The art of building a smooth cosmic distance ladder in a perturbed universe

How does a smooth cosmic distance ladder emerge from observations made from a single location in a lumpy Universe? Distances to Type Ia supernovae in the Hubble flow are anchored on local distance measurements to sources that are very nearby. We described how this configuration could be built in a perturbed universe where lumpiness is described as small perturbations on top of a flat Friedmann-Lema{\i}tre Robertson-Walker spacetime. We show that there is a non-negligible modification (about 11\%) to the background Friedmann-Lema{\i}tre Robertson-Walker area distance due to the presence of inhomogeneities in the immediate neighbourhood of an observer. We find that the modification is sourced by the electric part of the Weyl tensor indicating a tidal deformation of the local spacetime of the observer. We show in detail how it could impact the calibration of the Type Ia supernova absolute magnitude in the Hubble flow. We show that it could potentially resolve the Type Ia supernova absolute magnitude and Hubble tensions simultaneously without the need for early or late dark energy.Comment: Version accepted for publication by JCA

Emergence of smooth distance and apparent magnitude in a lumpy Universe

The standard interpretation of observations such as the peak apparent magnitude of Type Ia supernova made from one location in a lumpy Universe is based on the idealised Friedmann-Lema\^itre Robertson-Walker spacetime. All possible corrections to this model due to inhomogeneities are usually neglected. Here, we use the result from the recent concise derivation of the area distance in an inhomogeneous universe to study the monopole and Hubble residual of the apparent magnitude of Type Ia supernovae. We find that at low redshifts, the background FLRW spacetime model of the apparent magnitude receives corrections due to relative velocity perturbation in the observed redshift. We show how this velocity perturbation could contribute to a variance in the Hubble residual and how it could impact the calibration of the absolute magnitude of the Type Ia supernova in the Hubble flow. We also show that it could resolve the tension in the determination of the Hubble rate from the baryon acoustic oscillation and local measurements.Comment: Version accepted for publication by CQ

Sources of Anchor Data and Adjustment Amounts in the Valuation of Residential Properties

This paper ascertained how valuers generate anchor data based on past valuations experiences and how adjustments were made on the anchors to obtain capital values of residential properties. From a Total population of 260 registered firms, 164 were located. Yamane’s (1967) formula with 0.05 sampling error was adopted in determining sample size. It was found that sources of anchor and what valuers have been adjusting for varies. Additionally, generating anchor data from local experts was more common than from firms’ records; while general adjustment of anchor for differences in identified attributes has highest adoption rate (92.3%). Previous value experience of subject property is the most common of considered anchor sources. Externally generated anchor ranked higher in use than internally generated anchor; but ranked lower in terms of adjustment. Adjusting without identification of differences in attributes should be avoided to prevent misrepresentation of comparable and loss of clients’ confidence. Keywords: Adjustment, anchor, data, valuation, residential property

xPand: An algorithm for perturbing homogeneous cosmologies

In this paper, we develop in detail a fully geometrical method for deriving perturbation equations about a spatially homogeneous background. This method relies on the 3+1 splitting of the background space-time and does not use any particular set of coordinates: it is implemented in terms of geometrical quantities only, using the tensor algebra package xTensor in the xAct distribution along with the extension for perturbations xPert. Our algorithm allows one to obtain the perturbation equations for all types of homogeneous cosmologies, up to any order and in all possible gauges. As applications, we recover the well-known perturbed Einstein equations for Friedmann-Lemaitre-Robertson-Walker cosmologies up to second order and for Bianchi I cosmologies at first order. This work paves the way to the study of these models at higher order and to that of any other perturbed Bianchi cosmologies, by circumventing the usually too cumbersome derivation of the perturbed equations.Comment: 21 pages, 2 figure

The galaxy bias at second order in general relativity with Non-Gaussian initial conditions

We present a systematic study of galaxy bias in the presence of primordial non-Gaussianity in General Relativity (GR) at second order in perturbation theory. The non-linearity of the Poisson equation in GR and primordial non-Gaussianity are consistently included. We show that the inclusion of non-local primordial non-Gaussianity in addition to local non-Gaussianity is important to show the absence of the modulation of small scale clustering by the long-wavelength mode in the single field slow-roll inflation. We study the bispectrum of the relativistic galaxy density in several gauges and identify the effect of primordial non-Gaussianity and GR corrections.Comment: 1+14+4 pages, two figures. Version accepted for publication, the conclusion and discussion remain unchange

