percentage consists of baryonic **matter** [2]. Evidences for the existence of an unseen ‘**dark**’ component in the energy density of the universe comes from several independent observations at different length scales, rotations of peripheral stars in the galaxies, cosmic microwave background anisotropies universe large scale structure, gravitational field in cluster of galaxies etc. The baryonic content is well known, both from element abundances produced in primordial nucleosynthesis roughly 100 seconds after the Big Bang **and** the measurement of anisotropies in the CMB. The evidence for the existence of **Dark** **Matter** is overwhelming **and** comes from a wide variety of astrophysical measurements.

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The fixed points I.a, I.d, **and** I.e are the same points that were found for teleparallel **dark** energy in Refs. [22–24]. The scaling solutions I.b **and** I.c are new solutions that are not present in teleparallel **dark** energy. Such as in tele- parallel **dark** energy, in tachyonic teleparallel **dark** energy the Universe is attracted for the **dark**-energy-dominated de Sitter solution I.d or I.e. However, unlike the former sce- nario, in tachyonic teleparallel **dark** energy the Universe may present a phase MDE, that is, the scaling solution I.b or I.c, in which it has some portions of the energy density of in the **matter** dominated era. This type of phase MDE is also common in coupled **dark** energy in GR (see Refs. [7,9,10]). But since the scaling solutions I.b **and** I.c both require 1=2u 2

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In modern **cosmological** theories, a dynamic **cosmological** term Λ(t) remains a focal point of interest as it solves the cos- mological **constant** problem in a natural way. There are sig- nificant observational evidence for the detection of Einstein’s **cosmological** **constant**, Λ or a component of material content of the universe that varies slowly with time **and** space to act like Λ. A wide range of observations now compellingly sug- gest that the universe possesses a non-zero **cosmological** term [41]. In the context of quantum field theory, a **cosmological** term corresponds to the energy density of vacuum. The birth of the universe has been attributed to an excited vacuum fluc- tuation triggering off an inflationary expansion followed by the super-cooling. The release of locked up vacuum energy re- sults in subsequent reheating. The **cosmological** term, which is measure of the energy of empty space, provides a repulsive force opposing the gravitational pull between the galaxies. If the **cosmological** term exists, the energy it represents counts as mass because mass **and** energy are equivalent. If the cos- mological term is large enough, its energy plus the **matter** in the universe could lead to inflation. Unlike standard inflation, a universe with a **cosmological** term would expand faster with time because of the push from the **cosmological** term [42]. Some of the recent discussions on the **cosmological** **constant** “problem” **and** on cosmology with a time-varying cosmologi- cal **constant** by Ratra **and** Peebles [43], Dolgov [44] **and** Sahni **and** Starobinsky [45] point out that in the absence of any in- teraction with **matter** or radiation, the **cosmological** **constant** remains a “**constant**”. However, in the presence of interac- tions with **matter** or radiation, a solution of Einstein equations **and** the assumed equation of covariant conservation of stress- energy with a time-varying Λ can be found. This entails that energy has to be conserved by a decrease in the energy den- sity of the vacuum component followed by a corresponding increase in the energy density of **matter** or radiation (see also Weinberg [46], Carroll, Press **and** Turner [47], Peebles [48], Padmanabhan [49] **and** Pradhan et al. [50] ).

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In this work, we have developed an unification model where we describe, using the same field, an inflationary evolution **and** the **dark** **matter** content of the Universe, due to an incom- plete decay of the inflaton. At the same time, this incomplete decay introduces right-handed neutrinos that allow the generation of light neutrino masses **and** also the generation of the observed baryon asymmetry in the Universe through a thermal Leptogenesis evolution. We started with a review of the introductory topics for this thesis. First, we gave a descrip- tion of the basic features of neutrino physics including the seesaw mechanism, a description of neutrino mass **and** mixing matrices **and** neutrino oscillations. Moving to cosmology, we introduced the Standard **Cosmological** paradigm **and** then the inflationary evolution. In the latter, after describing the basic dynamics, we have detailed how the experimental observ- ables can be related to the metric **and** **matter** fluctuations **and** to the slow-roll parameters. We then discussed **Dark** **Matter** basic notions **and** reproduced the standard WIMP’s abundance calculation. Finally, we discussed the three Sakharov Conditions [2] to then introduce some models of Baryogenesis.

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In the second chapter, we have studied the relic abundance calculation when one assumes thermal equilibrium at the early Universe. We have spent most of the time working on the understanding of the methods involved in this calculation **and** on how to implemment them inside numerical calculations. The following subjects have been studied or reviewed: Basics of GR, Λ-CDM **Cosmological** Model, Thermodynamics of the Early Universe, arriving in the end at the Boltzmann equation (its properties have been analyzed carefully) **and** how it generates the current relic abundance for a generic particle. In the following chapter, an introduction to direct **and** indirect detection experiments was provided, where different techniques were exposed **and** discussed. Also, the necessary theoretical background on direct detection was provided because the final chapter would have to deal with the limits coming from these experiments **and** comparison to theory becomes necessary.

