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15 pags. -- This article belongs to the Special Issue Loop Quantum Gravity: A Themed Issue in Honor of Prof. Abhay Ashtekar. -- PACS: 04.60.Pp; 04.62.+v; 98.80.Qc, The hybrid and the dressed metric formalisms for the study of primordial perturbations in Loop Quantum Cosmology lead to dynamical equations for the modes of these perturbations that are of a generalized harmonic-oscillator type, with a mass that depends on the background but is the same for all modes. For quantum background states that are peaked on trajectories of the effective description of Loop Quantum Cosmology, the main difference between the two considered formalisms is found in the expression of this mass. The value of the mass at the bounce is especially important, since it is only in a short interval around this event that the quantum geometry effects on the perturbations are relevant. In a previous article, the properties of this mass were discussed for an inflaton potential of quadratic form, or with similar characteristics. In the present work, we extend this study to other interesting potentials in cosmology, namely the Starobinsky and the exponential potentials. We prove that there exists a finite interval of values of the potential (which includes the zero but typically goes beyond the sector of kinetically dominated inflaton energy density) for which the hybrid mass is positive at the bounce whereas the dressed metric mass is negative., This work has been supported by Project No. MICINN PID2020-118159GB-C41.

Assuming a geometrically closed universe, we predict a value for the cosmic curvature, , a value within current observational bounds. We also propose a thermodynamic heat engine model for the universe, which bypasses the need for an inflaton field. Our model is based on a Carnot Cycle where we have isothermal expansion, followed by adiabatic expansion, followed by isothermal contraction, followed by adiabatic contraction, bringing us back to our original starting point. For the working substance, we focus specifically on the CMB radiation filling the collective voids in the universe. Using this construct, we identify cosmic inflation as the isothermal expansion phase, which lasts just under, . The collective CMB volume we see today only increases by a factor of 5.65 times during this process, and homogeneity and perturbations in the CMB are explained. The singularity problem is avoided and we have a clear mechanism for the work done by the cosmos in causing expansion, and later contraction. For scaling laws with respect to the density parameters in Friedmann’s equations, we will assume a susceptibility model for space, where, , the smeared cosmic susceptibility, decreases with increasing cosmic scale parameter, . Within this framework, we can predict a maximum Hubble volume with minimum CMB temperature for the voids before contraction begins, as well as a minimum volume with maximum CMB temperature when expansion starts. The thermodynamic heat cycle deviates from efficiency in converting heat energy into mechanical energy (expansion) by a minuscule amount, namely, . The significance of this number is not known.

On the orthodox interpretation of bounce cosmologies, a preceding universe was compressed to a small size before ``bouncing'' to form the present expanding universe. William Lane Craig and James Sinclair have argued that the orthodox interpretation is incorrect if the entropy reaches a minimum at the bounce. In their view, the interface between universes represents the birth of two expanding universes, i.e., a ``double bang'' instead of a ``big bounce''. Here, I reply to Craig and Sinclair in defense of the orthodox interpretation. Contrary to their interpretation, features of one universe explain features of the other universe and so must precede the other universe in time. Moreover, contrary to a crucial part of Craig and Sinclair's interpretation, there are bounce cosmologies in which the thermodynamic arrow of time is continuous through the bounce even though the entropy is ``reset'' at the bounce., 34 pages, Published in Erkenntnis

We construct and study a simple noncommutative scheme (theta-deformation) for the effective loop quantum cosmology of the flat Friedmann-Lema\^{\i}tre-Robertson-Walker model in the presence of a homogeneous scalar field $\ensuremath{\phi}$ with a potential $\mathcal{V}(\ensuremath{\phi})=\frac{1}{2}{m}^{2}{\ensuremath{\phi}}^{2}$. We first conduct a simple analysis from the corresponding Hamilton equations of motion considering a generic term $\mathcal{V}(\ensuremath{\phi})$. It is observed that the characteristic big bounce of loop quantum cosmology is preserved under such noncommutative extension. When specializing to the quadratic case, numerical solutions to the corresponding Hamilton equations exhibiting an early inflationary epoch with a sufficiently large number of $e$-foldings are found. It is concluded that, in this noncommutative setup, solutions exist which are in the overall compatible with the early universe predicted by standard (effective) Loop Quantum Cosmology (i.e., a bouncing and inflationary early universe). The issue of the genericness of a sufficiently long inflationary period on the space of solutions in this noncommutative construct remains to be addressed.

