Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and empirical Gaussianisation transforms can reduce the amount of non-Gaussianity in a distribution. Alternatively, in this work, we employ methods from information geometry. The latter formulates a set of probability distributions for some given model as a manifold employing a Riemannian structure, equipped with a metric, the Fisher information. In this framework we study the differential geometrical meaning of non-Gaussianities in a higher order Fisher approximation, and their respective transformation behaviour under re-parameterisation, which corresponds to a chart transition on the statistical manifold. While weak non-Gaussianities vanish in normal coordinates in a first order approximation, one can in general not find transformations that discard non-Gaussianities globally. As an application we consider the likelihood of the supernovae distance-redshift relation in cosmology for the parameter pair ($Ω_{\mathrm{m_0}}$, $w$). We demonstrate the connection between confidence intervals and geodesic length and demonstrate how the Lie-derivative along the degeneracy directions gives hints at possible isometries of the Fisher metric.
The paper deals with the investigation of a homogeneous and anisotropic space-time described by Bianchi type III metric with perfect fluid in Lyra geometry setting. Exact solutions of the Einsten's field equations have been obtained under the assumption of quadratic equation of state (EoS) of the form p=a(rho)^2-(rho), where a is a constant and strictly a>0. The physical and geometrical aspects are also examined in details.
Exact solutions are obtained for an inhomogeneous cosmological model in normal gauge for Lyra geometry. Some properties of the model have also been discussed.
Field-level multi-tracers simulation-based inference of cosmological parameters from 3D maps
SISSA（国际高等研究学院）；INFN Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing（高性能计算、大数据与量子计算国家研究中心）；Imperial College London（帝国理工学院）；IFPU - Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）
Cosmological consequences of the noncommutative geometry spectral action are presented. Neglecting the nonminimal coupling of the Higgs field to the curvature, background cosmology remains unchanged, and only the inhomogeneous perturbations will evolve differently from the equivalent classical system. However, considering the nonminimal coupling, corrections will be obtained even at the level of the background cosmologies. Finally, the Higgs field may act as an inflaton field, due to its nonminimal coupling with geometry.
We construct the thermodynamic geometry of $2+1$ dimensional normal (exotic) BTZ black hole regarding to the fluctuation of cosmological constant. We argue that while the thermodynamic geometry of black hole without fluctuation of cosmological constant is a two dimensional flat spaces, the three dimensional thermodynamics parameters space including the cosmological constant as a fluctuating parameter will be curved. Some consequence of the fluctuation of cosmological constant will be investigated. We show that such fluctuation leads to a thermodynamics curvature which is correctly singular at …
Bermann [ Nuovo Cimento B (1983), 74, 182 ] presented a law of variation of Hubble parameter that yields constant deceleration parameter models of the Universe. In this paper, we study some cosmological models with negative constant deceleration parameter within the framework of Lyra geometry.
The recent analysis of the Planck results reveals a tension between the best fits for (Ωm0, H0) derived from the cosmic microwave background or baryonic acoustic oscillations on the one hand, and the Hubble diagram on the other hand. These observations probe the universe on very different scales since they involve light beams of very different angular sizes; hence the tension between them may indicate that they should not be interpreted the same way. More precisely, this Letter questions the accuracy of using only the (perturbed) Friedmann-Lemaître geometry to interpret all the cosmological ob…
We consider the cosmological evolution in an osculating point Barthel-Randers type geometry, in which to each point of the space-time manifold an arbitrary point vector field is associated. This Finsler type geometry is assumed to describe the physical properties of the gravitational field, as well as the cosmological dynamics. For the Barthel-Randers geometry the connection is given by the Levi-Civita connection of the associated Riemann metric. The generalized Friedmann equations in the Barthel-Randers geometry are obtained by considering that the background Riemannian metric in the Randers …
In this paper the observational consequence of the cosmological models and the expression for the neoclassical tests, luminosity distance, angular diameter distance and look back time are analyzed in the framework of Lyra geometry. It is interesting to note that the space time of the universe is not only free of Big Bang singularity but also exhibits acceleration during its evolution.
We have investigated an LRS Bianchi Type I models with bulk viscosity in the cosmological theory based on Lyra's geometry. A new class of exact solutions have been obtained by considering a time-dependent displacement field for a constant value of the deceleration parameter and viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density. The physical behaviour of the models is also discussed.
Exact cosmological models for a scalar field in Lyra geometry are studied in the presence of a time-varying effective cosmological term originated from the specific interaction of an auxiliary $Λ$ - term with the displacement vector. In this case, some exact solutions for the model equations are obtained with the help of the so-called superpotential method (or the first-order formalism). Some possible ways of further developing for such a model are offered.