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However, notwithstanding this success, theories of gravity going beyond General Relativity have been receiving increased attention for a variety of reasons, among which the search for an alternative explanation to the observed late-time accelerated expansion of the Universe stands out [4,5]. The standard—**and** simplest—explanation for this accelerated expansion, provided by the concordance (ΛCDM) model, resorts to a **cosmological** **constant**, but it turns out that the theoretical value of this **constant**, resulting from quantum field theory calculations, is overwhelmingly different from the one required by observations. This is the well known **cosmological**-**constant** problem [6,7], which, hopefully, could be avoided within the framework of a modified theory of gravity.

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This model was implemented in a hybrid inflation con- text by Masso´ **and** Zsembinszki [10]. A model similar to ours, in which the modulus field is responsible for inflation **and** the phase ’ produces **dark** **matter**, was studied in Ref. [11]. In models in which the axionlike field is the **dark** **matter**, a high energy scale for the axion decay **constant** f is also necessary, in order to suppress isocurva- ture fluctuations to acceptable levels. In our case, however, the axion field only becomes dynamical at such late times that the bounds from isocurvature fluctuations do not apply [12].

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It was investigated in subsection 4.1 whether a composition of specific IR **and** UV effects could alter a big rip singularity setting (cf. Ref. [42]). More concretely, it was employed a simple model: A DGP brane model, with phantom **matter** on the brane **and** a GB term in the bulk action. The DGP brane configuration has relevant IR effects, whereas the GB component is important at high energies; phantom **matter** (with a **constant** equation of state) in a standard FLRW model is known to induce the emergence of a big rip singularity [9]. This analysis indicates that the big rip can be replaced by a smoother singularity, named a sudden future singularity [13], through some intertwining between late time dynamics **and** high energy effects. Subsequently, it was determined values of the redshift **and** the future cosmic time, where the brane would reach the sudden singularity. These results can be contrasted with those for the big rip occurrence in a FLRW setting (e.g., see Ref. [11]). Notice that, these conclusions are based on a rather particular result, that was extracted from a specific model. Subsequent research work would assist in clarifying some remaining issues. For example, further studies of how other singularities can be appeased or removed by means of the herein combined IR **and** UV effects have been done in Ref. [215]. On the other hand, it might be interesting to consider a modified Einstein-Hilbert action on the brane, which in addition could alleviate the ghost problem present on the self-accelerating DGP model by self-accelerating the normal DGP branch [216], **and** see if some of the **dark** energy singularities can be removed or at least appeased in this setup.

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This short review focused on some alternative candi- dates to **dark** energy. This ubiquitous component plus the **dark** **matter** are responsible for nearly 95% of the **matter**- energy content filling the Universe. However, different from **dark** **matter**, the extra **dark** (energy) component is intrinsi- cally relativistic **and** its negative pressure is required by the present accelerating stage of the Universe. Its tiny density **and** weak interaction presumably preclude the possibility of identification in the terrestrial laboratory. Unfortunately, even considering that we are in the golden age of empirical cosmology, the existing data are still unable to discriminate among the different **dark** energy candidates, thereby signal- ing that we need better observations in order to test the basic predictions. In particular, this means that the determination of **cosmological** parameters will continue to be a central goal in the near future. The fundamental aim is to shed some light on the nature of the **dark** energy.

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Following each measurement, an initial data set was formed by passing the data files through the pulse validation routine which tagged signal events if their amplitude exceeded the noise level of the detector by 2 mV. All signals with less than five pulse spikes above threshold were rejected, since they do not form a pulse **and** are electromagnetic noise. The signal waveform, decay time **constant** **and** spectral density structure of the remaining single events were next inspected individually. As said before, a particle-induced nucleation event possesses a characteristic frequency response, with a time span of a few milliseconds, a decay **constant** of 5-40 ms, **and** a primary harmonic between 0.45-0.75 kHz; this response has been shown to differ significantly from gel-associated acoustic **and** local acoustic backgrounds.

