arXiv subjects

Moncy V. John

Publications and source records attributed to Moncy V. John.

At least 19 recordsLinked to original sources

arXiv2023

Cosmological significance of the early bright galaxies observed with JWST

The recent discovery of objects with redshift $z>10$ with the help of James Webb Space Telescope (JWST) poses serious challenges to the $Λ$CDM cosmological model, which has been in vogue for some time now. The new data indicate that galaxy formation must have taken place much earlier than expected in this model. Another viable class of cosmological models is that of the so-called coasting models, in which the scale factor of the universe varies proportionately with time. In these models, the universe at redshift $z=12$ has ample time ($\sim 1070$ Myrs) for galaxy formation. The earliest such model is the one proposed by E.A. Milne, based on his `kinematic relativity', but it is considered unrealistic for not treating gravity as relevant at cosmological scales. A closed version of an eternal coasting FLRW model was proposed by the present authors even before SNe Ia data began to pour in. Subsequently we developed a more general model of the same class, which is valid for all the three possible geometries, with open, closed or flat spatial sections. In the nonrelativistic era, this model makes the falsifiable prediction that the ratio of matter density to dark energy density is 2. This avoids the cosmic coincidence problem. Moreover, this eternal coasting model allows room for creation of matter from dark energy, that may speed up galaxy and structure formation at the early epochs, as implied by the JWST data. The paper also attempts to review some similar coasting models, but emphasizes the eternal coasting cosmology as the most probable candidate model capable of explaining the presence of high redshift galaxies discovered by JWST.

astro-ph.CO↗

arXiv2019

Position measurement-induced collapse states: Proposal of an experiment

The quantum mechanical treatment of diffraction of particles, based on the standard postulates of quantum mechanics and the postulate of existence of quantum trajectories, leads to the `position measurement-induced collapse' (PMIC) states. An experimental set-up to test these PMIC states is proposed. The apparatus consists of a modified Lloyd's mirror in optics, with two reflectors instead of one. The diffraction patterns for this case predicted by the PMIC formalism are presented. They exhibit quantum fractal structures in space-time called `quantum carpets', first discovered by Berry (1996). The PMIC formalism in this case closely follows the `boundary bound diffraction' analysed in a previous work by Tounli, Alverado and Sanz (2019). In addition to obtaining their results, we have shown that the time evolution of these collapsed states also leads to Fresnel and Fraunhofer diffractions. It is anticipated that the verification of PMIC states by this experiment will help to better understand collapse of the wave function during quantum measurements.

quant-ph↗

arXiv2019

$R_h=ct$ and the eternal coasting cosmological model

We point out that the nonempty $R_h=ct$ cosmological model has some known antecedents in the literature. Some of those eternal coasting models are published even before the discovery of the accelerated expansion of the universe and were shown to have none of the commonly discussed cosmological problems and also that $H_0t_0=1$. The $R_h=ct$ model is only the special (flat) case of the eternal coasting model. An additional feature in the coasting model is that $Ω_m/Ω_{dark \; energy}$ = some constant of the order of unity, so that also the cosmic coincidence problem is avoided.

astro-ph.CO↗

arXiv2018

Interfering Quantum Trajectories Without Which-Way Information

Quantum trajectory-based descriptions of interference between two coherent stationary waves in a double-slit experiment are presented, as given by the de Broglie-Bohm (dBB) and modified de Broglie-Bohm (MdBB) formulations of quantum mechanics. In the dBB trajectory representation, interference between two spreading wave packets can be shown also as resulting from motion of particles. But a trajectory explanation for interference between stationary states is so far not available in this scheme. We show that both the dBB and MdBB trajectories are capable of producing the interference pattern for stationary as well as wave packet states. However, the dBB representation is found to provide the `which-way' information that helps to identify the hole through which the particle emanates. On the other hand, the MdBB representation does not provide any which-way information while giving a satisfactory explanation of interference phenomenon in tune with the de Broglie's wave particle duality. By counting the trajectories reaching the screen, we have numerically evaluated the intensity distribution of the fringes and found very good agreement with the standard results.

