity (CGR), which differs from Einstein's General Relativity (GR) in that it requires action-integral invariance under local scale transformations in addition to general coordinate transformations. The theory is here introduced in the semiclassical approximation as a preliminary approach to a quantum theoretical implementation. The idea of a conformal-invariant extension of GR was introduced by Weyl in 1919. For several decades it had little impact, as CGR implies that all fields are massless. Today this does not appear to be an unsurmountable difficulty since nonzero mass parameters may result from the spontaneous breakdown of conformal symmetry. The theory leads to very interesting results and predictions: 1) the spontaneous breakdown of conformal symmetry is only possible in a 4D-spacetime with small negative curvature; 2) CGR requires the introduction of a ghost scalar field σ(x) invested with geometric meaning and a physical scalar field ϕ(x) of zero mass, both of which have nonzero vacuum expectation values; 3) in order to preserve S-matrix unitarity, σ(x) and ϕ(x) must interact in such a way that the total energy density is bounded from below; 4) this interaction makes ϕ(x) behave like a Higgs field of varying mass, which is capable of promoting a huge energy transfer from geometry to matter identifiable as the big bang; 5) in the course of time, the Higgs boson mass becomes a constant and CGR converges to GR.

EPJ Web of Conferences, 2016

We constructed the conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from the "usual" hydrodynamical description of the particle motion written in the Eulerian coordinates we substituted the particle number conservation law (which enters the formalism) by "the particle creation law", proportional to the square of the Weyl tensor (following the famous result by Ya. B. Zel'dovich and A. A. Starobinsky). Then, demanding the conformal invariance of the whole dynamical system, we have got both the (Weyl)-conformal gravity and the Einstein-Hilbert-dilaton gravity action integral. Thus, we obtained something like the induced gravity suggested first by A. D. Sakharov. It is shown that the resulting system is self-consistent. Some future developments of the theory are discussed in the concluding Chapter.

Physical Review D, 1999

We present a general formulation of the time-dependent initial value problem for a quantum scalar field of arbitrary mass and curvature coupling in a Friedmann-Robertson-Walker (FRW) cosmological model. We introduce an adiabatic number basis which has the virtue that the divergent parts of the quantum expectation value of the energy-momentum tensor T ab are isolated in the vacuum piece of T ab , and may be removed using adiabatic subtraction. The resulting renormalized T ab is conserved, independent of the cutoff, and has a physically transparent, quasiclassical form in terms of the average number of created adiabatic 'particles'. By analyzing the evolution of the adiabatic particle number in de Sitter spacetime we exhibit the time structure of the particle creation process, which can be understood in terms of the time at which different momentum scales enter the horizon. A numerical scheme to compute T ab as a function of time with arbitrary adiabatic initial states (not necessarily de Sitter invariant) is described. For minimally coupled, massless fields, at late times the renormalized T ab goes asymptotically to the de Sitter invariant state previously found by Allen and Folacci, and not to the zero mass limit of the Bunch-Davies vacuum. If the mass m and the curvature coupling ξ differ from zero, but satisfy m 2 + ξR = 0, the energy density and pressure of the scalar field grow linearly in cosmic time demonstrating that, at least in this case, backreaction effects become significant and cannot be neglected in de Sitter spacetime.

Journal of Cosmology and Astroparticle Physics, 2014

We formulate new conformal models of inflation and dark energy which generalise the Higgs-Dilaton scenario. We embed these models in unimodular gravity whose effect is to break scale invariance in the late time Universe. In the early Universe, inflation occurs close to a maximum of both the scalar potential and the scalar coupling to the Ricci scalar in the Jordan frame. At late times, the dilaton, which decouples from the dynamics during inflation, receives a potential term from unimodular gravity and leads to the acceleration of the Universe. We address two central issues in this scenario. First we show that the Damour-Polyalov mechanism, when non-relativistic matter is present prior to the start of inflation, sets the initial conditions for inflation at the maximum of the scalar potential. We then show that conformal invariance implies that matter particles are not coupled to the dilaton in the late Universe at the classical level. When fermions acquire masses at low energy, scale invariance is broken and quantum corrections induce a coupling between the dilaton and matter which is still small enough to evade the gravitational constraints in the solar system.

