Search Results (13)

In this paper, we study the conformal symmetry for locally rotationally symmetric Bianchi type I space-time. New exact conformal solutions of Einstein’s field equations for this space-time were obtained. The space-time geometry of these solutions is found to be non-vacuum, conformally flat, and shear-free. We show that in order for LRS Bianchi type I space-time to admit a conformal vector field it must reduce to the FRW space-time. Some physical and kinematic properties of the obtained conformal solutions are also discussed. Full article

We found statistical evidence for a mismatch between the (global) spatial curvature parameter K in the geodesic equation for incoming photons and the corresponding parameter in the Friedmann equation that determines the time evolution of the background spacetime and its perturbations. The mismatch, hereafter referred to as ‘curvature slip’, was especially evident when the SH0ES prior of the current expansion rate was assumed. This result is based on joint analyses of cosmic microwave background (CMB) observations with the PLANCK satellite (P18), the first year results of the Dark Energy Survey (DES), baryonic oscillation (BAO) data, and at a lower level of significance, the Pantheon SNIa (SN) catalog as well. For example, the betting odds against the null hypothesis were greater than ${10}^7$:1, 1400:1 and 1000:1 when P18+SH0ES, P18+DES+SH0ES and P18+BAO+SH0ES were considered, respectively. Datasets involving SNIa weakened this curvature slip considerably. Notably, even when the SH0ES prior was not imposed, the betting odds for the rejection of the null hypothesis were 70:1 and 160:1 in cases where P18+DES and P18+BAO were considered. When the SH0ES prior was imposed, the global fit of the modified model (that allows for a nonvanishing ‘curvature slip’) strongly outperformed that of $\Lambda$CDM, being manifested by significant deviance information criterion (DIC) gains ranging between 7 and 23, depending on the dataset combination considered. Even in comparison with K$\Lambda$CDM, the proposed model resulted in significant, albeit smaller, DIC gains when SN data were excluded. Our finding could possibly be interpreted as an inherent inconsistency between the (idealized) maximally symmetric nature of the FRW metric and the dynamical evolution of the GR-based homogeneous and isotropic $\Lambda$CDM models. As such, this implies that there is apparent tension between the metric curvature and the curvature-like term in the time evolution of the redshift. Full article

We uncover the general mechanism and the nature of today’s dark energy (DE). This is only based on well-known quantum physics and cosmology. We show that the observed DE today originates from the cosmological quantum vacuum of light particles, which provides a continuous energy distribution able to reproduce the data. Bosons give positive contributions to the DE, while fermions yield negative contributions. As usual in field theory, ultraviolet divergences are subtracted from the physical quantities. The subtractions respect the symmetries of the theory, and we normalize the physical quantities to be zero for the Minkowski vacuum. The resulting finite contributions to the energy density and the pressure from the quantum vacuum grow as $loga\left(t\right)$, where $a\left(t\right)$ is the scale factor, while the particle contributions dilute as $1/a^3\left(t\right)$, as it must be for massive particles. We find the explicit dark energy equation of state of today to be $P=w\left(z\right)\mathcal{H}$: it turns to be slightly $w\left(z\right)<-1$ with $w\left(z\right)$ asymptotically reaching the value $-1$ from below. A scalar particle can produce the observed dark energy through its quantum cosmological vacuum provided that (i) its mass is of the order of ${10}^{-3}$ eV = 1 meV, (ii) it is very weakly coupled, and (iii) it is stable on the time scale of the age of the universe. The axion vacuum thus appears as a natural candidate. The neutrino vacuum (especially the lightest mass eigenstate) can give negative contributions to the dark energy. We find that $w(z=0)$ is slightly below $-1$ by an amount ranging from $(-1.5\times {10}^{-3})$ to $(-8\times {10}^{-3})$ and we predict the axion mass to be in the range between 4 and 5 $\mathrm{meV}$. We find that the universe will expand in the future faster than the de Sitter universe as an exponential in the square of the cosmic time. Dark energy today arises from the quantum vacuum of light particles in FRW cosmological space-time in an analogous way to the Casimir vacuum effect of quantum fields in Minkowski space-time with non-trivial boundary conditions. Full article

The main objective of this article is to examine the stability of Einstein static universe using inhomogeneous perturbations in the context of energy–momentum squared gravity. For this purpose, we used FRW spacetime with perfect matter distribution and formulated static as well as perturbed field equations. We took a minimal model of this theory to investigate the stable regions of the Einstein universe for conserved and non-conserved energy–momentum tensors. We found that stable modes of the Einstein universe appeared in both conserved and non-conserved cases for all values of the equation of state and model parameters corresponding to both open and closed cosmic models. We found that stable solutions in this modified theory were obtained for a broader $\omega$-region compared to other modified theories. Full article

In this work, we would like to address the problem of the effect of bulk matter on the brane cosmological evolution in a general way. We assume that the spatial part of the brane metric is not maximally symmetric, and is, therefore, spatially inhomogeneous. However, we retain the conformal flatness property of the standard cosmological model (FRW), i.e., the Weyl tensor of the induced 4D geometry is zero. We refer to it as Spatially Inhomogeneous Irrotational (SII) brane. It is shown that the model can be regarded as the 5D generalization of the SII spacetimes found recently. Full article

