Non-minimal Coupling Constant Research Articles

Constraints on the chaotic inflationary scenario with a nonminimally coupled “inflaton” field from the cosmic microwave background radiation anisotropy

We investigate the possibility to restrict the chaotic inflationary scenario with the large nonminimally coupled inflaton field $\ensuremath{\varphi}$ considered by Fakir and Unruh by means of the observed cosmic microwave background radiation (CMBR) anisotropy. This model is characterized by the condition $\ensuremath{\xi}>1$ and $\ensuremath{\psi}\ensuremath{\equiv}8\ensuremath{\pi}G\ensuremath{\xi}{\ensuremath{\varphi}}^{2}\ensuremath{\gg}1$ where $\ensuremath{\xi}$ is the nonminimal coupling constant. We calculate the contributions of the long wavelength gravitational waves generated in the inflationary period to the CMBR anisotropy quadrupole moment. We obtain the constraint $\ensuremath{\lambda}/{\ensuremath{\xi}}^{2}=1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}/{\ensuremath{\psi}}_{i},$ where $\ensuremath{\lambda}$ is the self-coupling and ${\ensuremath{\psi}}_{i}$ means the initial value of $\ensuremath{\psi}.$ Combining this with the previously obtained constraint $\sqrt{\ensuremath{\lambda}/{\ensuremath{\xi}}^{2}}\ensuremath{\approx}(\ensuremath{\delta}{T/T)}_{\mathrm{rms}}=1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5},$ we conclude that the initial value has to be ${\ensuremath{\psi}}_{i}\ensuremath{\approx}1.6\ifmmode\times\else\texttimes\fi{}{10}^{3}.$ If the self-coupling has reasonable values of order ${10}^{\ensuremath{-}2},$ then $\ensuremath{\xi}\ensuremath{\approx}{10}^{4}$ and ${\ensuremath{\varphi}}_{i}\ensuremath{\approx}{10}^{\ensuremath{-}1}{m}_{\mathrm{Pl}}$ where ${m}_{\mathrm{Pl}}$ is the Planck mass.

Quantum cosmology and physics of transitions with a change of the spacetime signature

This paper examines elements of the general theory of transitions with changing spacetime signature in quantum gravity and cosmology as suggested in a pioneer work of A D Sakharov. Unlike the conventional formal method for functional integration, this approach uses as the starting point the Dirac–Wheeler–de Witt operator quantization and its reduction to quantization in Arnowitt–Deser–Misner variables. It has been demonstrated that motivation to consider Euclidean–Lorentzian transitions consists in global ambiguity of physical reduction on the phase space of the theory (a gravitational analog of the problem of Gribov's copies). This ambiguity in particular results in the indefinite sign of the physical inner product of quantum states and leads to the concept of third quantization. An alternative approach is quantization in the York gauge and in special variables of conformal superspace. This quantization is likely to provide a global solution of the ambiguity problem, but the problems of Euclidean–Lorentzian transitions arise in this formalism in the language of complexification of a conformal space of the Wick-rotation type for the time variable in the Klein–Gordon equation. The problem of origin of the early Universe via gravitational tunneling in Hartle–Hawking and Vilenkin quantum states is considered to illustrate applications of the general theory. The mechanism is described by which loop effects generate the normalizable distribution function for the ensemble of chaotic inflationary universes. In a model with a large non-minimal coupling constant for the scalar inflation, this mechanism gives rise to a sharp probability peak at sub-Planckian values for the Hubble constant which is in good agreement with the contemporary observational status of the cosmological inflation theory.

MODEL DEPENDENCE OF THE NON-MINIMAL SCALAR-GRAVITON EFFECTIVE COUPLING CONSTANT IN CURVED SPACE-TIME

We investigate the renormalization group behavior of the non-minimal scalar-graviton effective coupling constant in asymptotically free theories (where scalars are elementary) and in a simple four-fermion model (where scalars are composite). We find that this behavior is model-dependent in asymptotically free theories and is asymptotically conformally invariant in the four-fermion model. We observe that the behavior may be altered in more complicated four-fermion models.

Asymptotic behavior of the effective nonminimal coupling constants in curved spacetime with torsion

The asymptotic behavior of the effective coupling constants in two SU(2) field-theory models containing Weyl spinors in curved spacetime with torsion is studied. In flat space, these models are finite in the single-loop approximation.

Nonlinear electrodynamics in space-times with torsion

A nonminimal and nongauge invariant descirption of nonlinear electrodynamics in space-times with torsion is given. It is shown that in the case of the Weitzenbock teleparallel space-time, massive photons are produced by a mechanism which involves the nonminimal coupling constant and the divergence of the torsion vector.

On the renormalisation group equations in curved spacetime with torsion

The renormalisation structure of gauge models in curved spacetime with torsion is considered. For Abelian theory the classical action, leading to multiplicatively renormalised theory, is constructed. The multiplicativity of renormalisation requires nonminimal coupling of a vector Abelian field with torsion. The authors investigate the renormalisation group equations for effective nonminimal coupling constants in nonAbelian theory. They find that the equations for essential nonminimal couplings have the universal structure. Due to radiative corrections the interaction between spinor fields and torsion become more intense in the strong gravitational field.

Competition for toys in 9–11 month old boy-girl twins

We consider a Schwarzschild–de Sitter (SdS) black hole, and focus on the emission of massless scalar fields either minimally or non-minimally coupled to gravity. We use six different temperatures, two black-hole and four effective ones for the SdS spacetime, as the question of the proper temperature for such a background is still debated in the literature. We study their profiles under the variation of the cosmological constant, and derive the corresponding Hawking radiation spectra. We demonstrate that only few of these temperatures may support significant emission of radiation. We finally compute the total emissivities for each temperature, and show that the non-minimal coupling constant of the scalar field to gravity also affects the relative magnitudes of the energy emission rates.

Local and global existence of solutions to scalar equations on spatially flat universe as a background with non-minimal coupling

We prove the wellposedness of scalar wave equations on spatially flat universe as a background with nonminimal coupling with the scalar potential turned on by introducing the $k$-order linear energy and the corresponding energy norm. In the local case, we show that both the $k$-order linear energy and the energy norm are bounded for finite time with initial data in $H^{k+1}\times H^{k}$. Whereas in the global case, we have to add three assumptions related to the nonminimal coupling constant, the scale factor of spacetimes, and the form of the scalar that has to be a polynomial with a small positive parameter. Then, we show that the solution does globally exist with a particular decay estimate that depends on the scale factor of the spacetimes. Finally, we provide some physical models that support our general setup.