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Abstract: In the light of the energy crisis **and** the stringent environmental regulations, diesel engines are offering good hope for automotive vehicles. However, lot of work is needed to reduce the diesel exhaust emissions **and** give the way for full utilization of the diesel fuel’s excellent characteristics. This paper presents a theoretical study on the effect of **variable** stroke length technique on the emissions of a four-stroke, water-cooled direct injections diesel engine with the help of experimentally verified computer software designed mainly for diesel engines. The emission levels were studied over the speed range (1000 rpm to 3000 rpm) **and** stroke lengths (120 mm to 200 rpm) **and** were compared with those of the original engine design. The simulation results clearly indicate the advantages **and** utility of **variable** stroke technique in the reduction of the exhaust emission levels. A reduction of about 10% to 75% was achieved for specific particulate **matter** over the entire speed range **and** bore-to-stroke ratio studied. Further, a reduction of about 10% to 59% was achieved for the same range. As for carbon dioxide, a reduction of 0% to 37% was achieved. On the other hand, a less percent change was achieved for the case of nitrogen dioxide **and** nitrogen oxides as indicated by the results. This study clearly shows the advantage of VSE over fixed stroke engines. This study showed that the **variable** stroke technique proved a good way to curb the diesel exhaust emissions **and** hence helped making these engines more environmentally friendly.

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It is very common to find numerical studies of **dark** energy **and** **dark** **matter**. Among these, one can find the interesting proposal of unifying **dark** **matter** **and** **dark** energy with the use of a single component with an ‘exotic’ equation of state. However, there is a certain shortage of analyses involving exact analytic models following this proposal. Therefore, here are presented examples of simple exact **cosmological** models which can reproduce some of the desired properties of an unified **dark** **matter**/energy fluid.

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Jee et al. [1] claim that the analysis of gravitational lens- ing data from the HST observations of the galaxy cluster CL 0024+17 demonstrates the existence of a “**dark** **matter** ring”. While the lensing is clearly evident, as an observable phe- nomenon, it does not follow that this must be caused by some undetected form of **matter**, namely the putative “**dark** **matter**”. Here we show that the lensing can be given an alternative ex- planation that does not involve “**dark** **matter**”. This explana- tion comes from the new dynamics of 3-space [2, 3, 4, 5, 6]. This dynamics involves two **constant** G **and** — the fine structure **constant**. This dynamics has explained the bore hole anomaly, spiral galaxy flat rotation speeds, the masses of black holes in spherical galaxies, gravitational light bend- ing **and** lensing, all without invoking “**dark** **matter**”. The 3- space dynamics also has a Hubble expanding 3-space solution that explains the supernova redshift data without the need for “**dark** energy” [8]. The issue is that the Newtonian theory of gravity [9], which was based upon observations of planetary motion in the solar system, missed a key dynamical effect that is not manifest in this system. The consequences of this fail- ure has been the invoking of the fix-ups of “**dark** **matter**” **and** “**dark** energy”. What is missing is the 3-space self-interaction effect. Experimental **and** observational data has shown that the coupling **constant** for this self-interaction is the fine struc- ture **constant**, 1/137, to within measurement errors. It is shown here that this 3-space self-interaction effect gives a direct explanation for the reported ring-like gravitational lens- ing effect.

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No entanto, um dos maiores desafios tanto para a RG como para o Modelo Padr˜ ao da F´ısica de Part´ıculas viria a surgir em 1998, quando dados provenientes do estudo de supernovas de tipo Ia mostraram que o Universo est´ a a expandir de forma acelerada. O problema reside no facto de nenhum tipo de mat´ eria ou energia conhecida ou detetada at´ e ao momento ser capaz de explicar esta acelera¸ c˜ ao. Dentro do formalismo da RG, a explica¸ c˜ ao mais simples para o fen´ omeno em quest˜ ao passa pela introdu¸ c˜ ao da constante cosmol´ ogica, Λ, para descrever uma componente de mat´ eria/energia caracterizada por uma press˜ ao negativa constante. Sabe-se ainda que esta componente de natureza desconhecida, genericamente considerada como uma forma de Energia Escura (EE), precisa de ser a mais abundante no Universo de modo a ajustar os dados observacionais. Adicionalmente, uma grande quantidade e variedade de observa¸ c˜ oes apoia ainda a existˆ encia de um tipo de mat´ eria que aparenta n˜ ao absorver nem emitir radia¸ c˜ ao eletromagn´ etica. Esta componente, consequentemente designada de Mat´ eria Escura (ME), ´ e ainda restringida observacionalmente a ser n˜ ao relativista e de natureza n˜ ao bari´ onica. Part´ıculas de ME que se movem lentamente em compara¸ c˜ ao com a luz s˜ ao designadas por Mat´ eria Escura Fria (Cold **Dark** **Matter** - CDM).