A study of holographic superconductors

Includes bibliographical references (leaves 61-68).The proposal that the physics of quantum critical phase transition in strongly coupled condensed matter systems can be described by a gravitational theory within the frame work of gauge/gravity correspondence is investigated more extensively for s-wave superconductors. We consider a gravitational theory with a black hole solution in anti de Sitter spacetime, coupled to an Abelian-Higgs system in (d + 1)-dimensions. A wide range of negative mass squared for the scalar field that satisfied the Brietenlolmer-Freedman stability bound and the unitarity bound are considered in the probe limit. The dependence of the some of the physical quantities on the scaling dimensions of the dual condensates were thoroughly investigated. We observe that the holographic superconductors can be consistently classified into two, based on the scaling dimensions and the charge of the dual condensates. Holographic superconductors of dimension λ- exhibit features of type II superconductors while those of dimension λ+ show features of type 1. The validity of this classification was confirmed by solving the bulk equations of motion perturbatively near the quantum critical point in order to calculate the superconducting characteristic lengths at a fixed charge q. The results show that there is a critical scaling dimension beyond which a holographic superconductor behave as type I and below this value it is a type II. The properties of holographic superconductors presented in this report are in qualitative agreement with the Ginzburg-Landau theory

Consequences of using a smooth cosmic distance in a lumpy Universe. I.

How do we appropriately fit a model based on an idealised Friedmann-Lemaˆıtre Robertson-Walker spacetime to observations made from a single location in a lumpy Universe? We address this question for surveys that measure the imprints of the baryon acoustic oscillation in galaxy distribution and the peak apparent magnitude of the Type Ia supernova. These observables are related to the cosmological model through the Alcock-Paczy´nski parameters and the distance-redshift relation. Using the corresponding inhomogeneous spacetime expressions of these as observed data, we perform a parameter inference assuming that the background Friedmann-Lemaˆıtre Robertson-Walker model is the correct model of the Universe. This process allows us to estimate the best fit Hubble rate and the deceleration parameter. We find that the inferred Hubble rate from the monopole of the AlcockPaczy´nski parameters is in tension with the Hubble rate determined using the distance-redshift relation

The influence of structure formation on the evolution of the universe

Includes abstract.Includes bibliographical references.The next generation of telescopes will usher in a new era of precision cosmology capable of determining key parameters of a cosmological model to percent level and beyond. For this to be effective, the theoretical model must be understood to at least the same level of precision. A range of subtle physical spacetime effcts remain to be explored theoretically, for example, the effect of backreaction on cosmological observables. A good understanding of this effect is paramount given that it is a consequence of any space-time theory of gravity. We provide a comprehensive study of this effect from the perspective of geometric averaging on a hyper-surface and averaging on the celestial sphere. We concentrate on Friedmann-Lemaitre-Robertson-Walker spacetime with small perturbation up to non-linear order . This enables us to quantify by how much this effect could change the standard model interpretation of the universe. We study in great detail key parameters of the standard model, Hubble rate, deceleration parameter and area distance

Cosmological evolution of the gravitational entropy of the large-scale structure

We consider the entropy associated with the large-scale structure of the Universe in the linear regime, where the Universe can be described by a perturbed Friedmann-Lema\^itre spacetime. In particular, we compare two different definitions proposed in the literature for the entropy using a spatial averaging prescription. For one definition, the entropy of the large-scale structure for a given comoving volume always grows with time, both for a CDM and a $\Lambda$CDM model. In particular, while it diverges for a CDM model, it saturates to a constant value in the presence of a cosmological constant. The use of a light-cone averaging prescription in the context of the evaluation of the entropy is also discussed.Comment: 10 pages, 4 figures. Presentation improved, typos corrected, previous subsection III.B merged with subsection II.C, comments, clarifications and a reference added. Version accepted for publication in GR