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Haggard and Rovelli delineated an outer radius as to the range of quantum effects, which extends past the Schwartzshield radius. This is defined as 7/3 times the mass of the initial cosmological system. We also have a range of perturbative effects as delineated by Turok’s article which gives a range of values of for which second order perturbative terms in cosmological evolution may play a role, where we have second order perturbation terms for which . Right afterwards, there are no perturbative behavior and no perturbation if . This is the 2nd order term for perturbing term for GW (Gravitational wave) as denoted by , and near the “zero point” of cosmological expansion, and from there we determine the size of the quantum effects, i.e. when they initiate, the relevant initial entropy, so as to determine the radii of initial cosmology, so quantum gravity may initiate its activity, in our toy universe. The criteria of Turok is used to obtain the relevant mass, m, used in the initial radii so that it is 7/3 times the mass of the initial cosmological system. We use the “Criteria of Turok” to delineate the start of quantum gravity effects. Mass m is done via appealing to graviton mass, and that times initial entropy, which is commented upon in Equation (9).

journal of high energy physics, gravitation and cosmology

Gedanken Experiment for Delineating the Regime for the Start of Quantum Effects, and Their End, Using Turok’s Perfect Bounce Criteria and Radii of a Bounce Maintaining Quantum Effects, as Delineated by Haggard and Rovelli