Cosmological Constant

It is likely that the holographic principle will be a consequence of the would be theory of quantum gravity. Thus, it is interesting to try to go in the opposite direction: can the holographic principle fix the gravitational interaction? It is shown that the classical gravitational interaction is well inside the set of potentials allowed by the holographic principle. Computations clarify which role such a principle could have in lowering the value of the cosmological constant computed in QFT to the observed one.

In this work we study a Newtonian cosmological model in the context of a Noncommutative space. We show that the trajectories of test particles undergo modifications by considering a simplectic structure with a noncommutative parameter, \Theta, in the coordinates. In the case of a positive cosmological constant, we obtain trajectories which develop spirals and we also find a correction to the Hubble constant. We finally show that in the strong \Theta limit, there is a relation with a Godel-type metric.

We present an exact solution of Einstein's field equations in toroidal coordinates. The solution has three regions: an interior with a string equation of state; an Israel boundary layer; and an exterior with constant isotropic pressure and constant density, locally isometric to anti-de Sitter space-time. The exterior can be a cosmological vacuum with negative cosmological constant. The size and mass of the toroidal loop depend on the size of Lambda.

I proposed a new expansion force to explain the flat rotation curves of plane galaxies, in a Newtonian approach in 2016. This force is validated here in General Relativity for an inhomogeneous radially symmetrical universe. It can be deduced from the solution of Einstein's equation with a cosmological constant. A pseudo-Schwarzschild "twin-potential" metric is considered, with two different potentials for the space and time dimensions. The expansion force results as a repulsive dual gravity. Negative masses are needed. The necessary mass repartitions are computed, in connection with the radial dynamics and the expansion rate's evolution. A linear model and a quadratic model are studied, connected with the observation representations of a universe in accelerated expansion. It is a first step towards a better representation of an inhomogeneous universe. The framework can be applied to deduce the universe mass repartition form the measured values of the expansion rate variation. Résumé J'ai proposé en 2016 une nouvelle force d'expansion pour expliquer les courbes de rotation plates des galaxies spirales dans une approche Newtonienne. Cette force est validée ici dans le cadre de la Relativité Générale pour un univers inhomogène à symétrie radiale. On peut la déduire comme solution de l'équation d'Einstein avec Constante Cosmologique. On considère une métrique à « potentiels jumelés », avec deux potentiels différents pour les dimensions spatiales et temporelles. Il en résulte une force d'expansion agissant comme une gravité duale répulsive. Il faut des masses négatives. On calcule les répartitions de masses nécessaires, en liaison avec la dynamique radiale et l'évolution du taux d'expansion. On étudie un modèle linéaire et un modèle quadratique, en lien avec les représentations d'un univers observé en expansion accélérée. Il s'agit là d'une première étape vers une meilleure représentation d'un univers inhomogène. Ce cadre peut être appliqué pour déduire la répartition de masses de l'univers à partir des valeurs mesurées du taux d'expansion.

It will be argued here that the cosmological constant problem exists because of the way the vacuum is defined in quantum field theory. It has been known for some time that for QFT to be gauge invariant certain terms--such as part of the vacuum polarization tensor--must be eliminated either explicitly or by some form of regularization followed by renormalization. It has recently been shown that lack of gauge invariance is a result of the way the vacuum is defined, and redefining the vacuum so that the theory is gauge invariant may also offer a solution to the cosmological constant problem.

We derive quantization relations in the case when torsion effects are added in a De Sitter spacetime metric with or without a black hole at the Planck mass and Planck length limit. To this end we use Zeldovich's definition of the cosmological constant.

In this paper (part II), we analyze some Measure Theory equations and Ramanujan formulas with the developments of the MRB Constant. We obtain new possible mathematical connections with some Cosmological parameters and sectors of String Theory.

The following assumptions of the Big Bang theory are challenged and found to be false: the cosmological principle, the assumption that all matter formed at the same time and the assumption regarding the cause of the cosmic microwave background radiation (CMBR).

The evolution of the universe is described based on the conclusion that the universe is finite with a space boundary. The CMBR is coming from a source located within the event horizon of the universe. There is sufficient mass in the universe to create an event horizon at the Schwarzschild radius.

Galaxies form over time due to the energy released by the expansion of space. When a galaxy forms the matter formation is in the form of neutrons. Pairs of neutrons bond to form dark matter (dineutrons) and single neutrons decay to form protons and electrons which combine to form hydrogen.

Conservation of energy must consider total energy which is mass (+ve) plus energy (+ve) plus spacetime curvature (-ve) so that the total energy of the universe is always zero. The predominant position of galaxy formation moves over time from the centre of the universe towards the boundary so that today the majority of new galaxy formation is taking place beyond our horizon of observation at 14 billion light years.

The distribution of galaxies in a finite universe is such that there is a variation in gravitational acceleration depending on the distance from the centre of the universe. This gravitational acceleration results in the difference in the recession velocity of galaxies previously attributed to dark energy.