2021

While a theory calculating a cosmological generation of particles ina case of the expanding space-time is quite developed, we study here a theory of a cosmological generation of particles in a case of a space- time which is expanding and then contracting back. The simplest case of fields studied in this connection is a scalar field. We will show in our paper that the quantum scalar field has delocalized in the conformal time η particle-like modes uⁱⁿ and two localized in the conformal time modes uⁱⁿ and uⁱⁿ for our choosen scale factor C(η). The vacuum for these states | 0, out > defined through massive modes uᵒᵘᵗ and through modes uᵒᵘᵗ and uᵒᵘᵗ is the same as the vacuum | 0, in >. A detector shows that there are no mass particles and no localized states forη → +∞ for non-accelerating case. For η → −∞ a Minkowski space- time is realized, as it is realized also in the out case. The quantum field has delocalized in the conformal time η particle-like modes uᵒᵘᵗ which in the -out ...

Journal of Geometry and Physics, 2012

A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the presence of matter it is possible to construct a conformal gauge which allows to know a priori the location of the conformal boundary. In vacuum this gauge reduces to the so-called conformal Gaussian gauge. These ideas are applied to obtain: (i) a new proof of the stability of Einstein-Maxwell de Sitterlike spacetimes; (ii) a proof of the semi-global stability of purely radiative Einstein-Maxwell spacetimes.

Electronic Journal of Theoretical Physics

This is the second of three papers on Conformal General Relativity (CGR). The conformal group is introduced here as the invariance group of the partial order of causal events in nD spacetime. Its general structure, discrete symmetries and field representations are described in detail. The spontaneous breakdown of conformal symmetry is then discussed and the role played by a ghost scalar field and a physical scalar field in 4D spacetime are evidenced. Kinematic-, conformal-and proper-time hyperbolic coordinates are introduced in a negatively curved Milne spacetime for the purpose of providing three different but equivalent representations of CGR. The first of these is grounded in a Riemannian manifold and is manifestly conformal invariant, the second is grounded in a conformally connected Cartan manifold but its conformal invariance is hidden, the third is grounded in the Riemannian manifold of the Milne spacetime and has the formal structure of General Relativity (GR). The relation between CGR and standard inflationary cosmology is also briefly discussed. Lastly, in view of the detailed study of Higgs-field dynamics carried out in the third paper, the action integrals, motion equations and total energy-momentum tensors of the Higgs field interacting with the dilation field are described in the three representations mentioned above.

Physics Letters B, 2010

The General Relativity formulated with the aid of the spin connection coefficients is considered in the finite space geometry of similarity with the Dirac scalar dilaton. We show that the redshift evolution of the General Relativity describes the vacuum creation of the matter in the empty Universe at the electroweak epoch and the dilaton vacuum energy plays a role of the dark energy.

Journal of Cosmology and Astroparticle Physics, 2015

Physical equivalence between different conformal frames in scalar-tensor theory of gravity is a known fact. However, assuming that matter minimally couples to the metric of a particular frame, which we call the matter Jordan frame, the matter point of view of the universe may vary from frame to frame. Thus, there is a clear distinction between gravitational sector (curvature and scalar field) and matter sector. In this paper, focusing on a simple power-law inflation model in the Einstein frame, two examples are considered; a super-inflationary and a bouncing universe Jordan frames. Then we consider a spectator curvaton minimally coupled to a Jordan frame, and compute its contribution to the curvature perturbation power spectrum. In these specific examples, we find a blue tilt at short scales for the super-inflationary case, and a blue tilt at large scales for the bouncing case.

Physical Review D, 2003

We study the back-reaction effect of a massless minimally coupled scalar field at finite temperatures in the background of an Einstein universe. Substituting for the vacuum expectation value of the components of the energy-momentum tensor on the right hand side of the Einstein equation, we deduce a relationship between the radius of the universe and its temperature. This relationship exhibits a maximum temperature, below the Planck scale, at which the system changes its behavior drastically. The results are compared with the case of a conformally coupled field. An investigation into the values of the cosmological constant exhibits a remarkable difference between the conformally coupled case and the minimally coupled one.