arXiv subjects

G. A. Monerat

Publications and source records attributed to G. A. Monerat.

At least 19 recordsLinked to original sources

arXiv2026

Resonances in the early Universe

In the present paper, we study a Friedmann-Lemaître-Robertson-Walker (FLRW) quantum cosmology model with positively curved spatial sections. The matter content of the model is given by a radiation fluid, a constant vacuum energy, and an ad hoc potential. After writing the Hamiltonian of the model, we notice that the effective potential ($V_{eff}$) depends on two parameters: $ρ_v$, the constant vacuum energy density and $σ$, associated with the ad hoc potential. Depending on the values of these parameters $V_{eff}$ becomes a double barrier potential. We quantize the model and obtain the Wheeler-DeWitt equation. We solve that equation using the WKB approximation and compute the corresponding probability ($TP_{WKB}$) that the wavefunction of the universe tunnels through the double barrier potential $V_{eff}$. We study how $TP_{WKB}$ behaves as a function of the parameters $ρ_v$, $σ$ and the radiation energy $E$. We notice the occurrence of resonances in $TP_{WKB}$ when we vary it as a function of $E$, $ρ_v$ and $σ$. It is a very interesting phenomenon because it may cause the universe to be born with selected values of $E$, $ρ_v$ and $σ$.

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arXiv2024

Primordial dust universe in the Hořava-Lifshitz theory

We apply quantum cosmology to investigate the early moments of a Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological model, using Hořava-Lifshitz (HL) as the gravitational theory. The matter content of the model is a dust perfect fluid. We start studying the classical model. Then, we write the total Hamiltonian of the model, quantize it and find the appropriate Wheeler-DeWitt equation. In order to avoid factor ordering ambiguities, in the Wheeler-DeWitt equation, we introduce a canonical transformation. We solve that equation using the Wentzel-Kramers-Brillouin (WKB) approximation and compute the tunneling probabilities for the birth of that universe ($TP_{WKB}$). Since the WKB wavefunction depends on the dust energy and the free coupling constants coming from the HL theory, we compute the behavior of $TP_{WKB}$ as a function of all these quantities.

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arXiv2023

Tunneling probability for the birth of an universe with radiation in Horava-Lifshitz theory

In the present work, we study the birth of a homogeneous and isotropic Friedmann Lemaitre Robertson Walker (FLRW) cosmological model, considering Horava Lifshitz (HL) as the gravitational theory. The matter content of the model is a radiation perfect fluid. In order to study the birth of the universe in the present model, we consider the quantum cosmology mechanism of creation from nothing. In that mechanism, the universe appears after the wavefunction associated to that universe tunnels through a potential barrier. We started studying the classical model. We draw the phase portrait of the model and identify qualitatively all types of dynamical behaviors associated to it. Then, we write the Hamiltonian of the model and apply the Dirac quantization procedure to quantize a constrained theory. We find the appropriate Wheeler-DeWitt equation and solve it using the Wentzel Kramers Brillouin (WKB) approximation. Using the WKB solution, to the Wheeler DeWitt equation, we compute the tunneling probabilities for the birth of that universe (TPWKB). Since the WKB wavefunction depends on the radiation energy (E) and the free parameters coming from the HL theory (gc, gr, gs, gLambda), we compute the behavior of TPWKB as a function of E and all the HL parameters gc, gr, gs, gLambda.

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arXiv2023

Tunneling probability for the birth of universes with radiation, cosmological constant and an ad hoc potential

In this work we study the birth of Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) models with zero ($k=0$) and negative ($k=-1$) curvatures of the spatial sections. The material content of the models is composed of a radiation perfect fluid and a positive cosmological constant. The models also have the presence of an ad hoc potential which origin is believed to be of geometrical nature. In order to describe the birth of these universes, we quantize them using quantum cosmology. Initially, we obtain the Wheeler-DeWitt equations and solve them using the WKB approximation. We notice that the presence of the ad hoc potential produces a barrier for any value of $k$. It means that we may describe the birth of the universe through a tunneling mechanism, for any curvature of the spatial sections, not only for the usual case $k=1$. We, explicitly, compute the tunneling probabilities for the birth of the different models of the universe and compare these tunneling probabilities.

