Trace dynamics, and a ground state in spontaneous quantum gravity

We have recently proposed a Lagrangian in trace dynamics to describe a possible unification of gravity, Yang–Mills fields, and fermions, at the Planck scale. This Lagrangian for the unified entity — called the aikyon — is invariant under global unitary transformations, and as a result possesses a novel conserved charge, known as the Adler–Millard charge. In this paper, we derive an eigenvalue equation, analogous to the time-independent Schrödinger equation, for the Hamiltonian of the theory. We show that in the emergent quantum theory, the energy eigenvalues of the aikyon are characterized in terms of a fundamental frequency times Planck’s constant. The eigenvalues of this equation can, in principle, determine the values of the parameters of the standard model. We also report a ground state, in this theory of spontaneous quantum gravity, which could characterize a non-singular initial epoch in quantum cosmology.

Rip cosmologies, wormhole solutions and big trip in the f(T,𝒯 ) theory of gravity

Rip cosmological models have been investigated in the framework of [Formula: see text] theory of gravity, where [Formula: see text] denotes the torsion and [Formula: see text] is the trace of the energy–momentum tensor. These phantom cosmological models revealed that at initial epoch a EoS parameter [Formula: see text] tends asymptotically at late phase to [Formula: see text] [Formula: see text]. On the other hand, Wormhole Solutions and Big Trip have been subject to an investigation. The wormhole throat radius [Formula: see text] and the conditions to be satisfied to produce the Big Trip phenomenon have been discussed.

Calendar as a Criterion in the Study of Culture

The paper considers the calendar as a link between the cosmos and mankind, and itintroduces it as an instrument in studying culture. It uses the concept of calendars/calendar systemsas a criterion for recognition and formation of culture in general. Starting from an assumption thatthe calendar is a structurally organized system of events or holidays, it analyses the basic units of acalendar: day, month and year, and distinguishes a calendar holiday from a non-calendar holiday.It states that the calendars are a structural list of collective memory within a social group, wherethis memory is described in cyclical categories – calendar holidays. Furthermore, considering thatthe initial epoch of year counting may be different in different cultures, it discusses how culturalself-awareness is expressed through the epoch of the calendar era. Finally, it explores how and towhat extent the formation, interaction, and reforms of calendars and their systems reflect the changein culture. The paper concludes that calendars and their systems should be used as a criterion indefining culture.

The methodology of geodetic supporting Russian Federation digital economy

In the article the researches on developing modern methodology of supporting the national program “Digital economy of the Russian Federation” with geospatial data and, first of all, its base component, the systems of coordinate support are presented. As the main sentences of upgrading coordinate support it is offered to pass to kinematic model of evolution of coordinates in the state coordinate system GSK-2011 completely. The coordinates in this model are to be given to the consumer not on some separate instants (an initial epoch of installation of a coordinate system, an epoch of the last adjustment etc.), but for the current date, using a federal network of differential geodetic stations as the main tool for implementing this methodology. In order to avoid inconveniences of application the reference system for practical operations (as the coordinates are time-dependent), it is offered to use the additional coordinate system, “fixed” to an appropriate tectonic plate, spun round Euler’s pole within the state reference system GSK-2011.

Cosmological models with a hybrid scale factor in an extended gravity theory

A general formalism to investigate Bianchi type [Formula: see text] universes is developed in an extended theory of gravity. A minimally coupled geometry and matter field is considered with a rescaled function of [Formula: see text] substituted in place of the Ricci scalar R in the geometrical action. Dynamical aspects of the models are discussed by using a hybrid scale factor (HSF) that behaves as power law in an initial epoch and as an exponential form at late epoch. The power law behavior and the exponential behavior appear as two extreme cases of the present model.

Cosmological models constructed by van der Waals fluid approximation and volumetric expansion

The universe modeled with van der Waals fluid approximation, where the van der Waals fluid equation of state contains a single parameter [Formula: see text]. Analytical solutions to the Einstein’s field equations are obtained by assuming the mean scale factor of the metric follows volumetric exponential and power-law expansions. The model describes a rapid expansion where the acceleration grows in an exponential way and the van der Waals fluid behaves like an inflation for an initial epoch of the universe. Also, the model describes that when time goes away the acceleration is positive, but it decreases to zero and the van der Waals fluid approximation behaves like a present accelerated phase of the universe. Finally, it is observed that the model contains a type-III future singularity for volumetric power-law expansion.

Viscous Bianchi Type I Universe with Stiff Matter and Decaying Vacuum Energy Density

We examine homogeneous and anisotropic Bianchi type I cosmological model with viscous stiff matter and time-varying cosmological term which scales with Hubble parameter H. The resulting model approaches isotropy. The cosmological term relaxes to a genuine cosmological constant, and the model in the absence of bulk viscosity tends to a deSitter universe asymptotically. Our scenario presents an initial epoch with decelerating expansion followed by late-time acceleration consistent with observations. Bulk viscosity advances the accelerating phase in the model and prevents the matter density to vanish for large times.

HST Observations of 3 More Old LMC Clusters

We present color-magnitude diagrams (CMDs) based on HST F555W (“V”) and F814W (“I”) observations of three old LMC clusters: NGC 2210, NGC 1786, and Reticulum. The fiducial derived from the CMD of NGC 2257, another LMC cluster, provided a good fit to the data for the new clusters. Because NGC 2257 has a similar metallicity ([Fe/H]∼ −1.8) to NGC 2210, NGC 1786, and Reticulum, the agreement between the CMDs of all four clusters indicates that they have the same age. This preliminary analysis suggests that any age differences are smaller than 2 Gyr. These new results mean that there are now 11 old LMC clusters with similar ages. An initial epoch of star cluster formation therefore happened in a short period over a large volume of space, a volume much larger than is now covered by the present-day optical LMC.

Quantum fluctuations near a space–time singularity

The well-known operator technique in quantum mechanics is used to study quantum fluctuations near the space–time singularity using Kantowski–Sachs and Bianchi type VIo metrics. In both cases the wave function of the universe is found to diverge near the space–time singularity, indicating the divergence of the quantum uncertainty near the initial epoch.