Without violating the 4 natural laws of physics viz. cosmic censorship hypothesis, chronology protection conjecture, special and general theory of relativity, a theory has been established in this paper which would allow the phenomena of explaining the UFOs seen from Earth, International Space Station, Aerial Aircraft in such a way that, mysteries can be solved on how those UFOs can come to Earth either by crossing Mega Parsec (10 6 *3.28 Light Years), Giga Parsec (10 9 *3.28 Light Years) or from the faraway future Earth. Emphasis has been given to mathematical models to solve these mysteries without violating the aforesaid models of physical laws. Time has been treated as a physical dimension parameterized by measurements like other 3 D’s. This model aims to reduce space and time using a completely new idea called “Temporal Choke Point” and its associated mathematics by completely relying on known fundamental theories but without violating them in any proper ways possible. And apart from that, a detailed analysis has been done on ‘gravity’ from the perspectives of string theories and thereby concluding some interesting Phenomenology happening at the micro perspective of the ”Temporal Choke Point ξ³ᴰ.

There are more than a billion galaxies in our observable universe and every astrophysical phenomena concerning to the galaxies, to stars to planets can be easily approximated by Newtonian mechanics’, post-Newtonian kinematics and general relativity. However, the field equations of general relativity (GR) include a cosmological constant term, lambda, to interpret the negative pressures existing in our universe that accelerates expansion. However, this expansion can be overwhelmed by the inward movements of the galaxies and during the final fate when two galaxies collide, likewise, if ‘Milky-Way and Andromeda’ collides, the super massive black holes existing at the center of every galaxies, ranging from a million to a billion to even more than the typical solar mass, collides, and they got captured in a gravity generated quasi-equipotential topology where there exists five Lagrange points along with a specified limit of the capturing black holes where if one black hole becomes beyond the Roche lobe then, mass inflow rate starts and the mass would start to flow from the large black holes to small black holes and this creates a gravitational merger where the rotational angular momentum gets con- served to relativistic jets and an accretion disc is produced. This merger results in the whistling of a large proportional of sinusoidal gravitational waves which ripples thought the space-time dimensions and gets detected in ‘interferometer gravity detectors’ like LIGO. The final fate is the Larger SMBH which exists at the heart of the newly formed galaxies. Detailed astrophysical analysis has been done in this paper and related theory has been provided to cope with the recent findings and observations taking place resulting the super massive black holes in galactic collisions.

Novikov ring which has been used as a coefficient over the closed symplectic manifold that when encountered through an extension, Big one, from the ordinary cohomology to the quantum cohomology, then the ‘fuzzy’ quantum nature could be more precisely described by the ‘quantum cup product’ inducing the variations from the Riemann sphere connecting two points as analogous to the J – Holomorphic curves or Pseudoholomorphic curves between two points as in symplectic manifolds. Poincare duality as interpreted over the curves makes the associativity over two bubble–manifolds through Gromov connections which later makes a non–local invariance over the Gromov – Witten Invariants. Complex graded Novikov ring being associated over Poincare duality finds its way through the Riemann surface over genus – 0 and marked points – K, through the perturbed Cauchy – Riemann Equation. For the n – point Gromov – Witten Invariants, n=3 is taken for small quantum cohomology and n greater than or equal to 4 for big quantum cohomological models. This proves essential in establishing the duality (Topological) between Heterotic SO(32), Heterotic E8*E8 with Type II-A supersymmetric strings in M – Theory.

This paper focuses on a phase transition from the asymptotic safety approach of renormalizing the quantum gravity (QG) to a more granular approach of the loop quantum gravity (LQG) and then merging it with the Regge calculus for deriving the spin-(2) graviton. From loop-(2) onwards, the higher derivative curvatures make the momentum go to infinity which assaults a problem in renormalizing the QG. If the Einstein-Hilbert (E-H) action, is computed, and a localized path integral (or partition functions) is defined over a curved space, then that action is shown to be associated with the higher order dimension in a more compactified way, resulting in an infinite winding numbers being accompanied through the exponentiality coefficients of the partition integrals in the loop expansions of the second order term onwards. Based on that localization principle, the entire path integral got collapsed to discrete points that if corresponds the aforesaid actions, results in negating the divergences’ with an implied bijections’ and reverse bijections’ of a diffeormorphism of a continuous differentiable functional domains. If those domains are being attributed to the spatial constraints, Hamiltonian constraints and Master constraints then, through Ashtekar’s variables, it can be modestly shown that the behavior of quantum origin of asymptotic safety is similar to the LQG granules of spinfoam spacetime. Then, we will proceed with the triangulation of the entangled-points that results in the inclusion of Regge poles via the quantum number (+2,-2,0) as the produced variables of the spin-(2) graviton and spin-(0) dilaton.

