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In this work a series of methods are developed for understanding the Friedmann equation when it is beyond the reach of the Chebyshev theorem. First it will be demonstrated that every solution of the Friedmann equation admits a representation as a roulette such that information on the latter may be used to obtain that for the former. Next the Friedmann equation is integrated for a quadratic equation of state and for the Randall--Sundrum II universe, leading to a harvest of a rich collection of new interesting phenomena. Finally an analytic method is used to isolate the asymptotic behavior of the solutions of the Friedmann equation, when the equation of state is of an extended form which renders the integration impossible, and to establish a universal exponential growth law.
We completely classify Friedmann-Lema^{i}tre-Robertson-Walker solutions with spatial curvature $K=0,pm 1$ and equation of state $p=wrho$, according to their conformal structure, singularities and trapping horizons. We do not assume any energy conditi
Current astronomical observations are successfully explained by the present cosmological paradigm based on the concordance model ($Lambda_0$CDM + Inflation). However, such a scenario is composed of a heterogeneous mix of ingredients for describing th
A regularization procedure has been recently suggested for regularizing Big Bang singularities in Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes. We argue that this procedure is only appliable to one case of Big Bang singularities and does not affect other types of singularities.
We use an alternative interpretation of quantum mechanics, based on the Bohmian trajectory approach, and show that the quantum effects can be included in the classical equation of motion via a conformal transformation on the background metric. We app
We discuss the most general field equations for cosmological spacetimes for theories of gravity based on non-linear extensions of the non-metricity scalar and the torsion scalar. Our approach is based on a systematic symmetry-reduction of the metric-