In cosmology dark energy and dark matter are included in the CDM model, but they are still completely unknown. On the other hand the trans-Planckian problem leads to unlikely high photon energies for black holes. We introduce a model with quantized black hole matter. This minimizes the trans- Planckian problem extremely and leads to a scalar field in the oscillating universe model. We show that the scalar field has the same characteristics as a vacuum energy field and leads to the same Casimir effect. Shortly after the beginning of the big bounce this field decays locally and leads to the production of dark matter. In this model no inflation theory is needed. We emphasize that this model is mainly a phenomenological approach with the aim of new impetus to the discussion.

We extend the notion of the Nieh-Yan invariant to generic metric-affine geometries, where both torsion and nonmetricity are taken into account. Notably, we show that the properties of projective invariance and topologicity can be independently accommodated by a suitable choice of the parameters featuring this new Nieh-Yan term. We then consider a special class of modified theories of gravity able to promote the Immirzi parameter to a dynamical scalar field coupled to the Nieh-Yan form, and we discuss in more detail the dynamics of the effective scalar tensor theory stemming from such a revised theoretical framework. We focus, in particular, on cosmological Bianchi I models and we derive classical solutions where the initial singularity is safely removed in favor of a big bounce, which is ultimately driven by the nonminimal coupling with the Immirzi field. These solutions, moreover, turn out to be characterized by finite time singularities, but we show that such critical points do not spoil the geodesic completeness and wave regularity of these spacetimes.

35 pags., 5 figs., In this work, we compute the time-dependent masses that govern the dynamics of scalar and tensor perturbations propagating on an effective flat, homogeneous, and isotropic background within the framework of loop quantum cosmology (LQC), regularized according to the procedure put forward by Dapor and Liegener. To do so, we follow the two main approaches that, in the field of LQC, lead to hyperbolic equations for the perturbations in the ultraviolet sector: the hybrid and dressed metric formalisms. This allows us to compare the masses resulting from both proposals and analyze their positivity in regimes of physical interest: the big bounce and the contracting de Sitter phase in the asymptotic past that is a defining feature of the model under consideration., This work has been supported by Project No. FIS2017-86497-C2-2-P of MICINN from Spain. A GarciaQuismondo acknowledges that the project that gave rise to these results received the support of a fellowship from ‘la Caixa’ Foundation (ID 100010434). The fellowship code is LCF/BQ/DR19/11740028. G Sanchez Perez acknowledges support of the Grant No. CSIC JAEINT19_EX_0632.

We start from a hypothetical multi-fold universe UMF , where the propagation of everything is slower or equal to the speed of light and where entanglement extends the set of paths available to Path Integrals. This multifold mechanism enables EPR (Einstein-Podolsky-Rosen) “spooky actions at distance” to result from local interactions in the resulting folds. It produces gravity-like attractive effective potentials in the spacetime, between entangled entities, that are caused by the curvature of the folds. When quantized, multi-folds correspond to gravitons and they are enablers of EPR entanglement. Gravity emerges non-perturbative and covariant from EPR entanglement between virtual particles surrounding an entity. In UMF, we encounter mechanisms that predict gravity fluctuations when entanglement is present, including in macroscopic entanglements. Besides providing a new perspective on quantum gravity, when added to the Standard Model as (SMG), with non-negligible affects at its scales, and to the Standard Cosmology, UMF can contribute explanations of several open questions and challenges. It also clarifies some relationships and challenges met by other quantum gravity models and Theories of Everything. It leads to suggestions for these works. We also reconstruct the spacetime of UMF, starting from the random walks of particles in an early spacetime. UMF now appears as a noncommutative, discrete, yet Lorentz symmetric, spacetime that behaves roughly 2-Dimensional at Planck scales, when it is a graph of microscopic Planck size black holes on a random walk fractal structure left by particles that can also appear as microscopic black holes. Of course, at larger scales, spacetime appears 4-D, where we are able to explain curvature and recover Einstein’s General Relativity. We also discover an entanglement gravity-like contributions and massive gravity at very small scales. This is remarkable considering that no Hilbert Einstein action, or variations expressing area invariance, were introduced. Our model also explains why semi classical approaches can work till way smaller scale than usually expected and present a new view on an Ultimate Unification of all forces, at very small scales. We also explore opportunities for falsifiability and validation of our model, as well as ideas for futuristic applications, that may be worth considering, if UMF was a suitable model for our universe Ureal ., It is the original paper. Cite as: Cite as: Stephane H. Maes, (2020-2022) "Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe", HIJ, Vol 2, No 4, pp 136-219, Dec 2022, https://doi.org/10.55672/hij2022pp136-219‎, https://shmaesphysics.wordpress.com/2020/06/09/paper-published-as-preprint-quantum-gravity-emergence-from-entanglement-in-a-multi-fold-universe/, https://shmaesphysics.wordpress.com/2022/11/09/quantum-gravity-emergence-from-entanglement-in-a-multi-fold-universe-2/, and viXra:2006.0088, (June 9, 2020).