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MOND based on the theoretical modification of the Newtonian theory, is expected to provide successful fits for observed galaxies without DM. One of the biggest successes of MOND is no doubt its ability to fit spiral galaxies without DM (for a review, see e.g. Sanders **and** McGaugh 2002). However, when ETGs are modeled using MOND, the results are mixed **and** the existence of additional, **dark**, component cannot be excluded in numerous cases (see below, for more details). Also, it is well known that MOND has problems at the scales of clusters of galaxies (see, e.g. Sanders 2003) where additional **dark** mass ap- pears to be necessary. The well-known case of the Bullet Cluster (1E 0657-558) which consists of two colliding clusters of galaxies, was considered as the best example in favor of DM (Bradaˇc et al. 2006). Recently, MOND was also used in various numeri- cal simulations: see, e.g. the work of Angus et al. (2014) where the **cosmological** particle-mesh N-body code was used to investigate the feasibility of struc- ture formation in a framework involving MOND **and** light sterile neutrinos, which means that an addi- tional, hypothetical **dark** particle is needed. It is worth noting that an another interesting line of in- vestigation of MOND is that based on the study of shell galaxies **and** promising results have been ob- tained (B´ılek et al. 2015) which may lead to further tests of the DM/MOND dichotomy in the future. Therefore, as will be shown below, since the number of early-type galaxies studied using MOND is still small, it is important to study as many interesting objects as possible, **and** NGC 5128 being the nearest large elliptical galaxy is certainly worth investigat- ing.

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However, a direct comparison of our result for 0 DM with the CMB results is not possible, since the latter has been obtained in the context of uncoupled models. It is therefore important to see whether there are upper limits to 0 DM which are independent of the **cosmological** model. An upper limit to 0 DM which does not depend on the back- ground cosmology can be obtained from the galaxy cluster dynamics. However the current data yield very weak con- straints: Ref. [35] gives 0 m 0:30 0:17 0:07 so that even

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We discuss the dynamics of a spherically symmetric **dark** radiation vaccum in the Randall-Sundrum brane world scenario. Under certain natural assump- tions we show that the Einstein equations on the brane form a closed system. For a de Sitter brane we determine exact dynamical **and** inhomogeneous solu- tions which depend on the brane **cosmological** **constant**, on the **dark** radiation tidal charge **and** on its initial configuration. We define the conditions leading to singular or globally regular solutions. We also analyse the localization of gravity near the brane **and** show that a phase transition to a regime where gravity propagates away from the brane may occur at short distances during the collapse of positive **dark** energy density.

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We investigate the dynamics of a spherically symmetric vaccum on a Randall **and** Sundrum 3-brane world. Under certain natural conditions, the effective Einstein equations on the brane form a closed system for spherically symmetric **dark** radiation. We determine exact dynamical **and** inhomogeneous solutions, which are shown to depend on the brane **cosmological** **constant**, on the **dark** radiation tidal charge **and** on its initial energy configuration. We identify the conditions defining these solutions as singular or as globally regular. Finally, we discuss the confinement of gravity to the vicinity of the brane **and** show that a phase transition to a regime where gravity is not bound to the brane may occur at short distances during the collapse of positive **dark** energy density on a realistic de Sitter brane.

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Assuming spherical symmetry we analyse the dynamics of an inhomoge- neous **dark** radiation vaccum on a Randall **and** Sundrum 3-brane world. Under certain natural conditions we show that the effective Einstein equations on the brane form a closed system. On a de Sitter brane **and** for negative **dark** energy density we determine exact dynamical **and** inhomogeneous solutions which de- pend on the brane **cosmological** **constant**, on the **dark** radiation tidal charge **and** on its initial configuration. We also identify the conditions leading to the formation of a singularity or of regular bounces inside the **dark** radiation vaccum.

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Highly purified water is a bad electrical conductor. However, the addition of small amounts of sodium chloride (NaCl) to this liquid, can increase its electrical conductivity in a sub- stantial way. At the ambient temperature (295K), the wa- ter’s dielectric **constant** of 80, permits the Na+ **and** Cl- ions to move freely through the liquid **and** this feature can ac- count for the change in its conductive behavior. It seems that the concentration of free charge carriers has the most relevant role in determining the electrical conductivity of the substances. But what to say about electrical conductivity in metals? Isolated metallic atoms have their inner electrons belonging to closed shells **and** hence tightly bound to their corresponding atomic nucleus. However the electrons of the outer most shell are weakly bonded to its respective nucleus. When arranged in a crystal lattice structure, the bond weak- ness of these outer electrons is enhanced due to the interac- tions among neighbor atoms of the lattice, so that the elec- trons of conduction are free to travel through the whole crys- tal. Resistance to their motion is due to the thermal vibrations (phonons) **and** defects provoked by the presence of impurities **and** lattice dislocations. In a perfect crystal at zero absolute temperature, these free electrons can be described by using the quantum mechanical formalism of the Bloch waves [1,2]. The concentration of free electrons plays an important role in the description of the electrical conductivity in metals.

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