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Pantelis S. Apostolopoulos

Publications and source records attributed to Pantelis S. Apostolopoulos.

At least 19 recordsLinked to original sources
arXiv2024

Inhomogeneous brane models

The existence of a set of $10$ Intrinsic Conformal Symmetries, which acts on three-dimensional hypersurfaces (spacelike or timelike), leads to the existence of two distinct families of 5D geometries. These models represent the general solutions of the bulk field equations where their energy-momentum tensor, includes only two components: a negative cosmological constant and a parallel pressure $p_{\parallel}$ aligned with the extra spatial dimension. Significantly, these models offer a novel perspective for investigating the impacts of spatial inhomogeneity and anisotropy on the cosmological evolution of the Universe, particularly within the context of the braneworld scenarios. It is shown that one of these families reduces to a \emph{fully inhomogeneous, anisotropic and conformally flat brane model} with a \emph{perfect fluid equation of state} and corresponds to the Stephani Universe (i.e. a Stephani brane) which implies that our model can be matched smoothly with the standard FRW model. We provide the generalized Friedmann and Raychaudhuri equations and we present how the additional quantities could affect the cosmological evolution. In particular we show that the new constituents are the terms $p_{\parallel }$, $σ^{2}$ and the four acceleration of the brane observers that could affect the observational measurement of the Hubble parameter depending on which term dominates therefore provide us a potential answer to the Hubble tension and cosmic acceleration problems due to local inhomogeneities and anisotropies.

gr-qc↗
arXiv2023

Conformal Symmetries of the Strumia and Tetradis Metric

In a recent paper, a new conformally flat metric was introduced, describing an expanding scalar field in a spherically symmetric geometry. The spacetime can be interpreted as a Schwarzschild-like model with an apparent horizon surrounding the curvature singularity. For the above metric, we present the complete conformal Lie algebra consisting of a six-dimensional subalgebra of isometries (Killing Vector Fields or KVFs) and nine proper conformal vector fields (CVFs). An interesting aspect of our findings is that there exists a gradient (proper) conformal symmetry (i.e., its bivector vanishes) which verifies the importance of gradient symmetries in constructing viable cosmological models. In addition, the 9-dimensional conformal algebra implies the existence of constants of motion along null geodesics that allow us to determine the complete solution of null geodesic equations.

gr-qc↗
arXiv2023

A positive cosmological constant as a geometrical artifact

We revisit the classical mechanism to produce $d-$dimensional spacetimes via Kaluza-Klein compactification. We made the assumption that the $\left(d+1\right) -$dimensional bulk geometry $\mathcal{M}$ admits a Homothetic Vector Field (HVF) $\mathbf{H}$ relaxing the existence of a zero i.e. $\mathbf{H}\neq 0$ holds on $\mathcal{M}$ and the homothetic bivector $F_{ab}(\mathbf{H})=0$. Under these circumstances we identify the origin of a positive cosmological constant in the $d-$dimensional spacetime as the homothetic factor representing a geometrical artifact of late time state of the $\left( d+1\right) -$dimensional bulk spacetime.

gr-qc↗
arXiv2023

Constructing a family of conformally flat scalar field models

Using purely geometrical methods we present a mechanism to solve the scalar field equations of motion (non-minimally coupled with gravity) in a spherically symmetric background. We found that the \emph{full }set of spacetimes, which are of Petrov type O (conformally flat) and admit a \emph{gradient} Conformal Vector Field, can be determined completely. It is shown that the full group of scalar field equations reduced to a \emph{single} equation that depends only on the distance $w=r^{2}-t^{2}$ leaving the metric function (equivalently the functional form of the scalar field or the potential) freely chosen. Depending on the structure of the metric or the potential $V$ (as a function of $ϕ$) a solution can be found either analytically or via numerical integration. We provide physically sound examples and prove that (Anti)-de Sitter fits this scheme. We also reconstruct a recently found solution \cite{Strumia:2022kez} representing an expanding scalar bubble with metric that has a singularity and corresponds to what is termed as Anti-de Sitter crunch.

gr-qc↗
arXiv2023

A class of 5D inhomogeneous models with a cosmological constant

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, 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 [1].