In this Letter, we study analytically the evolutions of the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe and its linear perturbations in the framework of {\em the dressed metric approach} in loop quantum cosmology (LQC). Assuming that the evolution of the background is dominated by the kinetic energy of the inflaton at the quantum bounce, we find that both evolutions of the background and its perturbations are independent of the inflationary potentials during the pre-inflationary phase. During this period the effective potentials of the perturbations can be well approximated by a P\"oschl-Teller (PT) potential, from which we find analytically the mode functions and then calculate the corresponding Bogoliubov coefficients at the onset of the slow-roll inflation, valid for any inflationary model with a single scalar field. Imposing the Bunch-Davies (BD) vacuum in the contracting phase prior to the bounce when the modes are all inside the Hubble horizon, we show that particles are generically created due to the pre-inflation dynamics. Matching them to those obtained in the slow-roll inflationary phase, we investigate the effects of the pre-inflation dynamics on the scalar and tensor power spectra and find features that can be tested by current and forthcoming observations. In particular, to be consistent with the Planck 2015 data, we find that the universe must have expanded at least $141$ e-folds since the bounce., Comment: revtex4, 7 figures, 1 table. Further corrected some typos. Phys. Lett. B773 (2017) 196-202

The present paper embraces mainly the three-year period of 1966 to 1968 when the invariant integral of fracture mechanics appeared and became popular, and the last two years of 2015 to 2016 when the neoclassic cosmology based on the invariant integral came up. A mention is given to the previous works of Euler, Cauchy, Maxwell, Nother, Gunther and Eshelby who dealt with invariant integrals in mathematics, hydrodynamics, electrodynamics, and the theory of dislocations. A brief review is given of the creation of the invariant integral of fracture mechanics under static and dynamic conditions for a solid continuum including elastic, plastic and viscoelastic materials, as well as of some of its most important applications, ramifications and generalizations for other physical fields. The initial phase of the expansion and revolution of the large-scale universe is studied in the framework of the neoclassic approach, including the Big Bang and the Dark Energy; it is shown that the spheroidal shape of the universe assumed at the Big Bang retains its eccentricity constant in the initial phase. The assumption of a superphoton as a primordial universe was analyzed.

This article introduces recursive Heaviside step functions, as a potential of the known universe, for the first time in the history of mathematics, science, and engineering. In modern cosmology, various bouncing models have been suggested based on the postulation that the current universe is the result of the collapse of a previous universe. However, all Big Bounce models leave unanswered the question of what powered inflation. Recursive Heaviside step functions are analyzed to represent the warpage of spacetime during the crunch-bounce transition. In particular, the time shift appeared during the transition is modeled in the form of recursive Heaviside step functions and suggested as a possible answer for the immeasurable energy appeared for the Big Bounce.

The high-energy limit of Quantum Chromodynamics is generated by the contraction of its gauge groups. Contraction parameters are taken identical with those of the Electroweak Model and tend to zero when energy increases. At the infinite energy limit all quarks lose masses and have only one color degree of freedom. The limit model represents the development of Quantum Chromodynamics in the early Universe from the Big Bang up to the end of several milliseconds.

The causal set approach to the problem of quantum gravity is based on the hypothesis that spacetime is fundamentally discrete. Spacetime discreteness opens the door to novel types of dynamical law for cosmology and the Classical Sequential Growth (CSG) models of Rideout and Sorkin form an interesting class of such laws. It has been shown that a renormalisation of the dynamical parameters of a CSG model occurs whenever the universe undergoes a Big Crunch–Big Bang bounce. In this paper we propose a way to model the creation of a new universe after the singularity of a black hole. We show that renormalisation of dynamical parameters occurs in a CSG model after such a creation event. We speculate that this could realise aspects of Smolin's Cosmological Natural Selection proposal.

