Jaume García Haro - Academia.edu (original) (raw)
Papers by Jaume García Haro
arXiv (Cornell University), Nov 22, 2010
In these lectures we consider some topics of Quantum Field Theory in Curved Space. In the first o... more In these lectures we consider some topics of Quantum Field Theory in Curved Space. In the first one particle creation in curved space is studied from a mathematical point of view, especially, particle production at a given time using the so called "instantaneous diagonalization method". As a first application we study particle production in a no-oscillating model where reheating may be explained from gravitational particle creation. In the second one we recalculate , with all the mathematical details, particle production in the Starobinsky model. Particle production by strong electromagnetic fields (Schwinger's effect) and particle production by moving mirrors simulating black hole collapse are also studied. In the second lecture we calculate the re-normalized two-point function using the adiabatic regularization. The conformally and minimally coupled cases are considered for a scalar massive and massless field. We reproduce previous results in a rigorous mathematical form and clarify some empirical approximations and bounds. The re-normalized stress tensor is also calculated in several situations. Finally, in last lecture quantum correction due to a massless fields conformally coupled with gravity are considered in order to study the avoidance of singularities that appear in the flat Friedmann-Robertson-Walker (FRW) model. It is assumed that the universe contains a barotropic perfect fluid with state equation p = ωρ (being ρ the energy density and p the pressure). The dynamics of the model is studied for all values of the parameter ω, and also for all values of the two parameters, that we will call α and β, provided by the quantum corrections. We will see that only the case α > 0 could avoid the singularities. Then when ω > −1, in order to obtain an expanding Friedmann universe at late times (only a one-parameter family of solutions, no a general solution, has this behavior at late times), the initial conditions of the no-singular solutions at early times must be very fine tuned. These no-singular solutions are: a general solution (a two-parameter family) leaving the contracting de Sitter phase, and a one-parameter family leaving the contracting Friedmann stage. On the other hand for ω < −1 (phantom field), the problem of the avoidance of singularities is more involved because if one considers an expanding Friedmann stage at early times, then instead of fine tune the initial conditions one also has to fine tune the parameters α and β to obtain a behavior without future singularities, because only a one-parameter family of solutions follows a contracting Friedmann phase at late times, and only a particular solution behaves like a contracting de Sitter universe. The rest of solutions have future singularities.
Physical Review D, 2015
For bouncing cosmologies, a fine set of parameters is introduced in order to describe the nearly ... more For bouncing cosmologies, a fine set of parameters is introduced in order to describe the nearly matter dominated phase, and which play the same role that the usual slow-roll parameters play in inflationary cosmology. It is shown that, as in the inflation case, the spectral index and the running parameter for scalar perturbations in bouncing cosmologies can be best expressed in terms of these small parameters. Further, they explicitly exhibit the duality which exists between a nearly matter dominated Universe in its contracting phase and the quasi de Sitter regime in the expanding one. The results obtained also confirm and extend the known evidence that the spectral index for an exactly matter dominated Universe (i.e., a pressureless Universe) in the contracting phase is, in fact, the same as the spectral index for an exact de Sitter regime in the expanding phase. Finally, in both the inflationary and the matter bounce scenarios, the theoretical values of the spectral index and of the running parameter are compared with their experimental counterparts, obtained from the most recent PLANCK data, with the result that the bouncing models here discussed do fit well accurate astronomical observations.
International Journal of Theoretical Physics
We study the Klein-Gordon field coupled with an external uniform vector potential. We compute pai... more We study the Klein-Gordon field coupled with an external uniform vector potential. We compute pair production in a finite time t using the semiclassical approximation, and show that, after the interaction of the Klein-Gordon field with the external potential, when h → 0 the average number of produced pairs is zero. There is agreement with the classical limit because the classical limit involves no production of pairs. We compared our results with those of Schwinger. Finally we saw that the random variable N (t)= net number of pairs produced at time t is in the semiclassical limit a stochastic Poisson process.