We present the first joint inference of standard sirens and gravitational wave weak lensing by filtering of the same dataset. We imagine a post-LISA scenario emerging around the late 2030s when LISA will have accumulated a number of detections at high redshift; LIGO-VIRGO will have finished observing at low redshift, and Einstein Telescope will have started making new observations out to redshifts possibly overlapping with LISA. Euclid and other cosmological probes will have provided constraints at percent level by then, but mostly exhausted their ability to improve any further. We derive fore…
Cosmological models in Lyra's geometry are constructed and investigated with the assumption of a minimal interaction of matter with the displacement vector field and the dynamical $Λ$ - term. Exact solutions of the model equations are obtained for the different equations of state of the matter, that fills the universe, and for the certain assumptions on the decaying law for $Λ$.
In the present study, we comment on Brans-Dicke scalar field cosmological model in Lyra's geometry [Maurya \& Zia, Phys. Rev. D \textbf{100}, 023503 (2019)]. In this comment, we investigate that there is no acceleration in the model proposed by the authors of Phys. Rev. D \textbf{100}, 023503 (2019). Therefore, despite the claims to the contrary the Brans-Dicke Scalar Field Cosmological Model in Lyra's Geometry with high Brans-Dicke (BD) coupling parameter $ω$ and constant $β$ can not produce late time acceleration in the universe.
In this paper, we obtained a new class of axially symmetric cosmological mesonic stiff fluid models in the context of Lyra's geometry. Expressions for the energy, pressure and the massless scalar field are derived by considering the time dependent displacement field. We found that the mesonic scalar field depends on only $t$ coordinate. Some physical properties of the obtained models are discussed.
These are lectures for students at the summer school conducted by the Faculty of Fundamental Sciences, Bauman Moscow State Technical University at 2022.
We have investigated an inhomogeneous Bianchi type-I cosmological model with electromagnetic field based on Lyra geometry. A new class of exact solutions have been obtained by considering the potentials of metric and displacement field are functions of coordinates t and x. The physical behavior of the obtained model is discussed.
We discuss the cosmological evolution of the Weyl conformal geometry and its associated Weyl quadratic gravity. The Einstein gravity (with a positive cosmological constant) is recovered in the spontaneously broken phase of Weyl gravity; this happens after the Weyl gauge field ($ω_μ$) of scale symmetry, that is part of the Weyl geometry, becomes massive by Stueckelberg mechanism and then decouples. This breaking is a natural result of the cosmological evolution of Weyl geometry, in the absence of matter. Of particular interest in the analysis is the special limiting case of Weyl integrable geom…
We develop a cosmographic framework for analysing redshift drift signals of nearby sources model-independently, i.e., without making assumptions about the metric description of the Universe. We show that the Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) prediction is altered nontrivially by regional anisotropies and inhomogeneities. In particular, we find that the position drift of the sources is nontrivially linked to the redshift drift signal. The redshift drift signal for nearby sources might be formulated in terms of an effective deceleration parameter, which reduces to the FLRW deceleratio…
Finsler geometry is an important extension of Riemann geometry, in which to each point of the spacetime manifold an arbitrary internal variable is associated. Interesting Finsler geometries, with many physical applications, are the Randers and Kropina type geometries, respectively. A subclass of Finsler geometries is represented by the osculating Finsler spaces, in which the internal variable is a function of the base manifold coordinates only. In an osculating Finsler geometry one introduces the Barthel connection, which has the remarkable property that it is the Levi-Civita connection of a R…
We investigated the possibility of construction the homogeneous and isotropic cosmological solutions in Weyl geometry. We derived the self-consistency condition which ensures the conformal invariance of the complete set of equations of motion. There is the special gauge in choosing the conformal factor when the Weyl vector equals zero. In this gauge we found new vacuum cosmological solutions absent in General Relativity. Also, we found new solution in Weyl geometry for the radiation dominated universe with the cosmological term, corresponding to the constant curvature scalar in our special gau…
The advanced world-wide network of gravitational waves (GW) observatories is scheduled to begin operations within the current decade. Thanks to their improved sensitivity, they promise to yield a number of detections and thus to open a new observational windows for astronomy and astrophysics. Among the scientific goals that should be achieved, there is the independent measurement of the value of the cosmological parameters, hence an independent test of the current cosmological paradigm. Due to the importance of such task, a number of studies have evaluated the capabilities of GW telescopes in …
A gravity theory without masses can be constructed in Minkowski spaces using a geometric Minkowski potential. The related affine spacelike spheres can be seen as the regions of the Minkowski spacelike vectors characterized by a constant Minkowski gravitational potential. These spheres point out, for each dimension $n \geq 3$, spacetime models, the de Sitter ones, which satisfy Einstein's field equations in absence of matter. In other words, it is possible to generate geometrically the cosmological constant. Even if a lot of possible parameterizations have been proposed, each one highlighting s…
There are investigated such cosmological models which instead of the usual spatial homogeneity property only fulfil the condition that in a certain synchronized system of reference all spacelike sections t = const. are homogeneous manifolds. This allows time-dependent changes of the BIANCHI type. Discussing differential geometrical theorems it is shown which of them are permitted. Besides the trivial case of changing into type I there exist some possible changes between other types. However, physical reasons like energy inequalities partially exclude them.
