Related papers: Conformal Methods in Mathematical Cosmology
In this thesis, the symmetry structure of gravitational theories at null infinity is studied further, in the case of pure gravity in four dimensions and also in the case of Einstein-Yang-Mills theory in $d$ dimensions with and without a…
General Relativity and the $\Lambda$CDM framework are currently the standard lore and constitute the concordance paradigm. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the…
Penrose's idea of asymptotic flatness provides a framework for understanding the asymptotic structure of gravitational fields of isolated systems at null infinity. However, the studies of the asymptotic behaviour of fields near spatial…
In this paper we apply the ideas put forward by Ho\v{r}ava, and introduce anisotropic transformations to cosmology. We start with the Kantowski-Sachs cosmological model and impose anisotropic transformation invariance on the minisuperspace…
Standard cosmology has long been plagued by a number of persistent problems. The origin of the apparent acceleration of the cosmic expansion remains enigmatic. The cosmological constant has been reintroduced as a free parameter with a value…
We use the quantum unimodular theory of gravity to relate the value of the cosmological constant, $\Lambda$, and the energy scale for the emergence of cosmological classicality. The fact that $\Lambda$ and unimodular time are complementary…
A quantum-field model of the conformally flat space is formulated using a standard field-theoretical technique, a probability interpretation and a way to establish the classical limit. The starting point is the following: after conformal…
The high precision attained by cosmological data in the last few years has increased the interest in exact solutions. Analytic expressions for solutions in the Standard Model are presented here for all combinations of $\Lambda = 0$,…
In this manuscript, we show that three fundamental building blocks are supporting the Cosmological Principle. The first of them states that there is a special frame in the universe where the spatial geometry is intrinsically homogeneous and…
We propose a new cosmological model with a time-dependent cosmological constant ($\Lambda\propto 1/t^2$), which starting at the Planck time as $\Lambda_{Pl}\sim M^2_{Pl}$, evolves to the present-day allowed value of…
We simplify the gravitational equations which apply in accelerating spacetimes and are consistent with the cosmological principle. Solutions to these equations should be tantamount to all order re-summations of the perturbative leading…
The boundary behavior of the singular Yamabe problem has been extensively studied near sufficiently smooth boundaries, while less is known about the asymptotic behavior of solutions near singular boundaries. In this paper, we study the…
Local conformal transformations are known as a useful tool in various applications of the gravitational theory, especially in cosmology. We describe some new aspects of these transformations, in particular using them for derivation of…
A complete model of the universe needs at least three parts: (1) a complete set of physical variables and dynamical laws for them, (2) the correct solution of the dynamical laws, and (3) the connection with conscious experience. In quantum…
Time-symmetric cosmological theories, in which the initial and final states are arranged to have similar features or are independently fixed, have been quite extensively discussed in the literature. However, a more general and perhaps more…
An intrinsic definition in terms of conformal capacity is proposed for the conformal type of a Carnot--Carath\'eodory space (parabolic or hyperbolic). Geometric criteria of conformal type are presented. They are closely related to the…
The Cosmological Principle (CP) -- the notion that the Universe is spatially isotropic and homogeneous on large scales -- underlies a century of progress in cosmology. It is conventionally formulated through the…
We discuss how entropy bounds, which are not respected in the standard cosmology, constrain the parameters of a previously suggested cosmology with a finite total mass. In that alternative cosmology the matter density was postulated to be a…
The geometrical structure of a real four-dimensional space-time has been extended via the Conservation group with basic field variable being the orthonormal tetrad. Field equations were obtained from a variational principle which is…
We discuss a class of (local and non-local) theories of gravity that share same properties: i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; ii) the on-shell action of such a theory vanishes and iii)…