A new routine is proposed to relate Loop Quant Cosmology (LQC) to Loop Quantum Gravity (LQG) from the perspective of effective dynamics. We derive the big-bang singularity resolution and big bounce from the first principle of full canonical LQG. Our results are obtained in the framework of the reduced phase space quantization of LQG. As a key step in our work, we derive with coherent states a new discrete path integral formula of the transition amplitude generated by the physical Hamiltonian. The semiclassical approximation of the path integral formula gives an interesting set of effective equations of motion (EOMs) for full LQG. When solving the EOMs with homogeneous and isotropic ansatz, we reproduce the LQC effective dynamics in $\mu_0$-scheme. The solution replaces the big-bang singularity by a big bounce. In the end, we comment on the possible relation between the $\bar{\mu}$-scheme of effective dynamics and the continuum limit of the path integral formula., Comment: 30+10 pages, 2 figures

We explore the possibility of an Ekpyrotic contraction phase harbouring a mechanism for Baryogenesis. A Chern-Simons coupling between the fast-rolling Ekpyrotic scalar and the Standard Model Hypercharge gauge field enables the generation of a non-zero helicity during the contraction phase. The baryon number subsequently produced at the Electroweak Phase Transition is consistent with observation for a range of couplings and bounce scales. Simultaneously, the gauge field production during the contraction provides the seeds for galactic magnetic fields and sources gravitational waves, which may provide additional avenues for observational confirmation., Comment: 20 pages, 3 figures; revised version, consistent with that published in JCAP

In this article, we argue that the past of the Universe, extrapolated from standard physics and measured cosmological parameters, might be a non-singular bounce. We also show that, in this framework, quite stringent constraints can be put on the reheating temperature and number of inflationary e-folds, basically fixing $$T_{RH}\sim T_{GUT}$$TRH∼TGUT and $$N\sim 70$$N∼70. We draw some conclusions about the shape of the inflaton potential and raise the “naturalness” issue in this context. Finally, we argue that this could open a very specific window on the “pre big bounce" universe.

Whenever the condition of anomaly freedom is imposed within the framework of effective approaches to loop quantum cosmology, one seems to conclude that a deformation of general covariance is required. Here, starting from a general deformation we regain an effective gravitational Lagrangian including terms up to fourth order in extrinsic curvature. We subsequently constrain the form of the corrections for the homogeneous case, and then investigate the conditions for the occurrence of a big bounce and the realization of an inflationary era, in the presence of a perfect fluid or scalar field.

As a simplified, idealized understanding of a physical system the General Relativity model has been highly successful in its gravitational role. However, it fails to address the problem of sufficiently precise measurement of “Big G”, the Newtonian Gravitation Constant, and has failed to obtain connection of “Big G” to the rest of physics. Because “Big G” arises naturally from Newton’s treatment of gravitation, this paper elaborates the Modern Newtonian Model of Gravitation and through it resolves the problems of “Big G” at which General Relativity has failed. Specifically: The causes of the problems in measuring “Big G” are resolved, “Big G” is connected to the rest of physics, and a sufficiently precise value of “Big G” is obtained by calculation from other fundamental physical constants. The companion paper The Experimental Data Validation of Modern Newtonian Gravitation over General Relativity Gravitation, which is available in this journal, publishes the results of this paper’s “Part V—Testing the Hypothesis and the Derivation”.

General relativity (GR) and gravitation in flat space-time (GFST) are covariant theories to describe gravitation. The metric of GR is given by the form of proper-time and the metric of GFST is a flat space-time form different from that of proper-time. The source of GR is the matter tensor and the Einstein tensor describes the gravitational field. The source of GFST is the total energymomentum including gravitation. The field is described by a non-linear differential operator of order two in divergence form. The results of the two theories agree for weak gravitational fields to the order of measurable accuracy. It is well-known that homogeneous, isotropic, cosmological models of GR start from a point singularity of the universe, the so called big bang. The density of matter is infinite. Therefore, our observable big universe implies an expansion of space, in particular an inflationary expansion in the beginning. Doubts are stated because infinities don’t exist in physics. An explanation to the present, controversial discussion of expanding accelerating or non-accelerating universe as well as non-expanding universe is given. GFST starts in the beginning from a homogeneous, isotropic universe with uniformly distributed energy and no matter. In the course of time matter is created out of energy where the total energy is conserved. There is no singularity, i.e. no big bang. The space is flat and non-expanding.