gr-qc↗
arXiv2017

Intrinsic Conformal Symmetries in Szekeres models

We show that Spatially Inhomogeneous (SI) and Irrotational dust models admit a \emph{6-dimensional algebra } of \emph{Intrinsic Conformal Vector Fields} (ICVFs) $\mathbf{X}_{α}$ satisfying $p_{a}^{c}p_{b}^{d}\mathcal{L}_{\mathbf{X}_{α}}p_{cd}=2ϕ(\mathbf{X}_{α})p_{ab}$ where $p_{ab}$ is the associated metric of the 2d distribution $\mathcal{X}$ normal to the fluid velocity $u^{a}$ and the radial unit spacelike vector field $x^{a}$. The Intrinsic Conformal (IC) algebra is determined for each of the curvature value $ε$ that characterizes the structure of the screen space $\mathcal{X}$. In addition the conformal flatness of the hypersurfaces $\mathbf{u}=\mathbf{0}$ indicates the existence of a \emph{% 10-dimensional algebra} of ICVFs of the 3d metric $h_{ab}$. We illustrate this expectation and propose a method to derive them by giving explicitly the \emph{7 proper} ICVFs of the Lema\^ıtre-Tolman-Bondi (LTB) model which represents the simplest subclass within the Szekeres family.

gr-qc↗
arXiv2017

Szekeres models: a covariant approach

We exploit the 1+1+2 formalism to covariantly describe the inhomogeneous and anisotropic Szekeres models. It is shown that an \emph{average scale length} can be defined \emph{covariantly} which satisfies a 2d equation of motion driven from the \emph{effective gravitational mass} (EGM) contained in the dust cloud. The contributions to the EGM are encoded to the energy density of the dust fluid and the free gravitational field $E_{ab}$. We show that the quasi-symmetric property of the Szekeres models is justified through the existence of 3 independent \emph{Intrinsic Killing Vector Fields (IKVFs)}. In addition the notions of the Apparent and Absolute Apparent Horizons are briefly discussed and we give an alternative gauge-invariant form to define them in terms of the kinematical variables of the spacelike congruences. We argue that the proposed program can be used in order to express Sachs' optical equations in a covariant form and analyze the confrontation of a spatially inhomogeneous irrotational overdense fluid model with the observational data.

gr-qc↗
arXiv2017

Vacuum self similar anisotropic cosmologies in $F(R)-$gravity

The implications from the existence of a proper Homothetic Vector Field (HVF) on the dynamics of vacuum anisotropic models in $F(R)$ gravitational theory are studied. The fact that \emph{every} Spatially Homogeneous vacuum model is equivalent, formally, with a "flux" -free anisotropic fluid model in standard gravity and the induced power-law form of the functional $F(R)$ due to self-similarity enable us to close the system of equations. We found some new exact anisotropic solutions that arise as fixed points in the associated dynamical system. The non-existence of Kasner-like (Bianchi type I) solutions in proper $F(R)-$gravity (i.e. $R\neq 0$) strengthens the belief that curvature corrections will prevent the shear influence into the past thus permitting an isotropic singularity. We also discuss certain issues regarding the lack of vacuum models of type III, IV, VII$_{h}$ in comparison with the corresponding results in standard gravity.

gr-qc↗
arXiv2016

Spatially inhomogeneous and irrotational geometries admitting Intrinsic Conformal Symmetries

"Diagonal" spatially inhomogeneous (SI) models are introduced under the assumption of the existence of (proper) intrinsic symmetries and can be seen, in some sense, complementary to the Szekeres models. The structure of this class of spacetimes can be regarded as a generalization of the (twist-free) Locally Rotationally Symmetric (LRS) geometries without any global isometry containing, however, these models as special cases. We consider geometries where a six-dimensional algebra $\mathcal{IC}$ of Intrinsic Conformal Vector Fields (ICVFs) exists acting on a $2-$dimensional (pseudo)-Riemannian manifold. Its members $\mathbf{X}_{α}$, constituted of 3 Intrinsic Killing Vector Fields (IKVFs) and 3 \emph{proper} and \emph{gradient} ICVFs, as well as the specific form of the gravitational field are given explicitly. An interesting consequence, in contrast with the Szekeres models, is the immediate existence of \emph{conserved quantities along null geodesics}. We check computationally that the magnetic part $H_{ab}$ of the Weyl tensor vanishes whereas the shear $σ_{ab}$ and the electric part $E_{ab}$ share a common eigenframe irrespective of the fluid interpretation of the models. A side result is the fact that the spacetimes are foliated by a set of \emph{conformally flat } $3-$dimensional \emph{timelike} slices when the anisotropy of the \emph{flux-free} fluid is described only in terms of the 3 \emph{principal inhomogeneous "pressures"} $p_α$ or equivalently when the Ricci tensor shares the same basis of eigenvectors with $σ_{ab}$ and $E_{ab}$. The conformal flatness also indicates that a \emph{10-dimensional algebra} of ICVFs $\mathbfΞ$ acting on the $3-$dimensional timelike slices is highly possible to exist enriching in that way the set of conserved quantities admitted by the SI models found in the present paper.