quant-ph↗

arXiv2016

Realistic coasting cosmology from the Milne model

In the context of the recent synchronicity problem in $Λ$CDM cosmology, coasting models such as the classic Milne model and the $R_h=ct$ model have attracted much attention. Also, a very recent analysis of supernovae Ia data is reported to favour models with constant expansion rates. We point out that the nonempty $R_h=ct$ model has some known antecedents in the literature. Some of these are published even before the discovery of the accelerated expansion and were shown to have none of the cosmological problems and also that $H_0t_0=1$ and $Ω_m/Ω_{dark \; energy}$ = some constant of the order of unity. In this paper, we also derive such a model by a complex extension of scale factor in the Milne model.

astro-ph.CO↗

arXiv2015

Tunneling in energy eigenstates and complex quantum trajectories

Complex quantum trajectory approach, which arose from a modified de Broglie-Bohm interpretation of quantum mechanics, has attracted much attention in recent years. The exact complex trajectories for the Eckart potential barrier and the soft potential step, plotted in a previous work, show that more trajectories link the left and right regions of the barrier, when the energy is increased. In this paper, we evaluate the reflection probability using a new ansatz based on these observations, as the ratio between the total probabilities of reflected and incident trajectories. While doing this, we also put to test the complex-extended probability density previously postulated for these quantum trajectories. The new ansatz is preferred since the evaluation is solely done with the help of the complex-extended probability density along the imaginary direction and the trajectory pattern itself. The calculations are performed for a rectangular potential barrier, symmetric Eckart and Morse barriers, and a soft potential step. The predictions are in perfect agreement with the standard results for potentials such as the rectangular potential barrier. For the other potentials, there is very good agreement with standard results, but it is exact only for low and high energies. For moderate energies, there are slight deviations. These deviations result from the periodicity of the trajectory pattern along the imaginary axis and have a maximum value only as much as $0.1 \%$ of the standard value. Measurement of such deviation shall provide an opportunity to falsify the ansatz.

quant-ph↗

arXiv2015

Exact Classical Correspondence in Quantum Cosmology

We find a Friedmann model with appropriate matter/energy density such that the solution of the Wheeler-DeWitt equation exactly corresponds to the classical evolution. The well-known problems in quantum cosmology disappear in the resulting coasting evolution. The exact quantum-classical correspondence is demonstrated with the help of the de Broglie-Bohm and modified de Broglie-Bohm approaches to quantum mechanics. It is reassuring that such a solution leads to a robust model for the universe, which agrees well with cosmological expansion indicated by SNe Ia data.

gr-qc↗

arXiv2013

Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories

This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state complex quantum trajectories and the complex classical trajectories are identical to each other. This congruence in the complex plane, not restricted to high quantum numbers alone, illustrates that the harmonic oscillator in a coherent state executes classical motion. The quantum trajectories are those conceived in a modified de Broglie-Bohm scheme and we note that identical classical and quantum trajectories for coherent states are obtained only in the present approach. The study is extended to Gazeau-Klauder and SUSY quantum mechanics-based coherent states of a particle in an infinite potential well and that in a symmetric Poschl-Teller (PT) potential by solving for the trajectories numerically. For the coherent state of the infinite potential well, almost identical classical and quantum trajectories are obtained whereas for the PT potential, though classical trajectories are not regained, a periodic motion results as t --> \infty.

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arXiv2010

Complex Trajectories and Dynamical Origin of Quantum Probability

Complex quantum trajectories, which were first obtained from a modified de Broglie-Bohm quantum mechanics, demonstrate that Born's probability axiom in quantum mechanics originates from dynamics itself. We show that a normalisable probability density can be defined for the entire complex plane, though there may be regions where the probability is not locally conserved. Examining this for some simple examples such as the harmonic oscillator, we also find why there is no appreciable complex extended motion in the classical regime.