Theoretical and Mathematical Physics, 2010
ABSTRACT We calculate a renormalized two-point function using the adiabatic regularization method... more ABSTRACT We calculate a renormalized two-point function using the adiabatic regularization method. We study the conformally and minimally coupled cases for massless and massive scalar fields in full detail. We reproduce previous results in a rigorous mathematical form and clarify some empirical approximations and bounds. We consider some applications to inflationary models. Keywordstwo-point function–adiabatic regularization–de Sitter phase
Theoretical and Mathematical Physics, 2012
Using quantum corrections from massless fields conformally coupled to gravity, we study the possi... more Using quantum corrections from massless fields conformally coupled to gravity, we study the possibility of avoiding singularities that appear in the flat Friedmann-Robertson-Walker model. We assume that the universe contains a barotropic perfect fluid with the state equation p = ωρ, where p is the pressure and ρ is the energy density. We study the dynamics of the model for all values of the parameter ω and also for all values of the conformal anomaly coefficients α and β. We show that singularities can be avoided only in the case where α > 0 and β < 0. To obtain an expanding Friedmann universe at late times with ω > −1 (only a one-parameter family of solutions, but no a general solution, has this behavior at late times), the initial conditions of the nonsingular solutions at early times must be chosen very exactly. These nonsingular solutions consist of a general solution (a two-parameter family) exiting the contracting de Sitter phase and a one-parameter family exiting the contracting Friedmann phase. On the other hand, for ω < −1 (a phantom field), the problem of avoiding singularities is more involved because if we consider an expanding Friedmann phase at early times, then in addition to fine-tuning the initial conditions, we must also fine-tune the parameters α and β to obtain a behavior without future singularities: only a oneparameter family of solutions follows a contracting Friedmann phase at late times, and only a particular solution behaves like a contracting de Sitter universe. The other solutions have future singularities.
Physical Review Letters, 2006
A Hamiltonian approach is introduced in order to address some severe problems associated with the... more A Hamiltonian approach is introduced in order to address some severe problems associated with the physical description of the dynamical Casimir effect at all times. For simplicity, the case of a neutral scalar field in a one-dimensional cavity with partially transmitting mirrors (an essential proviso) is considered, but the method can be extended to fields of any kind and higher dimensions. The motional force calculated in our approach contains a reactive term-proportional to the mirrors' acceleration-which is fundamental in order to obtain (quasi)particles with a positive energy all the time during the movement of the mirrors-while always satisfying the energy conservation law. Comparisons with other approaches and a careful analysis of the interrelations among the different results previously obtained in the literature are carried out.
Physical Review Letters, 2012
Particle production from vacuum fluctuations during inflation is briefly revisited. The moduli pr... more Particle production from vacuum fluctuations during inflation is briefly revisited. The moduli problem occurring with light particles produced at the end of inflation is addressed, namely the fact that some results are in disagreement with nucleosynthesis constrains. A universal solution to this problem is found which leads to reasonable reheating temperatures in all cases. It invokes the assumption that, immediately after inflation, the moduli evolve like non-relativistic matter. The assumption is justified in the context of massive chaotic inflation were, at the end of inflation, the universe evolves as if it was matter-dominated.
Physical Review D, 2013
The big bang singularity could be understood as a breakdown of Einstein's general relativity at v... more The big bang singularity could be understood as a breakdown of Einstein's general relativity at very high energies. By adopting this viewpoint, other theories that implement Einstein cosmology at high energies might solve the problem of the primeval singularity. One of them is loop quantum cosmology (LQC) with a small cosmological constant that models a universe moving along an ellipse, which prevents singularities like the big bang or the big rip, in the phase space ðH; Þ, where H is the Hubble parameter and the energy density of the universe. Using LQC one considers a model universe filled by radiation and matter where, due to the cosmological constant, there are a de Sitter and an anti-de Sitter solution. This means that one obtains a bouncing nonsingular universe which is in the contracting phase at early times. After leaving this phase, i.e., after bouncing, it passes trough a radiation-and matter-dominated phase and finally at late times it expands in an accelerated way (current cosmic acceleration). This model does not suffer from the horizon and flatness problems as in big bang cosmology, where a period of inflation that increases the size of our universe in more than 60 e-folds is needed in order to solve both problems. The model has two mechanisms to avoid these problems: the evolution of the universe through a contracting phase and a period of super inflation (_ H > 0).
Physical Review D, 2012
Quantum corrections coming from massless fields conformally coupled with gravity are studied, in ... more Quantum corrections coming from massless fields conformally coupled with gravity are studied, in order to see if they can lead to avoidance of the annoying Big Rip singularity which shows up in a flat Friedmann-Robertson-Walker universe filled with dark energy and modeled by a scalar phantom field. The dynamics of the model are discussed for all values of the two parameters, named α > 0 and β < 0, corresponding to the regularization process. The new results are compared with the ones obtained in [1] previously, where dark energy was modeled by means of a phantom fluid with equation of state P = ωρ, with ω < −1.