gr-qc↗
arXiv2010

Effective cosmological equations of induced f(R) gravity

We expand the study of generalized brane cosmologies by allowing for an $f(\tilde{\cal R})$ gravity term on the brane, with $\tilde{\cal R}$ the curvature scalar derived from the induced metric. We also include arbitrary matter components on the brane and in the five-dimensional bulk. At low energies, the effect of the bulk on the brane evolution can be described through a mirage component, termed generalized dark radiation, in the effective four-dimensional field equations. Using the covariant formalism, we derive the exact form of these equations. We also derive an effective conservation equation involving the brane matter and the generalized dark radiation. At low energies the coupled brane-bulk system has a purely four-dimensional description. The applications of the formalism include generalizations of the Starobinsky model and the Dvali-Gabadadze-Porrati cosmology.

hep-th↗
arXiv2007

Modified brane cosmologies with induced gravity, arbitrary matter content and a Gauss-Bonnet term in the bulk

We extend the covariant analysis of the brane cosmological evolution in order to take into account, apart from a general matter content and an induced-gravity term on the brane, a Gauss-Bonnet term in the bulk. The gravitational effect of the bulk matter on the brane evolution can be described in terms of the total bulk mass as measured by a bulk observer at the location of the brane. This mass appears in the effective Friedmann equation through a term characterized as generalized dark radiation that induces mirage effects in the evolution. We discuss the normal and self-accelerating branches of the combined system. We also derive the Raychaudhuri equation that can be used in order to determine if the cosmological evolution is accelerating.

hep-th↗
arXiv2006

Late acceleration and $w=-1$ crossing in induced gravity

We study the cosmological evolution on a brane with induced gravity within a bulk with arbitrary matter content. We consider a Friedmann-Robertson-Walker brane, invariantly characterized by a six-dimensional group of isometries. We derive the effective Friedmann and Raychaudhuri equations. We show that the Hubble expansion rate on the brane depends on the covariantly defined integrated mass in the bulk, which determines the energy density of the generalized dark radiation. The Friedmann equation has two branches, distinguished by the two possible values of the parameter $\ex=\pm 1$. The branch with $\ex=1$ is characterized by an effective cosmological constant and accelerated expansion for low energy densities. Another remarkable feature is that the contribution from the generalized dark radiation appears with a negative sign. As a result, the presence of the bulk corresponds to an effective negative energy density on the brane, without violation of the weak energy condition. The transition from a period of domination of the matter energy density by non-relativistic brane matter to domination by the generalized dark radiation corresponds to a crossing of the phantom divide $w=-1$.

hep-th↗
arXiv2006

Cosmological Acceleration and Gravitational Collapse

The acceleration parameter defined through the local volume expansion is negative for a pressureless, irrotational fluid with positive energy density. In the presence of inhomogeneities or anisotropies the volume expansion rate results from averaging over various directions. On the other hand, the observation of light from a certain source in the sky provides information on the expansion along the direction to that source. If there are preferred directions in the underlying geometry one can define several expansion parameters. We provide such definitions for the case of the Tolman-Bondi metric. We then examine the effect of a localized inhomogeneity on the surrounding cosmological fluid. Our framework is similar in spirit to the model of spherical collapse. For an observer in the vicinity of a central overdensity, the perceived local evolution is consistent with acceleration in the direction towards the center of the overdensity, and deceleration perpendicularly to it. A negative mass leads to deceleration along the radial direction, and acceleration perpendicularly to it. If the observer is located at the center of an overdensity the null geodesics are radial. The form of the luminosity distance as a function of the redshift is consistent with acceleration for a certain range of redshifts.

