Modern problems in astrophysics tend to require large, complex computational frameworks to solve many aspects of the system simultaneusly. Calculation of the energy production through nuclear reactions is typically one of those aspects. The use of standard nuclear burning algorithms will take up the majority of the computational time with all but the smallest of networks. The explicit asymptotic method has shown promise in computing large networks faster than existing methods in various environments while retaining accuracy. The purpose of this thesis is to show that this method can be successfully used to solve complex systems using a network of realistic size in a reasonable amount of time, and to investigate some problems in the flame propagation for a Type Ia, which have never been investigated with a realistic network.

In the standard model of cosmology, the universe is currently dominated by dark energy in the form of the cosmological constant that drives the expansion to accelerate. While the cosmological constant hypothesis is consistent with all current data, models with dynamical behaviour of dark energy are still allowed by observations. Uncertainty also remains over whether the underlying assumption of a homogeneous and isotropic universe is valid, or if large-scale inhomogeneities in the matter distribution can be the cause of the apparent late-time acceleration.This thesis investigates inhomogeneous cosmological models in which dark energy clusters or where we live inside an underdense region in a matter-dominated universe. In both of these scenarios, we expect directional dependences in the redshift-luminosity distance relation of type Ia supernovae. Dynamical models of dark energy predict spatial variations in the dark energy density. Searches for angular correlated fluctuations in the supernova peak magnitudes, as expected if dark energy clusters, yield results consistent with no dark energy fluctuations. However, the current observational limits on the amount of correlation still allow for quite general dark energy clustering occurring in the linear regime. Inhomogeneous models where we live inside a large, local void in the matter density can possibly explain the apparent acceleration without invoking dark energy. This scenario is confronted with current cosmological distance measurements to put constraints on the size and depth of the void, as well as on our position within it. The model is found to explain the observations only if the void size is of the order of the visible universe and the observer is located very close to the center, in violation of the Copernican principle. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 4: Accepted.

Modern problems in astrophysics tend to require large, complex computational frameworks to solve many aspects of the system simultaneusly. Calculation of the energy production through nuclear reactions is typically one of those aspects. The use of standard nuclear burning algorithms will take up the majority of the computational time with all but the smallest of networks. The explicit asymptotic method has shown promise in computing large networks faster than existing methods in various environments while retaining accuracy. The purpose of this thesis is to show that this method can be successfully used to solve complex systems using a network of realistic size in a reasonable amount of time, and to investigate some problems in the flame propagation for a Type Ia, which have never been investigated with a realistic network.

<p>Type Ia supernovae can be used as distance indicators for probing the expansion history of the Universe. The method has proved to be an efficient tool in cosmology and played a decisive role in the discovery of a yet unknown energy form, dark energy, that drives the accelerated expansion of the Universe. The work in this thesis addresses the nature of dark energy, both by presenting existing data, and by predicting opportunities and difficulties related to possible future data.</p><p>Optical and infrared measurements of type Ia supernovae for different epochs in the cosmic expansion history are presented along with a discussion of the systematic errors. The data have been obtained with several instruments, and an optimal method for measuring the lightcurve of a background contaminated source has been used. The procedure was also tested by applying it on simulated images.</p><p>The future of supernova cosmology, and the target precision of cosmological parameters for the proposed SNAP satellite are discussed. In particular, the limits that can be set on various dark energy scenarios are investigated. The possibility of distinguishing between different inverse power-law quintessence models is also studied. The predictions are based on calculations made with the Supernova Observation Calculator, a software package, introduced in the thesis, for simulating the light propagation from distant objects. This tool has also been used for investigating how SNAP observations could be biased by gravitational lensing, and to what extent this would affect cosmology fitting. An alternative approach for estimating cosmological parameters, where lensing effects are taken into account, is also suggested. Finally, it is investigated to what extent strongly lensed core-collapse supernovae could be used as an alternative approach for determining cosmological parameters.</p>

Type Ia supernovae can be used as distance indicators for probing the expansion history of the Universe. The method has proved to be an efficient tool in cosmology and played a decisive role in the discovery of a yet unknown energy form, dark energy, that drives the accelerated expansion of the Universe. The work in this thesis addresses the nature of dark energy, both by presenting existing data, and by predicting opportunities and difficulties related to possible future data. Optical and infrared measurements of type Ia supernovae for different epochs in the cosmic expansion history are presented along with a discussion of the systematic errors. The data have been obtained with several instruments, and an optimal method for measuring the lightcurve of a background contaminated source has been used. The procedure was also tested by applying it on simulated images. The future of supernova cosmology, and the target precision of cosmological parameters for the proposed SNAP satellite are discussed. In particular, the limits that can be set on various dark energy scenarios are investigated. The possibility of distinguishing between different inverse power-law quintessence models is also studied. The predictions are based on calculations made with the Supernova Observation Calculator, a software package, introduced in the thesis, for simulating the light propagation from distant objects. This tool has also been used for investigating how SNAP observations could be biased by gravitational lensing, and to what extent this would affect cosmology fitting. An alternative approach for estimating cosmological parameters, where lensing effects are taken into account, is also suggested. Finally, it is investigated to what extent strongly lensed core-collapse supernovae could be used as an alternative approach for determining cosmological parameters.