Physical Review D, 2008
Creation of scalar massless particles in two-dimensional Minkowski space-time-as predicted by the... more Creation of scalar massless particles in two-dimensional Minkowski space-time-as predicted by the dynamical Casimir effect-is studied for the case of a semitransparent mirror initially at rest, then accelerating for some finite time, along a trajectory that simulates a black hole collapse (defined by Walker, and Carlitz and Willey), and finally moving with constant velocity. When the reflection and transmission coefficients are those in the model proposed by Barton, Calogeracos, and Nicolaevici [r(w) = −iα/(ω + iα) and s(w) = ω/(ω + iα), with α ≥ 0], the Bogoliubov coefficients on the back side of the mirror can be computed exactly. This allows us to prove that, when α is very large (case of an ideal, perfectly reflecting mirror) a thermal emission of scalar massless particles obeying Bose-Einstein statistics is radiated from the mirror (a black body radiation), in accordance with results previously obtained in the literature. However, when α is finite (semitransparent mirror, a physically realistic situation) the striking result is obtained that the thermal emission of scalar massless particles obeys Fermi-Dirac statistics. We also show here that the reverse change of statistics takes place in a bidimensional fermionic model for massless particles, namely that the Fermi-Dirac statistics for the completely reflecting situation will turn into the Bose-Einstein statistics for a partially reflecting, physical mirror.
Journal of Physics A: Mathematical and Theoretical, 2009
ABSTRACT Recently, an effective formulation of gravity which lies in between the Wheeler–DeWitt a... more ABSTRACT Recently, an effective formulation of gravity which lies in between the Wheeler–DeWitt approach and classical cosmology was discussed. It was shown that the Big Bang singularity of FRW cosmologies is avoided in a quite natural way. Here, we aim to prove that this formulation is able to avoid the Big Rip singularity too, in contradistinction with Schutz's formalism as applied to quantum cosmological perfect fluids. Actually, in using this last formalism, some authors have argued that such singularity would persist even after quantization, however, what we carried out, with our formulation as a guide, proved not to be the case. Also, it will be argued that it is the implicit regularization of the classical Hamiltonian performed in loop quantum cosmology, which is needed in loop cosmology in order to build a well-defined quantum (discrete) theory, which avoids the Big Rip singularity in that theory, this mechanism being different from other, ordinarily invoked quantum effects.
Journal of Physics A: Mathematical and Theoretical, 2011
ABSTRACT In this paper, particle creation in curved space is studied from a mathematical perspect... more ABSTRACT In this paper, particle creation in curved space is studied from a mathematical perspective. In particular, particle production is calculated at a given time using the so-called instantaneous diagonalization method. As an application, we study particle production in a non-oscillating model where re-heating may be explained from the point of view of gravitational particle creation. To conclude the paper, we re-calculate, with all mathematical detail, particle production in the Starobinsky model.
Journal of Physics A: Mathematical and Theoretical, 2009
Journal of Physics A: Mathematical and Theoretical, 2008
Creation of scalar massless particles in two-dimensional Minkowski space-time-as predicted by the... more Creation of scalar massless particles in two-dimensional Minkowski space-time-as predicted by the dynamical Casimir effect-is studied for the case of a semitransparent mirror initially at rest, then accelerating for some finite time, along a specified trajectory, and finally moving with constant velocity. When the reflection and transmission coefficients are those in the model proposed by Barton, Calogeracos, and Nicolaevici [r(w) = −iα/(ω + iα) and s(w) = ω/(ω+iα), with α ≥ 0], the Bogoliubov coefficients on the back side of the mirror can be computed exactly. This allows us to prove that, when α is very large (case of an ideal, perfectly reflecting mirror) a thermal emission of scalar massless particles obeying Bose-Einstein statistics is radiated from the mirror (a black body radiation), in accordance with previous results in the literature. However, when α is finite (semitransparent mirror, a physically realistic situation) the striking result is obtained that the thermal emission of scalar massless particles obeys Fermi-Dirac statistics. Possible consequences of this result are envisaged.