Any new gravitational theories can be built with the help of a gauge theory with local Poincare symmetry. This local Poincare symmetry can set up a space-time with torsion. In the present study, the authors working on the parametrization approach towards Hubble’s parameter in the frame of modified teleparallel Gauss-Bonnet gravity which is established on the torsion invariant $\mathcal{T}$ and the teleparallel equivalent of the Gauss-Bonnet term ${\mathcal{T}}_{\mathcal{G}}$, say $\mathcal{F}(\mathcal{T},{\mathcal{T}}_{\mathcal{G}})$ gravity. In particular, gravity is responsible for an integrated explanation of the cosmological history from early-time inflation to late-time acceleration expansion, by lacking the addition of a cosmological constant. The domino effect acquired is reliable with recent cosmological outcomes. A transition scenario from a decelerating phase to an accelerating phase of cosmic evolution has been detected. Using the combined datasets (SNe-Ia+BAO+CMB+$H\left(z\right)$), we have constrained the transition redshift $z_t$ (at which the universe transit from a decelerating phase to an accelerating) and established the best fit value of $z_t$. Next, we paralleled the renovated results of $q\left(z\right)$ and $\omega \left(z\right)$ and found that the outcomes are well-suited with a $\mathrm{\Lambda }$CDM universe. Full article

We consider the late-time accelerated universe in the Friedmann–Robertson–Walker (FRW) spacetime with a nonzero curvature, and investigate cosmological models when the cosmic fluid is taken to be inhomogeneous and viscous (bulk viscous), coupled to dark matter. We consider the influence from thermal effects caused by Hawking radiation on the formation of singularities of various classified types, within a finite time. It is shown that under the influence of Hawking radiation, the time of formulation of a singularity and the nature of the singularity itself can change. It is also shown that by jointly taking into account radiation, viscosity, and space curvature, one can obtain a singularity-free universe. The symmetry properties of this kind of theory lie in the assumption about spatial isotropy. The spatial isotropy is also reflected in our use of a bulk instead of a shear viscosity. Full article

In this paper, we explore the gravitational collapse of matter (dust) under the effect of zero-point length $l_0$. During the gravitational collapse, we neglect the backreaction effect of pre-Hawking radiation (in the sense that it is a small effect and cannot prevent the formation of an apparent horizon), then we recast the internal metric of a collapsing star as a closed FRW universe for any spherically symmetric case and, finally, we obtain the minimal value for the scale factor, meaning that the particles never hit the singularity. We argue that the object emerging at the end of the gravitational collapse can be interpreted as Planck stars (black hole core) hidden inside the event horizon of the black hole, with a radius proportional to ${(GM{l}_0^2/c^2)}^{1/3}$. Quite interestingly, we found the same result for the radius of the Planck star using a free-falling observer point of view. In addition, we point out a correspondence between the modified Friedmann’s equations in loop quantum gravity and the modified Friedmann’s equation in string T-duality. In the end, we discuss two possibilities regarding the final stage of the black hole. The first possibility is that we end up with Planck-size black hole remnants. The second possibility is that the inner core can be unstable and, due to the quantum tunneling effect, the spacetime can undergo a black-hole-to-white-hole transition (a bouncing Planck star). Full article

This article deals with the fractional problem of Sturm–Liouville and the Hilbert space associated with the solutions of this differential equation. We apply a quantization procedure to Schwarzschild space–time and obtain a fractional differential equation. The Hilbert space for these solutions is established. We used equations arising from quantization for the FRW and Reissner–Nordstron metrics to build the respective Hilbert spaces. Full article

Most quantum gravity theories quantize space-time on the order of Planck length (${\ell }_p^{}$). Some of these theories, such as loop quantum gravity (LQG), predict that this discreetness could be manifested through Lorentz invariance violations (LIV) over travelling particles at astronomical length distances. However, reports on LIV are controversial, and space discreetness could still be compatible with Lorentz invariance. Here, it is tested whether space quantization on the order of Planck length could still be compatible with Lorentz invariance through the application of a covariant geometric uncertainty principle (GeUP) as a constraint over geodesics in FRW geometries. Space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann–Lemaitre–Robertson–Walker solution to General Relativity (FLRW or FRW metric). A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared, and dependent on two contributions. The first is associated to the energy–time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories, and within experimental constraints on putative LIV. Full article

The objective of the present paper is to investigate an almost-pseudo-Ricci symmetric FRW spacetime with a constant Ricci scalar in a dynamic cosmological term $\Lambda \left(t\right)$ and equation of state (EoS) $\omega \left(t\right)$ scenario. Several cosmological parameters are calculated in this setting and thoroughly studied, which shows that the model satisfies the late-time accelerating expansion of the universe. We also examine all of the energy conditions to check our model’s self-stability. Full article

The aim of this work is to study a scalar-tensor theory where owing to Palatini’s variational method the space-time is endowed with a geometrical structure of Weyl integrable type. The geometrical nature of the scalar field is related to the non-metricity so that the theory is known as geometrical scalar-tensor. On the framework of Weyl transformations, a non-minimally coupled scalar-tensor theory on the Jordan frame corresponds to a minimally coupled Einstein–Hilbert action on the Einstein frame. The scalar potential is selected by the Noether symmetry approach in order to obtain conserved quantities for the FRW cosmological model. Exact solutions are obtained and analyzed in the context of the cosmological scenarios consistent with an expanding universe. A particular case is matched in each frame and the role of scalar field as a dark energy component is discussed. Full article

In this paper, we consider the flat FRW spacetime filled with interacting dark energy and dark matter in fractal universe. We work with the three models of dark energy named as Tsallis, Renyi and Sharma–Mittal. We investigate different cosmological implications such as equation of state parameter, squared speed of sound, deceleration parameter, statefinder parameters, ${\omega }_{eff}-\stackrel{\prime }{{\omega }_{eff}}$ (where prime indicates the derivative with respect to $lna$ , and a is cosmic scale factor) plane and Om diagnostic. We explore these parameters graphically to study the evolving universe. We compare the consistency of dark energy models with the accelerating universe observational data. All three models are stable in fractal universe and support accelerated expansion of the universe. Full article