Type Ia supernovae (SNe Ia) are currently the best probe of the expansion history of the universe. Their usefulness is due chiefly to their uniformity between supernovae (SNe). However, there are some slight variations amongst SNe that have yet to be understood and accounted for. The goal of this work is to uncover relationships between the spectral features and the light curve decline rate, [delta]m₁₅. Wavelet decomposition has been used to develop a new spectral index to measure spectral line strengths independent of the continuum and easily corrected for noise. This new method yields consistent results without the arbitrary uncertainties introduced by current methods and is particularly useful for spectra which do not have a clearly defined continuum. These techniques are applied to SN Ia spectra and correlations are found between the spectral features and light curve decline rate. The wavelet spectral indexes are used to measure the evolution of spectral features which are characterized by 3 or 4 parameters for the most complicated evolution. The three absorption features studied here are associated with sulfur and silicon and all show a transition in strength between 1 to 2 weeks after B-band maximum. Pearson correlation coefficients between spectral features and [delta]m₁₅ are found to be significant within a week of maximum brightness and 3 to 4 weeks post-maximum. These correlations are used to determine the principal components at each epoch among the set of SN spectra in this work. The variation contained in the first principal component (PC1) is found to be greater than 60% to 70% for most epochs and reaching as high as 80% to 90% for epochs with the highest correlations. The same first principal component can be used to relate spectral feature strengths to the decline rate. These relations were used to estimate a SN light curve decline rate from a set of spectra taken over the course of the explosion, from a single spectrum, or from even a single spectral feature. These relationships could be used for future surveys to estimate spectral characteristics from light curve data, such as photometric redshift.

<p>The propagation of light beams originating from synthetic ‘Type Ia’ supernovae, through an inhomogeneous universe with simplified dynamics, is simulated using a Monte-Carlo Ray-Tracing method. The accumulated statistical (redshift-magnitude) distribution for these synthetic supernovae observations, which is illustrated in the form of a Hubble diagram, produces a luminosity profile similar to the form predicted for a Dark-Energy dominated universe. Further, the amount of mimicked Dark-Energy is found to increase along with the variance in the matter distribution in the universe, converging at a value of Ω_X ≈ 0.7.</p><p>It can be thus postulated that at least under the assumption of simplified dynamics, it is possible to replicate the observed supernovae data in a universe with inhomogeneous matter distribution. This also implies that it is demonstrably not possible to make a direct correspondence between the observed luminosity and redshift with the distance of a cosmological source and the expansion rate of the universe, respectively, at a particular epoch in an inhomogeneous universe. Such a correspondences feigns an apparent variation in dynamics, which creates the illusion of Dark-Energy.</p>

The propagation of light beams originating from synthetic ‘Type Ia’ supernovae, through an inhomogeneous universe with simplified dynamics, is simulated using a Monte-Carlo Ray-Tracing method. The accumulated statistical (redshift-magnitude) distribution for these synthetic supernovae observations, which is illustrated in the form of a Hubble diagram, produces a luminosity profile similar to the form predicted for a Dark-Energy dominated universe. Further, the amount of mimicked Dark-Energy is found to increase along with the variance in the matter distribution in the universe, converging at a value of ΩX ≈ 0.7. It can be thus postulated that at least under the assumption of simplified dynamics, it is possible to replicate the observed supernovae data in a universe with inhomogeneous matter distribution. This also implies that it is demonstrably not possible to make a direct correspondence between the observed luminosity and redshift with the distance of a cosmological source and the expansion rate of the universe, respectively, at a particular epoch in an inhomogeneous universe. Such a correspondences feigns an apparent variation in dynamics, which creates the illusion of Dark-Energy.