We argue that the modified Landau–Raychaudhuri equations should first be analysed in a large class of spacetimes and in dependence on various equations of states, before endorsing any conclusion about (non)singular Big Bang. From the corrected entropy-area law in a large class of metrics, the generalized uncertainty principle (GUP) and the modified dispersion relation (MDR) approaches, and various equations of states, the modified Friedmann equations are derived. They are applied on Landau–Raychaudhuri equations in emergence of cosmic space framework from fixed point method. We show that any conclusion about (non)singular Big Bang is simply badly model-dependent, especially when utilizing GUP and MDR approaches, which can not replace a good theory for quantum gravity. We conclude that the various quantum gravity approaches, metrics and equations of state lead to different modifications in Friedmann and Landau–Raychaudhuri equations and thus to different (non)singular solutions for Big Bang theory.

In a recent paper, John J. Park argues (1) that an abstract object can bring a universe into existence, and (2) that, according to the Big Bang Theory, the initial singularity is an abstract object that brought the universe into existence. According to Park, if (1) and (2) are true, then the kalam cosmological argument fails to show that the cause of the universe must be divine. I argue, however, that both (1) and (2) are false. In my argument I analyse the abstract/concrete distinction and conclude that, by its nature, an abstract object is causally inefficacious in the sense that it cannot bring something into existence.

This paper presents a mathematical proposition based on zero point energy of the creation of singularity in the current Hot Bing Bang theory of the origin of the universe. The observable universe we live in and can see is finite and is defined by the speed of light. The entire universe is infinite and the observable universe is part of it. Zero point energy exists in the entire universe and at all frequencies up to the Planck frequency. Zero point energy was calculated by Planck. The Casimir effect, predicted by Hendrick Casimir, is caused by zero point energy and has been experimentally proven by S. Lamoreux and U. Mohideen. The author has mathematically calculated that the zero point energy waves up to Planck frequency can combine to create an energy source of colossal amount similar to the singularity of Hot Big Bang theory.

We offer a new proposal for cosmic singularity resolution based upon a quantum cosmology with a unitary bounce. This proposal is illustrated via a novel quantization of a mini-superspace model in which there can be superpositions of the cosmological constant. This possibility leads to a finite, bouncing unitary cosmology. Whereas the usual Wheeler--DeWitt cosmology generically displays pathological behaviour in terms of non-finite expectation values and non-unitary dynamics, the finiteness and unitarity of our model are formally guaranteed. For classically singular models with a massless scalar field and cosmological constant, we show that well-behaved quantum observables can be constructed and generic solutions to the universal Schr\"{o}dinger equation are singularity-free. Generic solutions of our model displays novel features including: i) superpositions of values of the cosmological constant; ii) universal effective physics due to non-trivial self-adjoint extensions of the Hamiltonian; and iii) bound `Efimov universe' states for negative cosmological constant. The last feature provides a new platform for quantum simulation of the early universe. A companion paper provides detailed interpretation and analysis of particular cosmological solutions that display a cosmic bounce due to quantum gravitational effects, a well-defined FLRW limit far from the bounce, and a semi-classical turnaround point in the dynamics of the scalar field which resembles an effective inflationary epoch., Comment: Version published in Classical Quantum Gravity. 21 pages, 4 figures

We discuss a $(3{+}1)$-dimensional covariant quantum space-time describing a FLRW cosmology with Big Bounce, obtained by a projection of the fuzzy hyperboloid $H^4_n$. This provides a background solution of the IKKT matrix model with mass term. We characterize the bosonic fluctuation spectrum, which consists of a tower of higher-spin modes, truncated at $n$. The modes are organized in terms of an underlying $SO(4,2)$ structure group, which is broken to the $SO(3,1)$ isometry of the background. The resulting higher-spin gauge theory includes all degrees of freedom required for gravity, and should be well suited for quantization. All modes propagate with the same speed of light, even though local boost invariance is not manifest. The propagating metric perturbation modes comprise those of a massless graviton, as well as a scalar mode. Gauge invariance allows to obtain the analog of the linearized Einstein-Hilbert action, which is expected to be induced upon quantization., 46 + 12 pages. V2: references added, minor corrections. V3: improved presentation, references added, on-shell modes corrected

We analyze the dynamics of a homogeneous and isotropic universe in the Einstein--Cartan theory of gravity. The spin of fermions produces spacetime torsion that prevents gravitational singularities and replaces the big bang with a nonsingular big bounce. We show that a closed universe exists only when a particular function of its scale factor and temperature is higher than some threshold value, whereas an open and a flat universes do not have such a restriction. We also show that a bounce of the scale factor is double: as the temperature increases and then decreases, the scale factor decreases, increases, decreases, and then increases., Comment: 5 pages, 3 tables, 2 figures