In the first part of this paper we consider expanding vacuum cosmological spacetimes with a free $T^N$-action. Among them, we give evidence that Gowdy spacetimes have AVTD (asymptotically velocity term dominated) behavior for their initial geometry, in any dimension. We then give sufficient conditions to reach a similar conclusion about a $T^2$-invariant four dimensional nonGowdy spacetime. In the second part of the paper we consider vacuum cosmological spacetimes with crushing singularities. We introduce a monotonic quantity to characterize Kasner spacetimes. Assuming scale-invariant curvatur…
If a subset of advanced civilizations in the universe choose to rapidly expand into unoccupied space, these civilizations would have the opportunity to grow to a cosmological scale over the course of billions of years. If such life also makes observable changes to the galaxies they inhabit, then it is possible that vast domains of life-saturated galaxies could be visible from the Earth. Here, we describe the shape and angular size of these domains as viewed from the Earth, and calculate median visible sizes for a variety of scenarios. We also calculate the total fraction of the sky that should…
We give an outline of an algorithm designed to reconstruct the background cosmological metric within the class of spherically symmetric dust universes that may include a cosmological constant. Luminosity and age data are used to derive constraints on the geometry of the universe up to a redshift of $z = 1.75$. It is shown that simple radially inhomogeneous void models that are sometimes used as alternative explanations for the apparent acceleration of the late time Universe cannot be ruled out by these data alone.
SU(2) flat connection on 2D Riemann surface is shown to relate to the generalized twisted geometry in 3D space with cosmological constant. Various flat connection quantities on Riemann surface are mapped to the geometrical quantities in discrete 3D space. We propose that the moduli space of SU(2) flat connections on Riemann surface generalizes the phase space of twisted geometry or Loop Quantum Gravity to include the cosmological constant.
We present the geometry of spacetimes that are tangentially approximated by de Sitter spaces whose cosmological constants vary over spacetime. Cartan geometry provides one with the tools to describe manifolds that reduce to a homogeneous Klein space at the infinitesimal level. We consider a Cartan geometry in which the underlying Klein space is at each point a de Sitter space, for which the combined set of pseudo-radii forms a nonconstant function on spacetime. We show that the torsion of such a geometry receives a contribution that is not present for a cosmological constant. The structure gro…
We identify certain general geometric conditions on a foliation of a spacetime (M,g) by timelike curves that will impede the existence of null geodesic lines, especially if (M,g) possesses a compact Cauchy hypersurface. The absence of such lines, in turn, yields well-known restrictions on the geometry of cosmological spacetimes, in the context of Bartnik's splitting conjecture. Since the (non)existence of null lines is actually a conformally invariant property, such conditions only need to apply for some suitable conformal rescaling of g.
Finite-size effects on the gravitational wave signal from a neutron star merger typically manifest at high frequencies where detector sensitivity decreases. Proposed sensitivity improvements can give us access both to stronger signals and to a myriad of weak signals from cosmological distances. The latter will outnumber the former and the relevant part of signal will be redshifted towards the detector most sensitive band. We study the redshift dependence of information about neutron star matter and find that single-scale properties, such as the star radius or the post-merger frequency, are bet…
We study an effective 4-dimensional scalar-tensor field theory, originated from an underlying brane-bulk warped geometry, to explore the scenario of inflation. It is shown that the inflaton potential naturally emerges from the radion energy-momentum tensor which in turn results into an inflationary model of the Universe on the visible brane that is consistent with the recent results from the Planck's experiment. The dynamics of modulus stabilization from the inflaton rolling condition is demonstrated. The implications of our results in the context of recent BICEP2 results are also discussed.
