Strategies to Ascertain the Sign of the Spatial Curvature

Abstract

Abstract:The second law of thermodynamics, in the presence of gravity, is known to hold at small scales, as in the case of black holes and self-gravitating radiation spheres. Using the Friedmann-Lemaître-Robertson-Walker metric and the history of the Hubble factor, we argue that this law also holds at cosmological scales. Based on this, we study the connection between the deceleration parameter and the spatial curvature of the metric, Ω k , and set limits on the latter, valid for any homogeneous and isotropic cosmological model. Likewise, we devise strategies to determine the sign of the spatial curvature index k. Finally, assuming the lambda cold dark matter model is correct, we find that the acceleration of the cosmic expansion is increasing today.

Does the second law hold at cosmic scales?

“…As it turns out, our study -which is purely kinematic -suggests that this may well be the case and, i.e., that the universe seems to tend to a state of maximum entropy in the long run. This outcome was suggested earlier (Ferreira & Pavón 2016). Here we strengthen this suggestion by employing an ampler dataset and using a somewhat different analysis.…”

Constraining the curvature density parameter in cosmology

“…Recently Ferreira and Pavón [35] gave a prescription to ascertain the signature of k from the second law of thermodynamics. It is a fair assumption that the entropy of the observable universe is dominated by that of the cosmic horizon S A [118].…”

“…It is a fair assumption that the entropy of the observable universe is dominated by that of the cosmic horizon S A [118]. So, the second law can be safely written as [35],…”

“…The other crucial addition in the present work is that we also check the consistency of the constraints on spatial curvature with thermodynamic requirements. Very recently, Ferreira and Pavón [35] imposed a relation using the generalized second law of thermodynamics, which reads as 1 + q ≥ Ω k , where q is the deceleration parameter. It is quite reassuring to see that constraints on Ω k0 quite comfortably satisfies the requirement.…”

Observational constraints on the free parameters of an interacting Bose–Einstein gas as a dark-energy model

“…Observational data can constrain the free parameters of the DE models by means of Bayesian methods [9]. Several IDE models have been tested in the literature, e.g., [10][11][12]. Some observational data are model independent such as the local Hubble constant measurements [13,14], the data from the history of the Hubble constant H(z) vs z obtained by the cosmic chronometer approach [15][16][17][18] or the type Ia supernova [19,20].…”