À la fin des années 90, deux équipes indépendantes ont montré l’expansion accélérée de notre Univers, à partir des mesures de distances de supernovas de type Ia (SNIa). Depuis, une des priorités de la cosmologie moderne est de caractériser ce phénomène et d’en comprendre ses fondements. L’amélioration des mesures de distance réalisées à partir des SNIa est une technique majeure permettant de mieux caractériser l’accélération et donc de déterminer la nature physique de ce phénomène. Ce document développe un nouveau modèle de distribution spectrale en énergie de SNIa nommé le Supernova Useful Generator And Reconstructor (SUGAR) permettant d’améliorer les mesures des distances. Ce modèle est construit à partir des propriétés spectrales des SNIa et des données spectrophotométriques de la collaboration The Nearby Supernova Factory. L’avancée principale, proposée dans SUGAR, réside dans l’ajout de deux paramètres supplémentaires pour caractériser la variabilité des SNIa. Le premier dépend des propriétés des vitesses des éjectas des SNIa, le deuxième dépend de leurs raies du calcium. L’ajout de ces paramètres, ainsi que la grande qualité des données de la collaboration the Nearby Supernova Factory font de SUGAR le meilleur modèle qui existe pour décrire la distribution spectrale en énergie des SNIa et améliore les mesures des distances de l’ordre de 15% par rapport à la méthode usuelle. Les performances de ce modèle en font un excellent candidat pour préparer les expériences futures comme LSST ou WFIRST. Par ailleurs, ce document présente une analyse sur l’effet de l’appartenance d’une SNIa à un amas de galaxies sur sa mesure de distance. Les galaxies d’un amas possèdent une vitesse propre largement supérieure à la valeur supposée lors de la mesure des distances avec les SNIa. Ceci a pour conséquence d’introduire une source d’erreur systématique sur la mesure de distance. Le fait de ne pas prendre en compte cet effet peut dégrader la mesure de distance de l’ordre de 2,5% pour les SNIa appartenant à un amas. Cette analyse à été réalisée en utilisant les données de la collaboration the Nearby Supernova Factory et des catalogues public d’amas de galaxies. / At the end of the 90s, two independent teams showed, based on distance measurements of type Ia supernovæ (SNIa), that expansion of our Universe is accelerating. Since then, one of the priorities of modern cosmology is to characterize this phenomenon and to understand its nature. The improvement of distance measurements of SNIa is one technique to improve the constraints on acceleration and to determine the physical nature of it. This document develops a new SNIa spectral energy distribution model, called the Supernova Useful Generator and Reconstructor (SUGAR), which improves distance measurement. This model is constructed from SNIa spectral properties and spectrophotometric data from The Nearby Supernova Factory collaboration. The main advancement proposed in SUGAR is the addition of two additional parameters to characterize the SNIa variability. The first depends on the properties of SNIa ejecta velocity, the second depends on their calcium lines. The addition of these parameters as well as the high quality of the data of The Nearby Supernova Factory collaboration make SUGAR the best model available to describe the spectral energy distribution of SNIa and improves distances measurements of the order of 15 % relative to the usual method. The performance of this model makes it an excellent candidate for preparing future experiments like LSST or WFIRST. In addition, this document presents an analysis of the effect of SNIa belonging to a galaxy cluster on its distance measurement. Galaxies of a cluster have a peculiar velocity much higher than the assumed value when measuring distances with SNIa. This has the effect of introducing a systematic error into the distance measurement. Failure to take into account this effect may degrade the distance measurement by 2.5% for SNIa belonging to a cluster. This analysis was carried out using data from the collaboration of the Nearby Supernova Factory and public catalogs of galaxy cluster.