We analyze some relevant semiclassical and quantum features of the implementation of Polymer Quantum Mechanics to the phenomenology of the flat isotropic Universe. We firstly investigate a parallelism between the semiclassical polymer dynamics of the flat isotropic Universe, as reduced to the effect of a modified simplectic structure, and the so-called Generalized Uncertainty Principle. We show how the difference in the sign of the fundamental Poisson bracket is reflected in a sign of the modified source term in the Friedmann equation, responsible for the removal of the initial singularity in the polymer case and for the survival of a singular point in the Universe past, when the Generalized Uncertainty Principle is concerned. Then, we study the regularization of the vacuum energy of a free massless scalar field, by implementing a second quantization formalism in the context of Polymer Quantum Mechanics. We show that, from this reformulation, naturally emerges a Cosmological Constant term for the isotropic Universe, whose value depends directly on the polymer parameter of the regularization. Finally, we investigate the behaviour of gravitational waves on the background of a modified dynamics, according to the semiclassical Friedmann equation. We demonstrate that the presence of a Bounce in the Universe past, naturally removes the divergence of the gravitational wave amplitude and they can, in principle, propagate across the minimum volume turning point. This result offers the intriguing perspective for the detection of gravitational signals coming from the pre-Big Bounce collapsing Universe., Comment: New submission to match published version

We analyze the cosmological implementation of Palatini $f(R)$ theories, constructed with a Nieh-Yan term and solved with respect to the torsion. We consider the relevant case of the quadratic correction to the Hilbert-Palatini action in the Ricci scalar, mimicking the Starobinsky model of the metric formulation. We point out the emergence of peculiar cosmological scenarios, depending on the sign of such correction, able to reproduce bouncing settings and to restore the standard Universe dynamics in the late asymptotic limit. Furthermore, we outline the settling of Little-Rip dynamics, which calls for a deeper investigation in order to be regularized via matter creation. Finally, we also show that in our model the Immirzi field is asymptotically frozen in time, resembling the morphology of Loop Quantum Gravity standard formulation., Comment: 9 pages

We present a gauge-invariant treatment of singularity resolution using loop quantum gravity techniques with respect to local SU(2) transformations. Our analysis reveals many novel features of quantum geometry which were till now hidden in models based on non-gauge-invariant discretizations. Quantum geometric effects resolve the big bang singularity replacing it with a non-singular bounce when spacetime curvature reaches Planckian value. The bounce is found to be generically asymmetric in the sense that pre-bounce and post-bounce branches are not mirrored to each other and effective constants, such as Newton's constant, are rescaled across the bounce. Furthermore, in the vicinity of the bounce, minimally coupled matter behaves as non-minimally coupled. These ramifications of quantum geometry open a rich avenue for potential phenomenological signatures., Comment: 12 pages, 2 figures. Published version in Classical and Quantum Gravity

We analyze the semiclassical polymer dynamics of the inhomogeneous Mixmaster model by choosing the cubed scale factor as the discretized configurational variable, while the anisotropies remain pure Einsteinian variables. Such a modified theory of gravity should be regarded as the appropriate framework to describe the behavior of quantum mean values, both in polymer quantum mechanics and in Loop Quantum Cosmology. We first construct the generalized Kasner solution, including a massless scalar field and a cosmological constant in the dynamics. They account for a quasi-isotropization, inflationary-like mechanism. The resulting scenario links a singularity-free Kasner-like regime with a homogeneous and isotropic de Sitter phase. Subsequently, we investigate the role of the three-dimensional scalar curvature, demonstrating that a bounce of the point-universe against the potential walls can always occur within the polymer framework, also in the presence of a scalar field. However, the absence of the singularity implies that the curvature is bounded. Therefore, the point-universe undergoes an oscillatory regime until it oversteps the potential walls (if the Big Bounce is not reached before). After that, a final stable Kasner-like regime will last all the way toward the Big Bounce. Thus, the present study demonstrates that, as soon as a discretization of the volume of the universe is performed, the generic cosmological solution is non-chaotic and free from singularities. It is likely that the same result can be achieved also in the loop quantum cosmology approach., 11 pages, 4 figures, to appear on Physics Letters B