astro-ph↗
arXiv2005

The Generalized Dark Radiation and Accelerated Expansion in Brane Cosmology

The effective Friedmann equation describing the evolution of the brane Universe in the cosmology of the Randall-Sundrum model includes a dark (or mirage or Weyl) radiation term. The brane evolution can be interpreted as the motion of the brane in an AdS-Schwarzschild bulk geometry. The energy density of the dark radiation is proportional to the black hole mass. We generalize this result for an AdS bulk space with an arbitrary matter component. We show that the mirage term retains its form, but the black hole mass is replaced by the covariantly defined integrated mass of the bulk matter. As this mass depends explicitly on the scale factor on the brane, the mirage term does not scale as pure radiation. For low energy densities the brane cosmological evolution is that of a four-dimensional Universe with two matter components: the matter localized on the brane and the mirage matter. There is conservation of energy between the two components. This behaviour indicates a duality between the bulk theory and a four-dimensional theory on the brane. The equation of state of the generalized dark radiation is that of a conformal field theory, with an explicit breaking of the conformal invariance through the pressure of the bulk fluid. Accelerated expansion on the brane is possible only if there is negative pressure on the brane or in the bulk, or if the integrated mass of the bulk fluid is negative.

hep-th↗
arXiv2005

A geometric description of the intermediate behaviour for spatially homogeneous models

A new approach is suggested for the study of geometric symmetries in general relativity, leading to an invariant characterization of the evolutionary behaviour for a class of Spatially Homogeneous (SH) vacuum and orthogonal $γ-$law perfect fluid models. Exploiting the 1+3 orthonormal frame formalism, we express the kinematical quantities of a generic symmetry using expansion-normalized variables. In this way, a specific symmetry assumption lead to geometric constraints that are combined with the associated integrability conditions, coming from the existence of the symmetry and the induced expansion-normalized form of the Einstein's Field Equations (EFE), to give a close set of compatibility equations. By specializing to the case of a \emph{Kinematic Conformal Symmetry} (KCS), which is regarded as the direct generalization of the concept of self-similarity, we give the complete set of consistency equations for the whole SH dynamical state space. An interesting aspect of the analysis of the consistency equations is that, \emph{at least} for class A models which are Locally Rotationally Symmetric or lying within the invariant subset satisfying $N_α^α=0 $, a proper KCS \emph{always exists} and reduces to a self-similarity of the first or second kind at the asymptotic regimes, providing a way for the ``geometrization'' of the intermediate epoch of SH models.

gr-qc↗
arXiv2005

Mirage effects on the brane

We discuss features of the brane cosmological evolution that arise through the presence of matter in the bulk. As these deviations from the conventional evolution are not associated with some observable matter component on the brane, we characterize them as mirage effects. We review an example of expansion that can be attributed to mirage non-relativistic matter (mirage cold dark matter) on the brane. The real source of the evolution is an anisotropic bulk fluid with negative pressure along the extra dimension. We also study the general problem of exchange of real non-relativistic matter between the brane and the bulk, and discuss the related mirage effects. Finally, we derive the brane cosmological evolution within a bulk that contains a global monopole (hedgehog) configuration. This background induces a mirage curvature term in the effective Friedmann equation, which can cause a brane Universe with positive spatial curvature to expand forever.

hep-th↗
arXiv2005

Brane cosmological evolution with a general bulk matter configuration

Using a fully covariant treatment for the description of the bulk geometry, we study the brane cosmological evolution in the presence of a smooth bulk matter distribution. We focus on the case of a Friedmann-Robertson-Walker (FRW) brane, invariantly characterized by the existence of a six-dimensional group of isometries acting on 3D spacelike orbits. With a FRW brane, the bulk geometry can be regarded as the 5D generalization of the \emph{inhomogeneous orthogonal family of Locally Rotationally Symmetric (LRS)} spacetimes. We show that, for \emph{any bulk matter configuration}, the expansion rate on the brane depends only on the covariantly defined \emph{comoving mass} $\mathcal{M}$ of the bulk fluid within a radius equal to the average length scale of the 3D spacelike hypersurfaces of constant curvature. This unique contribution incorporates the effects of the 5D Weyl tensor and the projected tensor related to the bulk matter, and gives a transparent physical picture that includes an effective conservation equation between the brane and the bulk matter.

hep-th↗