A white dwarf is most likely the end stage of a low mass star like our Sun, which results when the parent star consumes all the hydrogen in its core, thus bringing fusion to a halt. It is a dense and compact object, where the inward gravitational pull is balanced by the outward pressure arising due to the motion of its constituent degenerate electrons. The theory of non-magnetized and non-rotating white dwarfs was formulated extensively by S. Chandrasekhar in the 1930s, who also proposed a maximum possible mass for this objects, known as the Chandrasekhar limit (Chandrasekhar 1935)1. White dwarfs are believed to be the progenitors of extremely bright explosions called type Ia supernovae (SNeIa). SNeIa are extremely important and popular astronomical events, which are hypothesized to be triggered in white dwarfs having mass close to the famous Chandrasekhar limit ∼ 1.44M⊙. The characteristic nature of the variation of luminosity with time of SNeIa is believed to be powered by the decay of 56Ni to 56Co and, finally, to 56Fe. This feature, along with the consistent mass of the exploding white dwarf, is deeply linked with their utilization as “standard candles” for cosmic distance measurement. In fact, SNeIa measurements were instrumental in establishing the accelerated nature of the current expansion of the universe (Perlmutter et al. 1999). However, several recently observed peculiar SNeIa do not conform to this traditional explanation. Some of these SNeIa are highly over-luminous, e.g. SN 2003fg, SN 2006gz, SN 2007if, SN 2009dc (Howell et al. 2006; Scalzo et al. 2010), and some others are highly under-luminous, e.g. SN 1991bg, SN 1997cn, SN 1998de, SN 1999by, SN 2005bl (Filippenko et al. 1992; Taubenberger et al. 2008). The luminosity of the former group of SNeIa implies a huge Ni-mass (often itself super-Chandrasekhar), invoking highly super-Chandrasekhar white dwarfs, having mass 2.1 − 2.8M⊙, as their most plausible progenitors (Howell et al. 2006; Scalzo et al. 2010). On the other hand, the latter group produces as low as ∼ 0.1M⊙ of Ni (Stritzinger et al. 2006), which rather seem to favor sub-Chandrasekhar explosion scenarios. In this thesis, as the title suggests, we have endeavored to establish the existence of exotic, super- and sub-Chandrasekhar limiting mass white dwarfs, in order to explain the aforementioned peculiar SNeIa. This is an extremely important puzzle to solve in order to comprehensively understand the phenomena of SNeIa, which in turn is essential for the correct interpretation of the evolutionary history of the universe. Effects of magnetic field: White dwarfs have been observed to be magnetized, having surface fields as high as 105 − 109 G (Vanlandingham et al. 2005). The interior field of a white dwarf cannot be probed directly but it is quite likely that it is several orders of magnitude higher than the surface field. The theory of weakly magnetized white dwarfs has been investigated by a few authors, however, their properties do not starkly contrast with that of the non-magnetized cases (Ostriker & Hartwick 1968). In our venture to find a fundamental basis behind the formation of super-Chandrasekhar white dwarfs, we have explored in this thesis the impact of stronger magnetic fields on the properties of white dwarfs, which has so far been overlooked. We have progressed from a simplistic to a more rigorous, self-consistent model, by adding complexities step by step, as follows: • spherically symmetric Newtonian model with constant (central) magnetic field • spherically symmetric general relativistic model with varying magnetic field • model with self-consistent departure from spherical symmetry by general relativis-tic magnetohydrodynamic (GRMHD) numerical modeling. We have started by exploiting the quantum mechanical effect of Landau quanti-zation due to a maximum allowed equipartition central field greater than a critical value Bc = 4.414 × 1013 G. To begin with, we have carried out the calculations in a Newtonian framework assuming spherically symmetric white dwarfs. The primary ef-fect of Landau quantization is to stiffen the equation of state (EoS) of the underlying electron degenerate matter in the high density regime, and, hence, yield significantly super-Chandrasekhar white dwarfs having mass much & 2M⊙ (Das & Mukhopadhyay 2012a,b). Consequently, we have proposed a new mass limit for magnetized white dwarfs which may establish the aforementioned peculiar, over-luminous SNeIa as new standard candles (Das & Mukhopadhyay 2013a,b). We have furthermore predicted possible evo-lutionary scenarios by which super-Chandrasekhar white dwarfs could form by accretion on to a commonly observed magnetized white dwarf, by invoking the phenomenon of flux freezing, subsequently ending in over-luminous, super-Chandrasekhar SNeIa (Das et al. 2013). Before moving on to a more complex model, we have justified the assumptions in our simplistic model, in the light of various related physics issues (Das & Mukhopad-hyay 2014b), and have also clarified, and, hence, removed some serious misconceptions regarding our work (Das & Mukhopadhyay 2015c). Next, we have considered a more self-consistent general relativistic framework. We have obtained stable solutions of magnetostatic equilibrium models for white dwarfs pertaining to various magnetic field profiles, however, still in spherical symmetry. We have showed that in this framework, a maximum stable mass as high as ∼ 3.3M⊙ can be realized (Das & Mukhopadhyay 2014a). However, it is likely that the anisotropic effect due to a strong magnetic field may cause a deformation in the spherical structure of the white dwarfs. Hence, in order to most self-consistently take into account this departure from spherical symmetry, we have constructed equilibrium models of strongly magnetized, static, white dwarfs in a general relativistic framework, first time in the literature to the best of our knowledge. In order to achieve this, we have modified the GRMHD code XNS (Pili et al. 2014), to apply it in the context of white