We present a class of simple scalar-tensor models of gravity with one scalar field (dilaton $\Phi$) and only one unknown function (cosmological potential $U(\Phi)$). These models might be considered as a stringy inspired ones with broken SUSY. They have the following basic properties: 1) Positive dilaton mass, $m_\Phi$, and positive cosmological constant $\Lambda$, define two extremely different scales. The models under consideration are consistent with the known experimental facts if $m_\Phi > 10^{-3} eV$ and $\Lambda=\Lambda^{obs}\sim 10^{-56} cm^{-2}$. 2) Einstein week equivalence principle is strictly satisfied and extended to scalar-tensor theories of gravity using a novel form of principle of "constancy of fundamental constants". 3) The dilaton plays simultaneously role of inflation field and quintessence field and yields a sequential hyper-inflation with graceful exit to asymptotic de Sitter space-time which is an attractor, and is approached as $\exp(-\sqrt{3\Lambda^{obs}} ct/2)$. The time duration of inflation is $\Delta t_{infl} \sim m_\Phi^{-1}$. 4) Ultra-high frequency ($\omega_\Phi \sim m_\Phi$) dilatonic oscillations take place in asymptotic regime. 5) No fine tuning. (The Robertson-Walker solutions of general type have the above properties.) 6) A novel adjustment mechanism for cosmological constant problem seems to be possible: the huge value of cosmological constant in the stringy frame is re-scaled to its observed value by dilaton after transition to phenomenological frame.

Over the last decade, there has been a respectable level of scientific interest regarding the concept of a ‘warp drive’. This is a hypothetical propulsion device that could theoretically circumvent the traditional limitations of special relativity which restricts spacecraft to sub-light velocities. Any breakthrough in this field would revolutionize space exploration and open the doorway to interstellar travel. This article discusses a novel approach to generating the ‘warp bubble’ necessary for such propulsion; the mathematical details of this theory are discussed in an article published in the Journal of the British Interpanetary Society [1]. The theory is based on some of the exciting predictions coming out of string theory and it is the aim of this article to introduce the warp drive idea from a non-mathematical perspective that should be accessible to a wide range of readers.

Rising to Mach, the problem of establishing the unity of the physical essence of the Universe on all space-time scales of its evolution is, apparently, one of the main problems in contemporary epistemology. The issues are primarily related to the problems of the dynamics of the Universe, namely, the need to postulate hypothetical entities - dark energy and dark matter, whose nature is unknown, but whose contribution to the energy content of the Universe is about 95%. A "severe trial for the entire fundamental theory" turned out to be a discrepancy of 120 orders of magnitude between the experimentally established value of the cosmological constant and the calculated value of the energy density of the physical vacuum. Sharp questions arise also regarding the physical essence of gravitation and the nature of its unique smallness as compared with other interactions - nuclear ones, strong and weak, as well as electromagnetic ones. Sufficiently acute problems in the perception of the Universe as a single holistic system arise also at the level of microscales. First of all, we mean here the so called low-energy nuclear reactions, which are realized in the conditions of nonequilibrium low temperature plasma. The fundamental problems of such processes are usually not widely discussed, and many physicists are very critical of the very possibility of implementing such processes. Our main hypothesis for understanding the key problems of contemporary fundamental physics, including the indicated cosmological problems as well as a new class of electron-initiated nuclear chemical processes, is to introduce the basic reference system associated with the electromagnetic component of physical vacuum - EM vacuum of the expanding Universe, with a selection of global time t, being common for all points of the expanding Universe and measured starting from the time of t = 0, which corresponds to the Big Bang.

We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language.

We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'.

We then adopt what may be labelled a finitary, evidence-based, `agnostic' perspective and argue that Brouwerian atheism is merely a restricted perspective within the finitary agnostic perspective, whilst Hilbertian theism contradicts the finitary agnostic perspective.

We then consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary, evidence-based, definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways.

We show that the two definitions correspond to two distinctly different---not necessarily evidence-based but complementary---assignments of satisfaction and truth to the compound formulas of PA over N.

We further show that the PA axioms are true over N, and that the PA rules of inference preserve truth over N, under both the complementary interpretations; and conclude some unsuspected constructive consequences of such complementarity for the foundations of mathematics, logic, philosophy, and the physical sciences.

In this thesis, we explore three phenomenological alternatives to the current paradigm of the standard inflationary big bang scenario. The three alternative themes are spin torsion (or Einstein-Cartan-Kibble-Sciama) theories, extra dimensions (braneworld cosmology) and changing global symmetry. In the spin torsion theories, we found new cosmological solutions with a cosmological constant as alternative to the standard scalar field driven inflationary

In this paper we review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating Universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

In 'The Hitchhiker's Guide to the Galaxy', by Douglas Adams, the Answer to the Ultimate Question of Life, the Universe, and Everything is found to be 42 { but
the meaning of this is left open to interpretation. We take it to mean that there are 42
fundamental questions which must be answered on the road to full enlightenment, and we attempt a first draft (or personal selection) of these ultimate questions, on topics ranging from the cosmological constant and origin of the universe to the origin of life and consciousness.