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arXiv2010

Probability and complex quantum trajectories: Finding the missing links

It is shown that a normalisable probability density can be defined for the entire complex plane in the modified de Broglie-Bohm quantum mechanics, which gives complex quantum trajectories. This work is in continuation of a previous one that defined a conserved probability for most of the regions in the complex space in terms of a trajectory integral, indicating a dynamical origin of quantum probability. There it was also shown that the quantum trajectories obtained are the same characteristic curves that propagate information about the conserved probability density. Though the probability density we now adopt for those regions left out in the previous work is not conserved locally, the net source of probability for such regions is seen to be zero in the example considered, allowing to make the total probability conserved. The new combined probability density agrees with the Born's probability everywhere on the real line, as required. A major fall out of the present scheme is that it explains why in the classical limit the imaginary parts of trajectories are not observed even indirectly and particles are confined close to the real line.

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arXiv2010

Bayesian model-independent evaluation of expansion rates of the universe

Marginal likelihoods for the cosmic expansion rates are evaluated using the `Constitution' data of 397 supernovas, thereby updating the results in some previous works. Even when beginning with a very strong prior probability that favors an accelerated expansion, we obtain a marginal likelihood for the deceleration parameter $q_0$ peaked around zero in the spatially flat case. It is also found that the new data significantly constrains the cosmographic expansion rates, when compared to the previous analyses. These results may strongly depend on the Gaussian prior probability distribution chosen for the Hubble parameter represented by $h$, with $h=0.68\pm 0.06$. This and similar priors for other expansion rates were deduced from previous data. Here again we perform the Bayesian model-independent analysis in which the scale factor is expanded into a Taylor series in time about the present epoch. Unlike such Taylor expansions in terms of redshift, this approach has no convergence problem.

astro-ph.CO↗

arXiv2009

Delineating cosmic expansion history with recent supernova data: A Bayesian model-independent approach

Marginal likelihoods for the cosmic expansion rates are evaluated using the recent `Constitution' data of 397 supernovas, thereby updating the results in some previous works. Even when beginning with a very strong prior probability that favors an accelerated expansion, we end up with a marginal likelihood for the deceleration parameter $q_0$ peaked around zero in the spatially flat case. This is in agreement with some other analysis of the Constitution data. It is also found that the new data significantly constrains the cosmic expansion rates, when compared to the previous analysis. Here again we adopt the model-independent approach in which the scale factor is expanded into a Taylor series in time about the present epoch; for practical purposes, it is truncated to polynomials of various orders, in different trials. Though one cannot regard the polynomials thus obtained as models, in this paper we evaluate the total likelihoods (Bayesian evidences) for them to find the order of the polynomial having the largest likelihood. Analysis using the Constitution data shows that the largest likelihood occurs for the fourth order polynomial and is of value $\approx 0.77 \times 10^{-102}$. It is argued that this value, which we call the likelihood for the model-independent approach, may be used to calibrate the performance of realistic models.

astro-ph.CO↗

arXiv2008

Probability and complex quantum trajectories

It is shown that in the complex trajectory representation of quantum mechanics, the Born's Psi^{\star}Ψprobability density can be obtained from the imaginary part of the velocity field of particles on the real axis. Extending this probability axiom to the complex plane, we first attempt to find a probability density by solving an appropriate conservation equation. The characteristic curves of this conservation equation are found to be the same as the complex paths of particles in the new representation. The boundary condition in this case is that the extended probability density should agree with the quantum probability rule along the real line. For the simple, time-independent, one-dimensional problems worked out here, we find that a conserved probability density can be derived from the velocity field of particles, except in regions where the trajectories were previously suspected to be nonviable. An alternative method to find this probability density in terms of a trajectory integral, which is easier to implement on a computer and useful for single particle solutions, is also presented. Most importantly, we show, by using the complex extension of Schrodinger equation, that the desired conservation equation can be derived from this definition of probability density.

quant-ph↗

arXiv2005

Was There a Decelerating Past for the Universe?