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arXiv2021

An anisotropic Kantowski-Sachs universe with radiation, dust and a phantom fluid

In the present work, we study the dynamical evolution of an homogeneous and anisotropic KS cosmological model, considering general relativity as the gravitational theory, such that there are three different perfect fluids in the matter sector. They are radiation, dust and phantom fluid. Our main motivation is determining if the present model tends to an homogeneous and isotropic FRW model, during its evolution. Also, we want to establish how the parameters and initial conditions of the model, quantitatively, influence the isotropization of the present model. In order to simplify our task, we use the Misner parametrization of the KS metric. In terms of that parametrization the KS metric has two metric functions: the scale factor $a(t)$ and $β(t)$, which measures the spatial anisotropy of the model. We solve, numerically, the Einstein's equations of the model and find a solution where the universe starts to expand from a, small, initial size and continues to expand until it ends in a {\it Big Rip} singularity. We explicitly show that for the expansive solution, after same time, the universe becomes isotropic. Based on that result, we can speculate that the expansive solution may represent an initial, anisotropic, stage of our Universe, that later, due to the expansion, became isotropic.

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arXiv2020

The dynamics of the early universe in a model with radiation and a generalized Chaplygin gas

The early universe is modeled through the quantization of a Friedmann-Robertson-Walker model with positive curvature of the spatial hypersurfaces. In this model, the universe is filled by two fluids: radiation and a generalized Chaplygin gas. The quantization of this model is made following the prescriptions due to J. A. Wheeler and B. DeWitt. Using the Schutz's formalism, the time notion is recovered and the Wheeler-DeWitt equation transforms into a time dependent Schrödinger equation, which rules the dynamics of the early universe, under the action of an effective potential $V_{eff}$. That potential, depends on three parameters. Depending on the values of these parameters, $V_{eff}$ may have two different shapes. $V_{eff}(a)$ may have the shape of a barrier or the shape of a well followed by a barrier. We solve, numerically, the appropriate time dependent Schrödinger equation and obtain the time evolution of an initial wave function, for both cases. These wave functions satisfy suitable boundary conditions. For both shapes of $V_{eff}$, we compute the tunneling probability, which is a function of the mean kinetic energy associated to the radiation energy $E_m$ and of the three parameters of the generalized Chaplygin gas: $α$, $A$ and $B$. The tunneling probabilities, for both shapes of $V_{eff}$, indicates that the universe should nucleate with the highest possible values of $E_m$, $α$, $A$ and $B$. Finally, we study the classical universe evolution after the wavefunction has tunneled $V_{eff}$. The calculations show that the universe may emerge from the Planck era in an inflationary phase.

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arXiv2020

The effects of dark energy on the early universe with radiation and Bose-Einstein condensate

This work analyzes the effects of quantization on a Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) model with positive curvature and material content composed of a Bose-Einstein condensate, a radioactive fluid and a cosmological constant playing the role of the dark energy of the universe. The quantization of the model was performed using the finite difference method in the Crank-Nicolson scheme: solutions of the Wheeler-DeWitt equation are obtained, in the form of finite norm wave packets which are well defined in all space, even if the 3D-sphere is degenerate. The introduction of the Bose-Einstein condensate and cosmological constant preserves the existence of bounce solutions (for certain choices of parameters and initial conditions) with exits for inflation (de Sitter solutions). This occurs after the universe emerges from its quantum phase by a tunneling mechanism.

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arXiv2019

Quantum Cosmology with many fluids and the choice of cosmological time

In this work we propose the quantization of a cosmological model describing the primordial universe filled with five barotropic fluids, namely: radiation, dust, vacuum, cosmic strings and domain walls. We intend to identify which fluid is best suited to provide phenomenologically the temporal variable in accordance with the observable universe. Through the Galerkin spectral method and the finite difference method in the Crank-Nicolson scheme (vacuum case), the quantum cosmological solutions are obtained and compared. We, also, compare the quantum cosmological solutions with the corresponding classical ones. The vacuum case is especially interesting because it provides a tunneling transition mechanism from the quantum to the classical phase and the possibility of calculating quantum tunneling probabilities.

