How a projectively flat geometry regulates F(R)-gravity theory?

In the present paper we examine a projectively flat spacetime solution of F(R)-gravity theory. It is seen that once we deploy projective flatness in the geometry of the spacetime, the matter field has constant energy density and isotropic pressure. We then make the condition weaker and discuss the effects of projectively harmonic spacetime geometry in F(R)-gravity theory and show that the spacetime in this case reduces to a generalised Robertson-Walker spacetime with a shear, vorticity, acceleration free perfect fluid with a specific form of expansion scalar presented in terms of the scale factor. Role of conharmonic curvature tensor in the spacetime geometry is also briefly discussed. Some analysis of the obtained results are conducted in terms of couple of F(R)-gravity models.

Non-comoving cold dark matter in a $$\varLambda $$CDM background

We examine the evolution of peculiar velocities of cold dark matter (CDM) in localized arrays of inhomogeneous cosmic structures in a $$\varLambda $$ Λ CDM background that can be identified as a frame comoving with the Cosmic Microwave (CMB). These arrays are constructed by smoothly matching to this cosmological background regions of Szekeres-II models whose source is an imperfect fluid reinterpreted as non-comoving dust, keeping only first order terms in v/c. Considering a single Szekeres-II region matched along two comoving interfaces to a $$\varLambda $$ Λ CDM background, the magnitudes of peculiar velocities within this region are compatible with values reported in the literature, while the present day Hubble expansion scalar differs from that of the $$\varLambda $$ Λ CDM background value by a 10% factor, a result that might provide useful information to the ongoing debate on the $$H_0$$ H 0 tension. While the models cannot describe the virialization process, we show through a representative example that structures of galactic cluster mass reach the onset of this process at redshifts around $$z\sim 3$$ z ∼ 3 .

COSMIC INFLATION IN BIANCHI TYPE IX SPACE WITH BULK VISCOSITY

In present paper we have constructed the Bianchitype-IX inflationary universe under framework of the effect of bulk viscosity and flat potential. To developed inflationary model we have consider the supplementary criteria that shear coefficient is directly proportional to expansion scalar which provides an appropriate relation with coefficients of metric $b=a^n$ where n is non-negative constant other than one.We conclude that rate of Higgs field decreases with time and proper volume V is increasing function of time which indicates that universe is expanded continuously. To find solutions of fields equations, we assume $ \xi \theta = \alpha$ (constant) as given by Brevik et al. where $\xi $is coefficient of bulk viscosity and $\theta$ expansion in model. The presence of bulk viscosity provides inflationary solution in current model. The model isotropize in special case. The cosmological parameters of model are also studied.

Analysis of Bianchi Type V Holographic Dark Energy Models in General Relativity and Lyra’s Geometry

In this paper, we analyze anisotropic and homogeneous Bianchi type V spacetime in the presence of dark matter and holographic dark energy model components in the framework of general relativity and Lyra’s geometry. The solutions of differential equation fields have been obtained by considering two specific cases, namely, the expansion scalar θ in the model is proportional to the shear scalar σ and the average scale factor taken as hybrid expansion form. The solutions for field equations are obtained in general relativity and Lyra’s geometry. The energy density of dark matter in both natures was obtained and compared so that the energy density of dark matter in general relativity is slightly different from the energy density of dark matter in Lyra’s geometry. A similar behavior occurred in case of pressure and EoS parameter of holographic dark energy model in respective frameworks. Also, it is concluded that the physical parameters such as the average Hubble parameter, spatial volume, anisotropy parameter, expansion scalar, and shear scalar are the same in both frameworks. Moreover, it is observed that the gauge function β t is a decreasing function of cosmic time in Lyra’s geometry, and for late times, the gauge function β t converges to zero and Lyra’s geometry reduces to general relativity in all respects. Finally, we conclude that our models are a close resemblance to the Λ CDM cosmological model in late times and consistent with the recent observations of cosmological data.