Journal of Physics A: Mathematical and Theoretical, 2008
ABSTRACT The conditions of the Gibbons–Hawking effect, i.e., particle production in the Friedmann... more ABSTRACT The conditions of the Gibbons–Hawking effect, i.e., particle production in the Friedmann–Robertson–Walker chart of the de Sitter spacetime, are revisited. For a theory with a massive scalar and a fermionic field it is shown that, if one considers the Bunch–Davies vacuum state at early times, then only in the case that the condition mc2/H 1 is fulfilled can one assure that a thermal spectrum of radiation at temperature T = H/2πkB, where kB is the Boltzmann constant, will be obtained at late times. It is pointed out that this important proviso (which is nothing else than the adiabatic condition, as we shall see), is missing in several derivations of this effect in the literature, where the thermal spectrum was obtained without imposing any restriction on the relation between the mass of the field, m and the Hubble constant, H.
Journal of Physics A: Mathematical and General, 2006
ABSTRACT
Journal of Cosmology and Astroparticle Physics, 2012
Different approaches to quantum cosmology are studied in order to deal with the future singularit... more Different approaches to quantum cosmology are studied in order to deal with the future singularity avoidance problem. Our results show that these future singularities will persist but could take different forms. As an example we have studied the big rip which appear when one considers the state equation P = ωρ with ω < −1, showing that it does not disappear in modified gravity. On the other hand, it is well-known that quantum geometric effects (holonomy corrections) in loop quantum cosmology introduce a quadratic modification, namely proportional to ρ 2 , in Friedmann's equation that replace the big rip by a non-singular bounce. However this modified Friedmann equation could have been obtained in an inconsistent way, what means that the obtained results from this equation, in particular singularity avoidance, would be incorrect. In fact, we will show that instead of a nonsingular bounce, the big rip singularity would be replaced, in loop quantum cosmology, by other kind of singularity.
International Journal of Theoretical Physics, 2004
In this paper we study the production of pairs in no-analytic potentials. It is a well-known fact... more In this paper we study the production of pairs in no-analytic potentials. It is a well-known fact that, when the potential is analytic the average number of produced pairs is exponentially small in. On the other hand, when the potential is no-analytic, using the W.K.B. method, we prove that the average number of produced pairs is Ç´« ¾AE µ, where AE is the regularity of the potential and « is the fine structure constant. Finally, we give a rigorous proof of the Schwinger's formula.
International Journal of Theoretical Physics, 2006
ABSTRACT
arXiv (Cornell University), Nov 22, 2010
In these lectures we consider some topics of Quantum Field Theory in Curved Space. In the first o... more In these lectures we consider some topics of Quantum Field Theory in Curved Space. In the first one particle creation in curved space is studied from a mathematical point of view, especially, particle production at a given time using the so called "instantaneous diagonalization method". As a first application we study particle production in a no-oscillating model where reheating may be explained from gravitational particle creation. In the second one we recalculate , with all the mathematical details, particle production in the Starobinsky model. Particle production by strong electromagnetic fields (Schwinger's effect) and particle production by moving mirrors simulating black hole collapse are also studied. In the second lecture we calculate the re-normalized two-point function using the adiabatic regularization. The conformally and minimally coupled cases are considered for a scalar massive and massless field. We reproduce previous results in a rigorous mathematical form and clarify some empirical approximations and bounds. The re-normalized stress tensor is also calculated in several situations. Finally, in last lecture quantum correction due to a massless fields conformally coupled with gravity are considered in order to study the avoidance of singularities that appear in the flat Friedmann-Robertson-Walker (FRW) model. It is assumed that the universe contains a barotropic perfect fluid with state equation p = ωρ (being ρ the energy density and p the pressure). The dynamics of the model is studied for all values of the parameter ω, and also for all values of the two parameters, that we will call α and β, provided by the quantum corrections. We will see that only the case α > 0 could avoid the singularities. Then when ω > −1, in order to obtain an expanding Friedmann universe at late times (only a one-parameter family of solutions, no a general solution, has this behavior at late times), the initial conditions of the no-singular solutions at early times must be very fine tuned. These no-singular solutions are: a general solution (a two-parameter family) leaving the contracting de Sitter phase, and a one-parameter family leaving the contracting Friedmann stage. On the other hand for ω < −1 (phantom field), the problem of the avoidance of singularities is more involved because if one considers an expanding Friedmann stage at early times, then instead of fine tune the initial conditions one also has to fine tune the parameters α and β to obtain a behavior without future singularities, because only a one-parameter family of solutions follows a contracting Friedmann phase at late times, and only a particular solution behaves like a contracting de Sitter universe. The rest of solutions have future singularities.