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arXiv2019

Quantum cosmology of a Hořava-Lifshitz model coupled to radiation

In the present paper, we canonically quantize an homogeneous and isotropic Hořava-Lifshitz cosmological model, with constant positive spatial sections and coupled to radiation. We consider the projectable version of that gravitational theory without the detailed balance condition. We use the ADM formalism to write the gravitational Hamiltonian of the model and the Schutz variational formalism to write the perfect fluid Hamiltonian. We find the Wheeler-DeWitt equation for the model, which depends on several parameters. We study the case in which parameter values are chosen so that the solutions to the Wheeler-DeWitt equation are bounded. Initially, we solve it using the {\it Many Worlds} interpretation. Using wavepackets computed with the solutions to the Wheeler-DeWitt equation, we obtain the scalar factor expected value $\left $. We show that this quantity oscillates between finite maximum and minimum values and never vanishes. Such result indicates that the model is free from singularities, at the quantum level. We reinforce this indication by showing that by subtracting one standard deviation unit from the expected value $\left $, the latter remains positive. Then, we use the {\it DeBroglie-Bohm} interpretation. Initially, we compute the Bohm's trajectories for the scale factor and show that they never vanish. Then, we show that each trajectory agrees with the corresponding $\left $. Finally, we compute the quantum potential, which helps understanding why the scale factor never vanishes.

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arXiv2018

Primordial Universe with radiation and Bose-Einstein condensate

In this work we derive a scenario {in which} the early universe consists of {radiation fluid} and Bose-Einstein condensate. The possibility of gravitational self-interaction due to an attractive Bose-Einstein condensate is analyzed. The classical behavior of the scale factor of the universe is determined by a parameter associated with the Bose-Einstein fluid with bouncing or Big Crunch solutions. After we proceed to compute the finite-norm wave packet solutions to the Wheeler-DeWitt equation. The behavior of the scale factor is studied by applying the many-worlds interpretation of quantum mechanics. The quantum cosmological model is free from the singularities.

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arXiv2017

DeBroglie-Bohm interpretation of a Hořava-Lifshitz quantum cosmology model

In the present letter, we consider the DeBroglie-Bohm interpretation of a Hořava-Lifshitz quantum cosmology model in the presence of a radiation perfect fluid. We compute the Bohm's trajectories for the scale factor and show that it never goes to zero. That result gives a strong indication that this model is free from singularities, at the quantum level. We also compute the quantum potential. That quantity helps understanding why the scale factor never vanishes.

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arXiv2016

Noncommutativity in the early Universe

In the present work, we study the noncommutative version of a quantum cosmology model. The model has a Friedmann-Robertson-Walker geometry, the matter content is a radiative perfect fluid and the spatial sections have zero constant curvature. In this model the scale factor takes values in a bounded domain. Therefore, its quantum mechanical version has a discrete energy spectrum. We compute the discrete energy spectrum and the corresponding eigenfunctions. The energies depend on a noncommutative parameter $β$. We compute the scale factor expected value ($\left $) for several values of $β$. For all of them, $\left $ oscillates between maxima and minima values and never vanishes. It gives an initial indication that those models are free from singularities, at the quantum level. We improve this result by showing that if we subtract a quantity proportional to the standard deviation of $a$ from $\left $, this quantity is still positive. The $\left $ behavior, for the present model, is a drastic modification of the $\left $ behavior in the corresponding commutative version of the present model. There, $\left $ grows without limits with the time variable. Therefore, if the present model may represent the early stages of the Universe, the results of the present paper give an indication that $\left $ may have been, initially, bounded due to noncommutativity. We also compute the Bohmian trajectories for $a$, which are in accordance with $\left $, and the quantum potential $Q$. From $Q$, we may understand why that model is free from singularities, at the quantum level.

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arXiv2016

Quantum noncomutativity in quantum cosmology

In the present work, we study the noncommutative version of a quantum cosmology model. The model has a Friedmann-Robertson-Walker geometry, the matter content is a radiative perfect fluid and the spatial sections have positive constant curvatures. We work in the Schutz's variational formalism. We quantize the model and obtain the appropriate Wheeler-DeWitt equation. In this model the states are bounded. Therefore, we compute the discrete energy spectrum and the corresponding eigenfunctions. The energies depend on a noncommutative parameter ($θ$). The solutions to the Wheeler-DeWitt equation are function of the scale factor ($a$) and a time variable ($τ$), associated to the fluid. They also depend on an integer ($n$) and $θ$. The most general solution ($Ψ(a,τ)$) to the Wheeler-DeWitt equation is a sum, in the integer $n$, of the solutions mentioned above. We observe that, there is no $Ψ(a,τ)$ satisfying the appropriate boundary conditions. Therefore, we conclude that it is not possible to obtain a wavefunction satisfying the appropriate boundary conditions for the present model with the considered noncommutativity.