In this work we address the study of null geodesics in the background of Reissner-Nordstr\"om Anti de Sitter black holes. We compute the exact trajectories in terms of elliptic functions of Weierstrass, obtaining a detailed description of the orbits in terms of charge, mass and the cosmological constant. The trajectories of the photon are classified using the impact parameter.

According to the general theory of relativity, the current paradigm for gravitation and concordant observational data, about 95% of the Universe’s content is only perceivable through gravitational effects. Consolidating the predictions of this theory is then of primordial importance. Those predictions are structured around two dimensional constants : Newton’s and Einstein’s constants. The former, namely the universal constant, yields the universality of free fall of light and compact objects. The latter, also named cosmological constant, explains the late expansion acceleration of the Universe on cosmological scales. The main goal of this thesis is to explore the foundations of general relativity by promoting these constants as dynamical fields.

First of all, we propose a generic test seeking for possible Newton’s constant variations in the primeval plasma. The modified weight of baryons translates the equilibrium point of the acoustic oscillations. A constraint on the amplitude of such variations is extracted from the anisotropies of the cosmic microwave background.
Secondly, we scrutinize a simple modification of general relativity providing a minimal violation of the strong equivalence principle. Although the additional scalar field acts as a dark radiation at the cosmological expansion level, the imprint left on the matter field perturbations is clearly distinguishable from other radiations because of the particular scalar field anisotropic stress. Several constraints for this alternative gravitational theory are derived from the analysis of the cosmic microwave background, Type Ia supernovae and the measure of the Lemaître-Hubble constant.

Finally, we replace the cosmological constant by a quintessence field. For selected realistic models agreeing with current cosmological data, it is shown that the non-linear processes driving the growth of matter’s large scale structures encode the nature and the dynamics of dark energy.

Although the confrontation between the investigated alternative models and available cosmological data currently does not raise deviation to the concordant ΛCDM model, the present study shows that predictions and signatures of these models are unique compared to the standard scenario.

We consider the Universe deep inside the cell of uniformity. At these scales, the Universe is filled with inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies), which perturb the background Friedmann model. Here, the mechanical approach (Eingorn & Zhuk, 2012) is the most appropriate to describe the dynamics of the inhomogeneities which is defined, on the one hand, by gravitational potentials of inhomogeneities and, on the other hand, by the cosmological expansion of the Universe. In this paper, we present additional arguments in favor of this approach. First, we estimate the size of the cell of uniformity. With the help of the standard methods of statistical physics and for the galaxies of the type of the Milky Way and Andromeda, we get that it is of the order of 190 Mpc which is rather close to observations. Then, we show that the nonrelativistic approximation (with respect to the peculiar velocities) is valid for $z \lesssim 10$, i.e. approximately for 13 billion years from the present moment. We consider scalar perturbations and, within the $\Lambda$CDM model, justify the main equations. Moreover, we demonstrate that radiation can be naturally incorporated into our scheme. This emphasizes the viability of our approach. This approach gives a possibility to analyze different cosmological models and compare them with the observable Universe. For example, we indicate some problematic aspects of the spatially flat models. Such models require a rather specific distribution of the inhomogeneities to get a finite potential at any points outside gravitating masses. We also criticize the application of the Schwarzschild-de Sitter solution to the description of the motion of test bodies on the cosmological background.

The theory of massive gravity in three dimensions recently proposed by Bergshoeff, Hohm and Townsend (BHT) is considered. At the special case when the theory admits a unique maximally symmetric solution, a conformally flat space that contains black holes and gravitational solitons for any value of the cosmological constant is found. For negative cosmological constant, the black hole is characterized in terms of the mass and the "gravitational hair" parameter, providing a lower bound for the mass. For negative mass parameter, the black hole acquires an inner horizon, and the entropy vanishes at the extremal case. Gravitational solitons and kinks, being regular everywhere, are obtained from a double Wick rotation of the black hole. A wormhole solution in vacuum that interpolates between two static universes of negative spatial curvature is obtained as a limiting case of the gravitational soliton with a suitable identification. The black hole and the gravitational soliton fit within a set of relaxed asymptotically AdS conditions as compared with the ones of Brown and Henneaux. In the case of positive cosmological constant the black hole possesses an event and a cosmological horizon, whose mass is bounded from above. Remarkably, the temperatures of the event and the cosmological horizons coincide, and at the extremal case one obtains the analogue of the Nariai solution, $dS_{2}\times S^{1}$. A gravitational soliton is also obtained through a double Wick rotation of the black hole. The Euclidean continuation of these solutions describes instantons with vanishing Euclidean action. For vanishing cosmological constant the black hole and the gravitational soliton are asymptotically locally flat spacetimes. The rotating solutions can be obtained by boosting the previous ones in the $t-\phi$ plane.

In this paper, (part VI) we analyze further equations of Manuscript Book 2 of Srinivasa Ramanujan. We describe the new possible mathematical connections with the MRB (Marvin Ray Burns) Constant and several equations concerning some sectors of String Theory and  Cosmology