Physical Review D, 2015
For bouncing cosmologies, a fine set of parameters is introduced in order to describe the nearly ... more For bouncing cosmologies, a fine set of parameters is introduced in order to describe the nearly matter dominated phase, and which play the same role that the usual slow-roll parameters play in inflationary cosmology. It is shown that, as in the inflation case, the spectral index and the running parameter for scalar perturbations in bouncing cosmologies can be best expressed in terms of these small parameters. Further, they explicitly exhibit the duality which exists between a nearly matter dominated Universe in its contracting phase and the quasi de Sitter regime in the expanding one. The results obtained also confirm and extend the known evidence that the spectral index for an exactly matter dominated Universe (i.e., a pressureless Universe) in the contracting phase is, in fact, the same as the spectral index for an exact de Sitter regime in the expanding phase. Finally, in both the inflationary and the matter bounce scenarios, the theoretical values of the spectral index and of the running parameter are compared with their experimental counterparts, obtained from the most recent PLANCK data, with the result that the bouncing models here discussed do fit well accurate astronomical observations.
International Journal of Theoretical Physics
We study the Klein-Gordon field coupled with an external uniform vector potential. We compute pai... more We study the Klein-Gordon field coupled with an external uniform vector potential. We compute pair production in a finite time t using the semiclassical approximation, and show that, after the interaction of the Klein-Gordon field with the external potential, when h → 0 the average number of produced pairs is zero. There is agreement with the classical limit because the classical limit involves no production of pairs. We compared our results with those of Schwinger. Finally we saw that the random variable N (t)= net number of pairs produced at time t is in the semiclassical limit a stochastic Poisson process.
Theoretical and Mathematical Physics, 2010
ABSTRACT We calculate a renormalized two-point function using the adiabatic regularization method... more ABSTRACT We calculate a renormalized two-point function using the adiabatic regularization method. We study the conformally and minimally coupled cases for massless and massive scalar fields in full detail. We reproduce previous results in a rigorous mathematical form and clarify some empirical approximations and bounds. We consider some applications to inflationary models. Keywordstwo-point function–adiabatic regularization–de Sitter phase
Theoretical and Mathematical Physics, 2012
Using quantum corrections from massless fields conformally coupled to gravity, we study the possi... more Using quantum corrections from massless fields conformally coupled to gravity, we study the possibility of avoiding singularities that appear in the flat Friedmann-Robertson-Walker model. We assume that the universe contains a barotropic perfect fluid with the state equation p = ωρ, where p is the pressure and ρ is the energy density. We study the dynamics of the model for all values of the parameter ω and also for all values of the conformal anomaly coefficients α and β. We show that singularities can be avoided only in the case where α > 0 and β < 0. To obtain an expanding Friedmann universe at late times with ω > −1 (only a one-parameter family of solutions, but no a general solution, has this behavior at late times), the initial conditions of the nonsingular solutions at early times must be chosen very exactly. These nonsingular solutions consist of a general solution (a two-parameter family) exiting the contracting de Sitter phase and a one-parameter family exiting the contracting Friedmann phase. On the other hand, for ω < −1 (a phantom field), the problem of avoiding singularities is more involved because if we consider an expanding Friedmann phase at early times, then in addition to fine-tuning the initial conditions, we must also fine-tune the parameters α and β to obtain a behavior without future singularities: only a oneparameter family of solutions follows a contracting Friedmann phase at late times, and only a particular solution behaves like a contracting de Sitter universe. The other solutions have future singularities.
Physical Review Letters, 2006
A Hamiltonian approach is introduced in order to address some severe problems associated with the... more A Hamiltonian approach is introduced in order to address some severe problems associated with the physical description of the dynamical Casimir effect at all times. For simplicity, the case of a neutral scalar field in a one-dimensional cavity with partially transmitting mirrors (an essential proviso) is considered, but the method can be extended to fields of any kind and higher dimensions. The motional force calculated in our approach contains a reactive term-proportional to the mirrors' acceleration-which is fundamental in order to obtain (quasi)particles with a positive energy all the time during the movement of the mirrors-while always satisfying the energy conservation law. Comparisons with other approaches and a careful analysis of the interrelations among the different results previously obtained in the literature are carried out.
