New Derivation of Redshift Distance without Using Power Expansions

Here we use the flat Friedmann-Lemaitre-Robertson-Walker metric describing a spatially homogeneous and isotropic universe to derive the cosmological redshift distance in a way which differs from that which can be found in the astrophysical literature. We use the co-moving coordinate re (the subscript e indicates emission) for the place of a galaxy which is emitting photons and ra (the subscript a indicates absorption) for the place of an observer within a different galaxy on which the photons - which were traveling thru the universe - are absorbed. Therefore the real physical distance - the way of light - is calculated by D = a(t0) ra - a(te) re. Here means a(t0) the today’s (t0) scale parameter and a(te) the scale parameter at the time of emission (te) of the photons. Nobody can doubt this real travel way of light: The photons are emitted on the co-moving coordinate place re and are than traveling to the co-moving coordinate place ra. During this traveling the time is moving from te to t0 (te ≤ t0) and therefore the scale parameter is changing in the meantime from a(te) to a(t0). Using this right way of light we calculate some relevant classical cosmological equations (effects) and compare these theoretical results with some measurements of astrophysics. As one result we get e.g. the today’s Hubble parameter H0a ≈ 62.34 km/(s Mpc). This value is smaller than the Hubble parameter H0,Planck ≈ 67.66 km/(s Mpc) resulting from Planck 2018 data [12] which is discussed in the literature.

Quantum Cosmology with Third Quantisation

We reviewed the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analysed the information contained in the solutions of the Wheeler–DeWitt equation and showed their interpretation in terms of the customary boundary conditions that are typically imposed on the semiclassical wave functions. In particular, we reviewed three different paradigms for the quantum creation of a homogeneous and isotropic universe. For the quantisation of a non-simply connected manifold, the best framework is the third quantisation formalism, in which the wave function of the universe is seen as a field that propagates in the space of Riemannian 3-geometries, which turns out to be isomorphic to a (part of a) 1+5 Minkowski spacetime. Thus, the quantisation of the wave function follows the customary formalism of a quantum field theory. A general review of the formalism is given, and the creation of the universes is analysed, including their initial expansion and the appearance of matter after inflation. These features are presented in more detail in the case of a homogeneous and isotropic universe. The main conclusion in both cases is that the most natural way in which the universes should be created is in entangled universe–antiuniverse pairs.

An Overview on the Nature of the Bounce in LQC and PQM

We present a review on some of the basic aspects concerning quantum cosmology in the presence of cut-off physics as it has emerged in the literature during the last fifteen years. We first analyze how the Wheeler–DeWitt equation describes the quantum Universe dynamics, when a pure metric approach is concerned, showing how, in general, the primordial singularity is not removed by the quantum effects. We then analyze the main implications of applying the loop quantum gravity prescriptions to the minisuperspace model, i.e., we discuss the basic features of the so-called loop quantum cosmology. For the isotropic Universe dynamics, we compare the original approach, dubbed the μ0 scheme, and the most commonly accepted formulation for which the area gap is taken as physically scaled, i.e., the so-called μ¯ scheme. Furthermore, some fundamental results concerning the Bianchi Universes are discussed, especially with respect to the morphology of the Bianchi IX model. Finally, we consider some relevant criticisms developed over the last ten years about the real link existing between the full theory of loop quantum gravity and its minisuperspace implementation, especially with respect to the preservation of the internal SU(2) symmetry. In the second part of the review, we consider the dynamics of the isotropic Universe and of the Bianchi models in the framework of polymer quantum mechanics. Throughout the paper, we focus on the effective semiclassical dynamics and study the full quantum theory only in some cases, such as the FLRW model and the Bianchi I model in the Ashtekar variables. We first address the polymerization in terms of the Ashtekar–Barbero–Immirzi connection and show how the resulting dynamics is isomorphic to the μ0 scheme of loop quantum cosmology with a critical energy density of the Universe that depends on the initial conditions of the dynamics. The following step is to analyze the polymerization of volume-like variables, both for the isotropic and Bianchi I models, and we see that if the Universe volume (the cubed scale factor) is one of the configurational variables, then the resulting dynamics is isomorphic to that one emerging in loop quantum cosmology for the μ¯ scheme, with the critical energy density value being fixed only by fundamental constants and the Immirzi parameter. Finally, we consider the polymer quantum dynamics of the homogeneous and inhomogeneous Mixmaster model by means of a metric approach. In particular, we compare the results obtained by using the volume variable, which leads to the emergence of a singularity- and chaos-free cosmology, to the use of the standard Misner variable. In the latter case, we deal with the surprising result of a cosmology that is still singular, and its chaotic properties depend on the ratio between the lattice steps for the isotropic and anisotropic variables. We conclude the review with some considerations of the problem of changing variables in the polymer representation of the minisuperspace dynamics. In particular, on a semiclassical level, we consider how the dynamics can be properly mapped in two different sets of variables (at the price of having to deal with a coordinate dependent lattice step), and we infer some possible implications on the equivalence of the μ0 and μ¯ scheme of loop quantum cosmology.

Broadening quantum cosmology with a fractional whirl

We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically, we investigate and then discuss a model of stiff matter in a spatially flat homogeneous and isotropic universe. A new quantum cosmological solution, where fractional calculus implications are explicit, is presented and then contrasted with the corresponding standard quantum cosmology setting.

Scenario of accelerated universe expansion under exposure to entropic forces related to with the entropies of Barrow and Tsallis−Cirto

In the work within the framework of "entropic cosmology", the scenario of the cosmological accelerated expansion of a flat, homogeneous and isotropic Universe under the influence of entropic forces is considered without the concept of dark energy a hypothetical medium with negative pressure. Assuming that the horizon of the Universe has its own temperature and entropy, which arises during the holographic storage of information on the screen of the horizon surface, the entropy models of the Universe associated with the BekensteinHawking entropy and the non-extensive Barrow and Tsallis–Cirto entropies are considered. The modified equations of acceleration and continuity of Friedman with governing power terms having an entropic nature are derived both within the framework of Einstein's general theory of relativity and on the basis of a thermodynamic approach that allows modeling the non-adiabatic evolution of the Universe. At the same time, models based on nonextensive entropies predict the existence of both a decelerating and accelerating Universe.

Dynamics of quintessence in generalized uncertainty principle

We investigate the quintessence scalar field model modified by the generalized uncertainty principle in the background of a spatially flat homogeneous and isotropic universe. By performing a dynamical system analysis we examine the nature of the critical points and their stability for two potentials, one is the exponential potential and the other is a general potential. In the case of an exponential potential, we find some new critical points for this modified quintessence scenario that describe the de Sitter universes, and these critical points do not appear in the standard quintessence model with an exponential potential. This is one of the main results of this work. Now for the general potential our analysis shows that the physical properties of the critical points remain exactly the same as for the exponential potential which means that within this modified quintessence scenario all kind of potentials have same behaviour. This kind of result is completely new in cosmology because with the change of the potential, differences are usually expected in all respect.