In this talk, I argue that the method of analysing the m-z data of Type Ia Supernovae (SNe Ia) by assuming exotic energy densities with strange equations of state is misleading and the reasonable remaining option is to make a model-independent analysis of SNe data, without reference to the energy densities. Using this cosmographic method, we address an important question relevant to cosmology: Was there a decelerating past for the universe? To answer this, the Bayes's probability theory is employed, which is the most appropriate tool for quantifying our knowledge when it changes through the acquisition of new data. The cosmographic approach helps to sort out models which were always accelerating from those which decelerated for at least some time in the period of interest. Bayesian model comparison technique is used to discriminate these rival hypotheses with the aid of recent releases of supernova data. It is argued that the lessons learned using Bayesian theory are extremely valuable to avoid frequent U-turns in cosmology.

astro-ph↗

arXiv2005

Cosmography, Decelerating Past, and Cosmological Models: Learning the Bayesian Way

In this paper, using a significantly improved version of the model-independent, cosmographic approach to cosmology (John, M. V. 2004, ApJ, 614, 1), we address an important question: Was there a decelerating past for the universe? To answer this, the Bayes's probability theory is employed, which is the most appropriate tool for quantifying our knowledge when it changes through the acquisition of new data. The cosmographic approach helps to sort out the models in which the universe was always accelerating from those in which it decelerated for at least some time in the period of interest. Bayesian model comparison technique is used to discriminate these rival hypotheses with the aid of recent releases of supernova data. We also attempt to provide and improve another example of Bayesian model comparison, performed between some Friedmann models, using the same data. Our conclusion, which is consistent with other approaches, is that the apparent magnitude-redshift data alone cannot discriminate these competing hypotheses. We also argue that the lessons learnt using Bayesian theory are extremely valuable to avoid frequent U-turns in cosmology.

astro-ph↗

arXiv2004

Cosmographic evaluation of deceleration parameter using SNe Ia data

The apparent magnitude-redshift data of SNe Ia call for modifications in the standard model energy densities. Under the circumstance that this modification cannot be limited to the addition of a mere cosmological constant, a serious situation has emerged in cosmology, in which the energy densities in the universe have become largely speculative. In this situation, an equation of state of the form p=w ρitself is not well-motivated. In this paper, we argue that the reasonable option left is to make a model-independent analysis of SNe data, without reference to the energy densities. In this basically kinematic approach, we limit ourselves to the observationally justifiable assumptions of homogeneity and isotropy; i.e., to the assumption that the universe has a RW metric. This cosmographic approach is historically the original one to cosmology. We perform the analysis by expanding the scale factor into a polynomial of order 5, which assumption can be further generalised to any order. The present expansion rates h, q_0, r_0 etc. are evaluated by computing the marginal likelihoods for these parameters. These values are relevant, since any cosmological solution would ultimately need to explain them.

astro-ph↗

arXiv2003

A modified Ozer-Taha type cosmological model

A modified version of the Ozer and Taha nonsingular cosmological model is presented on the assumption that the universe's radius is complex if it is regarded as empty, but it contains matter when the radius is real. It also predicts the values: Omega_M =rho_M /rho_C \approx 4/3, Omega_V = rho_V /rho_C \approx 2/3, and Omega_ = rho_ /rho_C << 1 in the present nonrelativistic era, where rho_M = matter density, rho_V = vacuum density, rho_= negative energy density and rho_{C} = critical density.

gr-qc↗

arXiv2003

Modified de Broglie-Bohm approach to quantum mechanics

A modified de Broglie-Bohm (dBB) approach to quantum mechanics is presented. In this new deterministic theory, which uses complex methods in an intermediate step, the problem of zero velocity for bound states encountered in the dBB formulation does not appear. Also this approach is equivalent to standard quantum mechanics when averages of dynamical variables like position, momentum and energy are taken.

quant-ph↗