Physical Review Letters, 2012
Particle production from vacuum fluctuations during inflation is briefly revisited. The moduli pr... more Particle production from vacuum fluctuations during inflation is briefly revisited. The moduli problem occurring with light particles produced at the end of inflation is addressed, namely the fact that some results are in disagreement with nucleosynthesis constrains. A universal solution to this problem is found which leads to reasonable reheating temperatures in all cases. It invokes the assumption that, immediately after inflation, the moduli evolve like non-relativistic matter. The assumption is justified in the context of massive chaotic inflation were, at the end of inflation, the universe evolves as if it was matter-dominated.
Physical Review D, 2013
The big bang singularity could be understood as a breakdown of Einstein's general relativity at v... more The big bang singularity could be understood as a breakdown of Einstein's general relativity at very high energies. By adopting this viewpoint, other theories that implement Einstein cosmology at high energies might solve the problem of the primeval singularity. One of them is loop quantum cosmology (LQC) with a small cosmological constant that models a universe moving along an ellipse, which prevents singularities like the big bang or the big rip, in the phase space ðH; Þ, where H is the Hubble parameter and the energy density of the universe. Using LQC one considers a model universe filled by radiation and matter where, due to the cosmological constant, there are a de Sitter and an anti-de Sitter solution. This means that one obtains a bouncing nonsingular universe which is in the contracting phase at early times. After leaving this phase, i.e., after bouncing, it passes trough a radiation-and matter-dominated phase and finally at late times it expands in an accelerated way (current cosmic acceleration). This model does not suffer from the horizon and flatness problems as in big bang cosmology, where a period of inflation that increases the size of our universe in more than 60 e-folds is needed in order to solve both problems. The model has two mechanisms to avoid these problems: the evolution of the universe through a contracting phase and a period of super inflation (_ H > 0).
Physical Review D, 2012
Quantum corrections coming from massless fields conformally coupled with gravity are studied, in ... more Quantum corrections coming from massless fields conformally coupled with gravity are studied, in order to see if they can lead to avoidance of the annoying Big Rip singularity which shows up in a flat Friedmann-Robertson-Walker universe filled with dark energy and modeled by a scalar phantom field. The dynamics of the model are discussed for all values of the two parameters, named α > 0 and β < 0, corresponding to the regularization process. The new results are compared with the ones obtained in [1] previously, where dark energy was modeled by means of a phantom fluid with equation of state P = ωρ, with ω < −1.
Physical Review D, 2008
Creation of scalar massless particles in two-dimensional Minkowski space-time-as predicted by the... more Creation of scalar massless particles in two-dimensional Minkowski space-time-as predicted by the dynamical Casimir effect-is studied for the case of a semitransparent mirror initially at rest, then accelerating for some finite time, along a trajectory that simulates a black hole collapse (defined by Walker, and Carlitz and Willey), and finally moving with constant velocity. When the reflection and transmission coefficients are those in the model proposed by Barton, Calogeracos, and Nicolaevici [r(w) = −iα/(ω + iα) and s(w) = ω/(ω + iα), with α ≥ 0], the Bogoliubov coefficients on the back side of the mirror can be computed exactly. This allows us to prove that, when α is very large (case of an ideal, perfectly reflecting mirror) a thermal emission of scalar massless particles obeying Bose-Einstein statistics is radiated from the mirror (a black body radiation), in accordance with results previously obtained in the literature. However, when α is finite (semitransparent mirror, a physically realistic situation) the striking result is obtained that the thermal emission of scalar massless particles obeys Fermi-Dirac statistics. We also show here that the reverse change of statistics takes place in a bidimensional fermionic model for massless particles, namely that the Fermi-Dirac statistics for the completely reflecting situation will turn into the Bose-Einstein statistics for a partially reflecting, physical mirror.
Journal of Physics A: Mathematical and Theoretical, 2009
ABSTRACT Recently, an effective formulation of gravity which lies in between the Wheeler–DeWitt a... more ABSTRACT Recently, an effective formulation of gravity which lies in between the Wheeler–DeWitt approach and classical cosmology was discussed. It was shown that the Big Bang singularity of FRW cosmologies is avoided in a quite natural way. Here, we aim to prove that this formulation is able to avoid the Big Rip singularity too, in contradistinction with Schutz's formalism as applied to quantum cosmological perfect fluids. Actually, in using this last formalism, some authors have argued that such singularity would persist even after quantization, however, what we carried out, with our formulation as a guide, proved not to be the case. Also, it will be argued that it is the implicit regularization of the classical Hamiltonian performed in loop quantum cosmology, which is needed in loop cosmology in order to build a well-defined quantum (discrete) theory, which avoids the Big Rip singularity in that theory, this mechanism being different from other, ordinarily invoked quantum effects.