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arXiv2016

Can noncommutativity affect the whole history of the Universe?

We study a classical, noncommutative (NC), Friedmann-Robertson-Walker cosmological model. The spatial sections may have positive, negative or zero constant curvatures. The matter content is a generic perfect fluid. The initial noncommutativity between some canonical variables is rewritten, such that, we end up with commutative variables and a NC parameter. Initially, we derive the scale factor dynamic equations for the general situation, without specifying the perfect fluid or the curvature of the spatial sections. Next, we consider two concrete situations: a radiation perfect fluid and dust. We study all possible scale factor behaviors, for both cases. We compare them with the corresponding commutative cases and one with the other. We obtain, some cases, where the NC model predicts a scale factor expansion which may describe the present expansion of our Universe. Those cases are not present in the corresponding commutative models. Finally, we compare our model with another NC model, where the noncommutativity is between different canonical variables. We show that, in general, it leads to a scale factor behavior that is different from our model.

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arXiv2011

An Early Universe Model with Stiff Matter and a Cosmological Constant

In the present work, we study the quantum cosmology description of a Friedmann-Robertson-Walker model in the presence of a stiff matter perfect fluid and a negative cosmological constant. We work in the Schutz's variational formalism and the spatial sections have constant negative curvature. We quantize the model and obtain the appropriate Wheeler-DeWitt equation. In this model the states are bounded therefore we compute the discrete energy spectrum and the corresponding eigenfunctions. In the present work, we consider only the negative eigenvalues and their corresponding eigenfunctions. This choice implies that the energy density of the perfect fluid is negative. A stiff matter perfect fluid with this property produces a model with a bouncing solution, at the classical level, free from an initial singularity. After that, we use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation value of the scale factor. We find that it oscillates between maximum and minimum values. Since the expectation value of the scale factor never vanishes, we confirm that this model is free from an initial singularity, also, at the quantum level.

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arXiv2010

Canonical transformation for stiff matter models in quantum cosmology

In the present work we consider Friedmann-Robertson-Walker models in the presence of a stiff matter perfect fluid and a cosmological constant. We write the superhamiltonian of these models using the Schutz's variational formalism. We notice that the resulting superhamiltonians have terms that will lead to factor ordering ambiguities when they are written as operators. In order to remove these ambiguities, we introduce appropriate coordinate transformations and prove that these transformations are canonical using the symplectic method.

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arXiv2010

The Planck era with a negative cosmological constant and cosmic strings

In the present letter, we consider the DeBroglie-Bohm interpretation of quantum Friedmann-Robertson-Walker models in the presence of a negative cosmological constant and cosmic strings. We compute the Bohm's trajectories and quantum potentials for a quantity related to the scale factor. Then, we compare our results with the ones already in the literature, where the many worlds interpretation of the same models was used.

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arXiv2010

Probing singularities in quantum cosmology with curvature scalars

We provide further evidence that the canonical quantization of cosmological models eliminates the classical Big Bang singularity, using the {\it DeBroglie-Bohm} interpretation of quantum mechanics. The usual criterion for absence of the Big Bang singularity in Friedmann-Robertson-Walker quantum cosmological models is the non-vanishing of the expectation value of the scale factor. We compute the `local expectation value' of the Ricci and Kretschmann scalars, for some quantum FRW models. We show that they are finite for all time. Since these scalars are elements of general scalar polynomials in the metric and the Riemann tensor, this result indicates that, for the quantum models treated here, the `local expectation value' of these general scalar polynomials should be finite everywhere. Therefore, we have further evidence that the quantization of the models treated here eliminates the classical Big Bang singularity. PACS: 04.40.Nr, 04.60.Ds, 98.80.Qc.

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