If reality is being augmented as a simulation; then from the modern norm of physics, it is possible that everywhere around us, including us and what we perceive is a simulation simulated by a super powerful computer from a farfetched future times, taken the Einstein’an notion, that, past, present and future occur simultaneously. It is quite probable between two consecutive amplitudes that, the simulation can either be done by the super advanced civilization in greater than or equal to Kardashev 3.0 scale or by some higher order entities existing in a dimensional domain beyond our perceiveness and notion of our understanding. To agree to the fact of the simulation hypothesis, there exists a mathematical foundation of the desired logic behind this simulation, which will be investigated throughout this paper whose another consequence might be the déjà vu or the Mandela effect. The errors arise in this simulation is a form of glitch in the matrix that should happen because of the commutable lagging of the super-intelligent computers of either future ones or higher-order ones. Preciseness about the calculations of dimensions opened a way for t + s = 2 + 10 where the non-locality of the time being perceived as a 2-dimensional entity opens up the door for further investigations. The more will be discussed in detail in this paper.

Time and space average of an ergodic systems following the 5-tuple relations (A,~,J,Σ,μ) through the initial increment from a+bθ to a+c+bθ indicates the entropy to be reserved in the deterministic yet dynamical and conservative systems to hold for the set S_p= S_1 ∑_(i=2)^∞_S_i keeping S as the entropy ∃(S_∞=⋯S_3=S_2 )>S_1 obeying the Poincare ̵́ recurrence theorem throughout the constant attractor A. This in turn states the facts of the equivalence closure as the property of the induced systems to resemblance an entropy conserving scenarios.

If in future, the highly intelligent machines control the world, then what would be its advantages and disadvantages? Will, those artificial intelligence powered superintelligent machines become an anathema for humanity or will they ease out the human works by guiding humans in complicated tasks, thereby extending a helping hand to the human works making them comfortable. Recent studies in theoretical computer science especially artificial intelligence predicted something called ‘technological singularity’ or the ‘intelligent explosion’ and if this happens then there can be a further stage as transfused machinery intelligence and actual intelligence where the machines being immensely powerful with a cognitive capacity more than that of humans for solving ‘immensely complicated tasks’ can takeover the humans and even the machines by more intelligent machines of superhuman intelligence. Therefore, it is troublesome and worry-full to think that ‘if in case the machines turned out against humans for their optimal domination in this planet’. Can humans have any chances to avoid them by bypassing the inevitable ‘hard singularity’ through a set of ‘soft singularity’. This paper discusses all the facts in details along with significant calculations showing humanity, how to avoid the hard singularity when the progress of intelligence is inevitable.

A document by Deep Bhattacharjee . Click on the document to view its contents.

Any quantum groups can be filtered via PBW Theorem over a graded algebra where the structure representation for any supercommutator [𝗶,𝗷] when reduced asserts a linear monomial of a canonical origin. Thus, being independent on the swapping order, isomorphism can be seen for any injective takeovers giving the map ψ: ℓ ⟶ U(ℓ) with the Lie ℓ through the U(ℓ) group. This satisfies direct connectivity over 𝙊𝙨𝙥(𝙢,𝙣)⋂𝙊𝙨𝙥(𝙣,𝙢) in Kac-Moody algebras.