Journal of Physics A: Mathematical and Theoretical, 2011
ABSTRACT In this paper, particle creation in curved space is studied from a mathematical perspect... more ABSTRACT In this paper, particle creation in curved space is studied from a mathematical perspective. In particular, particle production is calculated at a given time using the so-called instantaneous diagonalization method. As an application, we study particle production in a non-oscillating model where re-heating may be explained from the point of view of gravitational particle creation. To conclude the paper, we re-calculate, with all mathematical detail, particle production in the Starobinsky model.
Journal of Physics A: Mathematical and Theoretical, 2009
Journal of Physics A: Mathematical and Theoretical, 2008
Creation of scalar massless particles in two-dimensional Minkowski space-time-as predicted by the... more Creation of scalar massless particles in two-dimensional Minkowski space-time-as predicted by the dynamical Casimir effect-is studied for the case of a semitransparent mirror initially at rest, then accelerating for some finite time, along a specified trajectory, and finally moving with constant velocity. When the reflection and transmission coefficients are those in the model proposed by Barton, Calogeracos, and Nicolaevici [r(w) = −iα/(ω + iα) and s(w) = ω/(ω+iα), with α ≥ 0], the Bogoliubov coefficients on the back side of the mirror can be computed exactly. This allows us to prove that, when α is very large (case of an ideal, perfectly reflecting mirror) a thermal emission of scalar massless particles obeying Bose-Einstein statistics is radiated from the mirror (a black body radiation), in accordance with previous results in the literature. However, when α is finite (semitransparent mirror, a physically realistic situation) the striking result is obtained that the thermal emission of scalar massless particles obeys Fermi-Dirac statistics. Possible consequences of this result are envisaged.
Journal of Physics A: Mathematical and Theoretical, 2008
ABSTRACT The conditions of the Gibbons–Hawking effect, i.e., particle production in the Friedmann... more ABSTRACT The conditions of the Gibbons–Hawking effect, i.e., particle production in the Friedmann–Robertson–Walker chart of the de Sitter spacetime, are revisited. For a theory with a massive scalar and a fermionic field it is shown that, if one considers the Bunch–Davies vacuum state at early times, then only in the case that the condition mc2/H 1 is fulfilled can one assure that a thermal spectrum of radiation at temperature T = H/2πkB, where kB is the Boltzmann constant, will be obtained at late times. It is pointed out that this important proviso (which is nothing else than the adiabatic condition, as we shall see), is missing in several derivations of this effect in the literature, where the thermal spectrum was obtained without imposing any restriction on the relation between the mass of the field, m and the Hubble constant, H.
Journal of Physics A: Mathematical and General, 2006
ABSTRACT
Journal of Cosmology and Astroparticle Physics, 2012
Different approaches to quantum cosmology are studied in order to deal with the future singularit... more Different approaches to quantum cosmology are studied in order to deal with the future singularity avoidance problem. Our results show that these future singularities will persist but could take different forms. As an example we have studied the big rip which appear when one considers the state equation P = ωρ with ω < −1, showing that it does not disappear in modified gravity. On the other hand, it is well-known that quantum geometric effects (holonomy corrections) in loop quantum cosmology introduce a quadratic modification, namely proportional to ρ 2 , in Friedmann's equation that replace the big rip by a non-singular bounce. However this modified Friedmann equation could have been obtained in an inconsistent way, what means that the obtained results from this equation, in particular singularity avoidance, would be incorrect. In fact, we will show that instead of a nonsingular bounce, the big rip singularity would be replaced, in loop quantum cosmology, by other kind of singularity.
International Journal of Theoretical Physics, 2004
In this paper we study the production of pairs in no-analytic potentials. It is a well-known fact... more In this paper we study the production of pairs in no-analytic potentials. It is a well-known fact that, when the potential is analytic the average number of produced pairs is exponentially small in. On the other hand, when the potential is no-analytic, using the W.K.B. method, we prove that the average number of produced pairs is Ç´« ¾AE µ, where AE is the regularity of the potential and « is the fine structure constant. Finally, we give a rigorous proof of the Schwinger's formula.
International Journal of Theoretical Physics, 2006
ABSTRACT