Cosmological alpha-attractors give a natural explanation for the spectral index n_s of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r, consistent with all observations, to be measured more precisely in future detection of gravity waves. Their embedding into supergravity exploits the hyperbolic geometry of the Poincare disk or half-plane. These geometries are isometric under Mobius transformations, which include the shift symmetry of the inflaton field. We introduce a new Kahler potential frame that explicitly preserves this symmetry, enabling the infl…
The imposition of symmetries or special geometric properties on submanifolds is less restrictive than to impose them in the full space-time. Starting from this idea, in this paper we study irrotational dust cosmological models in which the geometry of the hypersurfaces generated by the fluid velocity is flat, which supposes a relaxation of the restrictions imposed by the Cosmological Principle. The method of study combines covariant and tetrad methods that exploits the geometrical and physical properties of these models. This procedure will allow us to determine all the space-times within this…
Loop Quantum Gravity (LQG) is an attempt to describe the quantum gravity regime. Introducing a non-zero cosmological constant $Λ$ in this context has been a withstanding problem. Other approaches, such as Chern-Simons gravity, suggest that quantum groups can be used to introduce $Λ$ in the game. Not much is known when defining LQG with a quantum group. Tensor operators can be used to construct observables in any type of discrete quantum gauge theory with a classical/quantum gauge group. We illustrate this by constructing explicitly geometric observables for LQG defined with a quantum group and…
We extend General Relativity by promoting Planck scale and the cosmological constant into integration constants, interpreted as fluxes of $4$-forms hiding in the theory. When we include the charges of the $4$-forms, these `constants' can vary discretely from region to region. We explain how the cosmological constant problem can be solved in this new framework. When the cosmological constant picks up contributions from two different $4$-forms, with an irrational ratio of charges, the spectrum of its values is a very fine discretuum. When the charges are mutually irrational, $\frac{2κ_{\tt eff}^…
We study the Laplace spectra of the intrinsic instantaneous metrics on the event and cosmological horizons of a Kerr-Newman de Sitter space-time and prove that the spectral data from these horizons uniquely determine the space-time. This is accomplished by exhibiting formulae relating the parameters of the space-time metric to the traces of invariant and equivariant Green's operators associated with these Laplacians. In particular, an interesting explicit formula for the cosmological constant is found.
This article analyzes the present anomalies of cosmology from the point of view of integrable Weyl geometry. It uses P.A.M. Dirac's proposal for a weak extension of general relativity, with some small adaptations. Simple models with interesting geometrical and physical properties, not belonging to the Friedmann-Lema\^ıtre class, are studied in this frame. Those with positive spatial curvature (Einstein-Weyl universes) go well together with observed mass density $Ω_m$, CMB, supernovae Ia data, and quasar frequencies. They suggest a physical role for an equilibrium state of the Maxwell field pro…
We describe the dynamics of a cosmological term in the spherically symmetric case by an r-dependent second rank symmetric tensor Λ_{μν} invariant under boosts in the radial direction. The cosmological tensor Λ_{μν} represents the extension of the Einstein cosmological term Λg_{μν} which allows a cosmological constant be variable. This possibility is based on the Petrov classification scheme and Einstein field equations in the spherically symmetric case. The inflationary equation of state is satisfied by the radial pressure p_r^Λ=-ρ^Λ. The tangential pressure is calculated from the conservation…
We consider a very general scenario of our universe where its geometry is characterized by the Finslerian structure on the underlying spacetime manifold, a generalization of the Riemannian geometry. Now considering a general energy-momentum tensor for matter sector, we derive the gravitational field equations in such spacetime. Further, to depict the cosmological dynamics in such spacetime proposing an interesting equation of state identified by a sole parameter $γ$ which for isotropic limit is simply the barotropic equation of state $p= (γ- 1) ρ$ ($γ\in \mathbb{R}$ being the barotropic index)…
Inhomogeneous Bianchi type-I cosmological model with electro-magnetic field based on Lyra geometry is investigated. Using separated method, the Einstein field equations have been solved analytically with the aid of Mathematica programm. A new class of exact solutions have been obtained by considering the potentials of metric and displacement field are functions of coordinates t and x. We have assumed that F(12) is the only non-vanishing component of electro-magnetic field tensor F(ij). The Maxwells equations show that F(12) is the function of x alone whereas the magnetic permeability is the fu…
Space-times which allow a slicing into homogeneous spatial hypersurfaces generalize the usual Bianchi models. One knows already that in these models the Bianchi type may change with time. Here we show which of the changes really appear. To this end we characterize the topological space whose points are the 3-dimensional oriented homogeneous Riemannian manifolds; locally isometric manifolds are considered as same.