The ghost condensation of the early universe in a pre-big bang phase has been presented in this paper through duration of a non-singular bounce. The undergoing universe contracts and passes smoothly in an expanding universe via a post-big bang phase. Initially developing and then taming any ghost like instabilities, the Null Energy Condition (NEC) is explicitly violated through the curvature mechanism of an adiabatic perturbed metric. The vacuum state of the ongoing phase is stabilized via a La-grangian that in essence stabilizes the vacuum state under the higher order derivatives. The violation of the NEC regards a catastrophic vacuum instability, which re-emerges with a correction valid at small energies and momenta, below the UV-cutoff scale that, could potentially be problematic if one tries to construct a UV-completed theory of this Ekpyrotic model. The scale-invariant curvature perturbation, that arises and is sourced out of the scale-invariant entropy perturbations sourced by 2-Ekpyrotic scalar fields, that, in contrast, becomes constant on the super-horizon limits, due to the non-singular nature of the background geometry. Apart, from the ghost condensates, this theory addresses the new Ekpyrotic theory which in order becomes a distinguishable alternative to inflation theory for the birth of the universe. As per the recent WMAP data, the Ekpyrotic model has a spectral red tilt that shows the bounced scalar potential falling through a negative phase shift during the matter-fluid fluctuations in the hot big bang phase.

A detailed analysis of the blazars detected by the Fermi/LAT (3LAC) and (4LAC) along with the 𝛾 −ray Narrow line – Seyfert 1 Galaxies (𝛾-NLSy1s) has been provided here with emphasize to the weak anti-correlation between synchrotron peak frequency and peak luminiosity, jet kinetic power and synchrotron peak frequency along with the properties of FSRQs, BL Lacs (Chen et al, 2020) with the central engine properties that is, the accretion luminosity (𝐿𝑑𝑖𝑠𝑘 ) and black hole mass (𝑀𝐵𝐻 ) where study has been done regarding the broad emission spectral line systems along with the association of more massive black holes with absorption line systems where computations has been made in Eddington units (𝐿𝑑𝑖𝑠𝑐 /𝐿𝐸𝑑𝑑 ) having the broad line objects to have a higher accretion rate (𝐿𝑑𝑖𝑠𝑐 /𝐿𝐸𝑑𝑑 > 0.01) with the sources being identified in recurrence with the HighCompton Dominated (HCD-CD > 1) and Low-Compton Dominated (LCD- CD ≲ 1) objects where according to (Paliya et al, 2021) the physical properties of the Fermi Blazars are to be controlled by the accretion rate in Eddington units. From the known redshifts of the Fermi satellite data, the spectral energy distributions (SEDs) have been computed where the proton dominated jet powers and the luminosity has been computed which is of the same order of (or slightly larger than) the disc luminosity (Ghisellini et al, 2010). In case of Flat Spectrum Radio quasars (FSRQs), the high energy peak of the SED increases with the luminosity where the X-ray spectra becomes harder and harder for larger luminosities, however in case of BL Lacs, they become redder with a softer 𝛾-ray slope and high energy for peak luminosities. For all the blazars (FRSQs + BL Lacs), the higher luminosity bin is vastly populated by FRSQs while the lower luminosity bin is populated by BL Lacs (Ghisellini et al, 2017). In the Fermi LAT – Bright AGN Sample (LBAS) by combining the Fermi 𝛾-ray spectra with Swift, optical, infra-red, radio, hard X-ray, 𝛾-ray data it has been observed with accuracy that in case of 50% of the radio bright high energy peaked BL Lacs (HBL) detected in the LABS Sample, only less than 13% of the known FSRQs and LBL BL Lacs are included. The synchrotron peak frequency (𝑣𝑝𝑒𝑎𝑘 𝑠 ) has been positioned between 1012.5 and 1014.5 Hz in FSRQs and between 1013 and 1017 Hz in featureless BL Lac objects. The LAC detector being more sensitive to flat spectrum 𝛾-ray sources, the exact correlation between 𝑣𝑝𝑒𝑎𝑘 𝑠 and 𝛾-ray spectral index highly favors the detection of the high energy peaked blazars having the Fermi overabundance compared to radio and Energetic Gamma Ray Experiment Telescope (EGRET) samples. This in turn makes a selection effect where in the soft X-ray band, HBL BL Lacs are the most dominant types of blazars (Abdo et al, 2010).

A document by Deep Bhattacharjee . Click on the document to view its contents.