Regge calculus models of the closed vacuumΛ-FLRW universe

AbstractThe system under study is the $$\Lambda $$ Λ -Kantowski–Sachs universe. Its canonical quantization is provided based on a recently developed method: the singular minisuperspace Lagrangian describing the system, is reduced to a regular (by inserting into the dynamical equations the lapse dictated by the quadratic constraint) possessing an explicit (though arbitrary) time dependence; thus a time-covariant Schrödinger equation arises. Additionally, an invariant (under transformations $$t=f({\tilde{t}})$$ t = f ( t ~ ) ) decay probability is defined and thus “observers” which correspond to different gauge choices obtain, by default, the same results. The time of decay for a Gaussian wave packet localized around the point $$a=0$$ a = 0 (where a the radial scale factor) is calculated to be of the order $$\sim 10^{-42}{-}10^{-41}~\text {s}$$ ∼ 10 - 42 - 10 - 41 s . The acquired value is near the end of the Planck era (when comparing to a FLRW universe), during which the quantum effects are most prominent. Some of the results are compared to those obtained by following the well known canonical quantization of cosmological systems, i.e. the solutions of the Wheeler–DeWitt equation.

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PRE-INFLATION IN THE PRESENCE OF CONFORMAL COUPLING

Modern Physics Letters A ◽

10.1142/s0217732304013386 ◽

2004 ◽

Vol 19 (11) ◽

pp. 807-816

Author(s):

APOSTOLOS KUIROUKIDIS ◽

DEMETRIOS B. PAPADOPOULOS

Keyword(s):

Scalar Field ◽

Exact Solutions ◽

Hubble Parameter ◽

Field Potential ◽

Critical Value ◽

Big Bang ◽

Massless Scalar ◽

Massless Scalar Field ◽

Conformal Parameter ◽

Flrw Universe

We consider a massless scalar field, conformally coupled to the Ricci scalar curvature, in the pre-inflation era of a closed FLRW Universe. The scalar field potential can be of the form of the Coleman–Weinberg one-loop potential, which is flat at the origin and drives the inflationary evolution. For positive values of the conformal parameter ξ, less than the critical value ξ c =(1/6), the model admits exact solutions with nonzero minimum scale factor and zero initial Hubble parameter. Thus these solutions can be matched smoothly to the so-called Pre-Big-Bang models. At the end of this pre-inflation era one can match inflationary solutions by specifying the form of the potential and the whole solution is of the class C(1).

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