The generic cosmological solution is analyzed both for the non-asymptotic limit to the cosmological singularity and in the asymptotic limit analytically. The Bianchi I solution and the Bianchi IX solution, described as a sequence of Bianchi I reparameterized solutions, are analyzed with respect to the asymptotic symmetry implied by the space part of the metric tensor. Numerical studies are explained. The semiclassical regime is proposed by using the degrees of freedom for the initial conditions to the Einstein field equations, i.e. those which are not necessarily characterizing for a Bianchi s…
We compute Zero Point Energy in a spherically symmetric background with the help of the Wheeler-DeWitt equation. This last one is regarded as a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The graviton contribution, at one loop is extracted with the help of a variational approach together with Gaussian trial functionals. The divergences handled with a zeta function regularization are compared with the results obtained using a Noncommutative Geometry (NCG) and Modified Dispersion Relations (MDR). In both NCG and MDR no renormalization scheme is…
In this paper, we have developed a new cosmological model in Einstein's modified gravity theory using two types of modification.(i) Geometrical modification, in which we have used Lyra's geometry in the left hand side of the Einstein field equations (EFE) and (ii) Modification in gravity (energy momentum tensor) on right hand side of EFE, as per Brans-Dicke (BD) model. With these two modifications, we have investigated a spatially homogeneous and anisotropic Bianchi type-I cosmological models of Einstein's Brans-Dicke theory of gravitation in Lyra geometry. The model represents accelerating un…
We generalize the results of Randall and Sundrum to a wider class of four-dimensional space-times including the four-dimensional Schwarzschild background and de Sitter universe. We solve the equation for graviton propagation in a general four dimensional background and find an explicit solution for a zero mass bound state of the graviton. We find that this zero mass bound state is normalizable only if the cosmological constant is strictly zero, thereby providing a dynamical reason for the vanishing of cosmological constant within the context of this model. We also show that the results of Rand…
This paper discusses noncommutative-geometry wormholes in the context of a cosmological model due to Sung-Won Kim. An ansatz suggested by the Friedmann-Lemaitre-Robertson-Walker (FLRW) model leads to the assumption that the matter content can be divided into two parts, a cosmological part depending only on time and a wormhole part depending only on space. These assumptions are sufficient for deriving a complete zero-tidal force wormhole solution. The wormhole is evolving due to the scale factor in the FLRW model; it is restricted, however, to the curvature parameters $k=0$ and $k=-1$. Unlike p…
We investigate the possible effects on the evolution of perturbations in the inflationary epoch due to short distance physics. We introduce a suitable non local action for the inflaton field, suggested by Noncommutative Geometry, and obtained by adopting a generalized star product on a Friedmann-Robertson-Walker background. In particular, we study how the presence of a length scale where spacetime becomes noncommutative affects the gaussianity and isotropy properties of fluctuations, and the corresponding effects on the Cosmic Microwave Background spectrum.
[Abridged] This study presents the first Bayesian investigation of the accuracy with which the cosmological parameters can be measured using information coming \emph{only} from the gravitational wave observations of binary neutron star systems by Einstein Telescope. We find, by direct simulation of $10^3$ detections of binary neutron stars, that, within our simplifying assumptions, $H_0,Ω_m,Ω_Λ,w_0$ and $w_1$ can be measured at the $95\%$ level with an accuracy of $\sim 8\%,65\%,39\%,80\%$ and $90\%$, respectively. We also find, by extrapolation, that a measurement accuracy comparable with cur…
Using a non-Riemannian geometry that is adapted to the 4+1 decomposition of space-time in Kaluza-Klein theory, the translational part of the connection form is related to the electromagnetic vector potential and a Stueckelberg scalar. The consideration of a five-dimensional gravitational action functional that shares the symmetries of the chosen geometry leads to a unification of the four-dimensional cosmological term and a mass term for the vector potential.
We consider implications of the microscopic dynamics of spacetime for the evolution of cosmological models. We argue that quantum geometry effects may lead to stochastic fluctuations of the gravitational constant, which is thus considered as a macroscopic effective dynamical quantity. Consistency with Riemannian geometry entails the presence of a time-dependent dark energy term in the modified field equations, which can be expressed in terms of the dynamical gravitational constant. We suggest that the late-time accelerated expansion of the Universe may be ascribed to quantum fluctuations in th…
We construct new classes of cosmological solution to the five dimensional Einstein-Maxwell-dilaton theory, that are non-stationary and almost conformally regular everywhere. The base geometry for the solutions is the four-dimensional Bianchi type IX geometry. In the theory, the dilaton field is coupled to the electromagnetic field and the cosmological constant term, with two different coupling constants. We consider all possible solutions with different values of the coupling constants, where the cosmological constant takes any positive, negative or zero values. In the ansatzes for the metric,…