Models of non-static and inhomogeneous gravitating source in Rastall gravity

In this paper, we have explored the non-static anisotropic gravitational collapse and expansion solutions in Rastall theory of gravity. The field equations have been formulated for the non-static and inhomogeneous gravitating source. The Misner–Sharp mass function, auxiliary solution and trapped condition have been used to obtained a trapped surface. The auxiliary solutions have been used to obtain the expansion and collapse solutions; these solutions depend on [Formula: see text] and parameter [Formula: see text] (which appears due to parametric form of metric components); also the range of parameter [Formula: see text] has been examined. The expansion scalar [Formula: see text] depends on parameter [Formula: see text], in the case of expansion [Formula: see text] for [Formula: see text], while for collapse [Formula: see text] with [Formula: see text]. Also, the dynamics of the gravitating spherical source has been discussed graphically with the effects of Rastall parameter [Formula: see text]. For the physically reasonable fluid, the validity of energy conditions has been discussed for expansion and collapse solutions with the various values of [Formula: see text].

Eikonal Equations for Null Radial Geodesics in the Schwarzschild Metric

We study the eikonal function φ corresponding to outgoing and ingoing radial null geodesics (light rays in the short wave length limit) in the Schwarzschild spacetime. Contrary to the behavior of the expansion scalar θ at the singularities (past and future), φ turns out to be finite at r = 0 (except for light travelling along the horizons) and inversely proportional to M, the mass of the black hole, and so proportional to the Hawking temperature.

Axial gravitational waves in Bianchi I universe

In this paper, we have studied the propagation of axial gravitational waves in Bianchi I universe using the Regge–Wheeler gauge. In this gauge, there are only two nonzero components of [Formula: see text] in the case of axial waves: [Formula: see text] and [Formula: see text]. The field equations in absence of matter have been derived both for the unperturbed as well as axially perturbed metric. These field equations are solved simultaneously by assuming the expansion scalar [Formula: see text] to be proportional to the shear scalar [Formula: see text] (so that [Formula: see text], where [Formula: see text], [Formula: see text] are the metric coefficients and [Formula: see text] is an arbitrary constant), and the wave equation for the perturbation parameter [Formula: see text] has been derived. We used the method of separation of variables to solve for this parameter, and have subsequently determined [Formula: see text]. We then discuss a few special cases to interpret the results. We find that the anisotropy of the background spacetime is responsible for the damping of the gravitational waves as they propagate through this spacetime. The perturbations depend on the values of the angular momentum [Formula: see text]. The field equations in the presence of matter reveal that the axially perturbed spacetime leads to perturbations only in the azimuthal velocity of the fluid leaving the matter field undisturbed.

Is the Axionic Dark Matter an Equilibrium System?

We consider an axionic dark matter model with a modified periodic potential for the pseudoscalar field in the framework of the axionic extension of the Einstein-aether theory. The modified potential is assumed to be equipped by the guiding function, which depends on the expansion scalar constructed as the trace of the covariant derivative of the aether velocity four-vector. The equilibrium state of the axion field is defined as the state, for which the modified potential itself and its first derivative with respect to the pseudoscalar field are equal to zero. We apply the developed formalism to the homogeneous isotropic cosmological model, and find the basic function, which describes the equilibrium state of the axionic dark matter in the expanding Universe.

Spontaneous Color Polarization as A Modus Originis of the Dynamic Aether

We suggest the phenomenological model of emergence of the dynamic aether as a result of decay of the SU(N) symmetric field configuration containing the multiplet of vector fields. The scenario of the transition to the dynamic aether, which is characterized by one unit timelike vector field that is associated with the aether velocity, is based on the idea of spontaneous color polarization analogous to the spontaneous electric polarization in ferroelectric materials. The mechanism of spontaneous color polarization is described in the framework of anisotropic cosmological model of the Bianchi-I type; it involves consideration of the idea of critical behavior of the eigenvalues of the tensor of color polarization in the course of the Universe accelerated expansion. The interim stage of transition from the color aether to the canonic dynamic aether takes the finite period of time, the duration of which is predetermined by the phenomenologically introduced critical value of the expansion scalar.