dwarfs. Interestingly, we have found that signifi-cantly super-Chandrasekhar white dwarfs, in the range ∼ 1.7 − 3.4M⊙, are obtained for many possible field configurations, namely, poloidal, toroidal and mixed (Das & Mukhopadhyay 2015a). Furthermore, due to the inclusion of deformation caused by a strong magnetic field, super-Chandrasekhar white dwarfs are obtained for relatively lower central magnetic field strengths (∼ 1014 G) compared to that in the simplistic model — as correctly speculated in our first work of this series (Das & Mukhopadhyay 2012a). We have also found that although the characteristic deformation induced by a purely toroidal field is prolate, the overall shape remains quasi-spherical — justifying our earlier spherically symmetric assumption while constructing at least some models of strongly magnetized white dwarfs (Das & Mukhopadhyay 2014a). Indeed more accurate and extensive numerical analysis seems to have validated our analytical findings. Thus, very interestingly, our investigation has established that magnetized white dwarfs can indeed have mass that significantly exceeds the Chandrasekhar limit, irre-spective of the origin of the underlying magnetic effect — a discovery which is not only of theoretical importance, but also has a direct astrophysical implication in explaining the progenitors of the peculiar, over-luminous, super-Chandrasekhar SNeIa. Effects of modified Einstein’s gravity: A large array of models has been required to explain the peculiar, over- and under- luminous SNeIa. However, it is unlikely that nature would seek mutually antagonistic scenarios to exhibit sub-classes of apparently the same phenomena, i.e., triggering of thermonuclear explosions in white dwarfs. Hence, driven by the aim to establish a unification theory of SNeIa, we have invoked in the last part of this thesis a modification to Einstein’s theory of general relativity in white dwarfs. The validity of general relativity has been tested mainly in the weak field regime, for example, through laboratory experiments and solar system tests. However, the question remains, whether general relativity requires modification in the strong gravity regime, such as, the expanding universe, the region close to a black hole and neutron star. For instance, there is evidence from observational cosmology that the universe has undergone two epochs of cosmic acceleration, the theory behind which is not yet well understood. The period of acceleration in the early universe is known as inflation, while the current accelerated expansion is often explained by invoking a mysterious dark energy. An alternative approach to explain the mysteries of inflation and dark energy is to modify the underlying gravitational theory itself, as it conveniently avoids involving any exotic form of matter. Several modified gravity theories have been proposed which are extensions of Einstein’s theory of general relativity. A popular class of such theories is known as f (R) gravity (e.g. see de Felice & Tsujikawa 2010), where the Lagrangian density f of the gravitational field is an arbitrary function of the Ricci scalar R. In the context of astrophysical compact objects, so far, modified gravity theories have been applied only to neutron stars, which are much more compact than white dwarfs, in order to test the validity of such theories in the strong field regime (e.g. Cooney et al. 2010; Arapoˇglu et al. 2011). Moreover, a general relativistic correction itself does not seem to modify the properties of a white dwarf appreciably when compared to Newtonian calculations. Our venture of exploring modified gravity in white dwarfs in this thesis, is a first in the literature to the best of our knowledge. We have exploited the advantage that white dwarfs have over neutron stars, i.e., their EoS is well established. Hence, any change in the properties of white dwarfs can be solely attributed to the modification of the underlying gravity, unlike in neutron stars, where similar effects could be produced by invoking a different EoS. We have explored a popular, yet simple, model of f (R) gravity, known as the Starobinsky model (Starobinsky 1980) or R−squared model, which was originally pro-posed to explain inflation. Based on this model, we have first shown that modified gravity reproduces those results which are already explained in the paradigm of general relativity (and Newtonian framework), namely, low density white dwarfs in this context. This is a very important test of the modified gravity model and is furthermore necessary to constrain the underlying model parameter. Next, depending on the magnitude and sign of a single model parameter, we have not only obtained both highly super-Chandrasekhar and highly sub-Chandrasekhar limiting mass white dwarfs, but we have also established them as progenitors of the peculiar, over- and under-luminous SNeIa, respectively (Das & Mukhopadhyay 2015b). Thus, an effectively single underlying the-ory unifies the two apparently disjoint sub-classes of SNeIa, which have so far hugely puzzled astronomers. To summarize, in the first part of the thesis, we have established the enormous significance of magnetic fields in white dwarfs in revealing the existence of significantly super-Chandrasekhar white dwarfs. These super-Chandrasekhar white dwarfs could be ideal progenitors of the peculiar, over-luminous SNeIa, which can, hence, be used as new standard candles of cosmic distance measurements. In the latter part of the thesis, we have established the importance of a modified theory of Einstein’s gravity in revealing both highly super- and highly sub-Chandrasekhar limiting mass white dwarfs. We have furthermore demonstrated how such a theory can serve as a missing link between the peculiar, super- and sub-Chandrasekhar SNeIa. Thus, the significance of the current thesis lies in the fact that it not only questions the uniqueness of the Chandrasekhar mass-limit for white dwarfs, but it also argues for the need of a modified theory of Einstein’s gravity to explain astrophysical observations.