Related papers: Measure and Probability in Cosmology
A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is shown that such an order that satisfies some plausible axioms can be represented by a quantum probability in two cases: pure state and uniform…
In generic models of cosmological inflation, quantum fluctuations strongly influence the spacetime metric and produce infinitely many regions where the end of inflation (reheating) is delayed until arbitrarily late times. The geometry of…
Inflationary models of the early universe provide a natural mechanism for the formation of large scale structure. This success brings to forefront the question of naturalness: Does a sufficiently long slow roll inflation occur generically…
The cosmological constant, i.e., the energy density stored in the true vacuum state of all existing fields in the Universe, is the simplest and the most natural possibility to describe the current cosmic acceleration. However, despite its…
There has not been an established mathematical measure of evidence. Some Bayesians have argued that probability can be an objectively correct measure of ``rational degrees of belief,'' which we do not distinguish from evidence. However,…
This paper is a pedagogical introduction to models of gravity and how to constrain them through cosmological observations. We focus on the Horndeski scalar-tensor theory and on the quantities that can be measured with a minimum of…
Counts-in-cells (CIC) measurements contain a wealth of cosmological information yet are seldom used to constrain theories. Although we can predict the shape of the distribution for a given cosmology, to fit a model to the observed CIC…
The "new standard cosmology", based on the theory of inflation, has very impressive observational support. I review some outstanding problems of the new cosmology and the global view of the universe -- the multiverse -- that it suggests. I…
Modern cosmology relies on the assumption of large-scale isotropy and homogeneity of the Universe. However, locally the Universe is inhomogeneous and anisotropic. So, how can local measurements (at the 100 Mpc scale) be used to determine…
Homogeneity is a crucial, but poorly tested, assumption in cosmology. We introduce a new approach which allows us to place limits on the presence of localized structures within essentially our entire observable volume, using cosmic…
In a previous work General Relativity has been presented as a microscopic theory of finite and discrete point-like fields that we associate to a classical description of gravitons. The standard macroscopic continuous field is retrieved as…
The statistical uncertainty in measuring the primordial density perturbations on a given comoving scale is dictated by the number of independent regions of that scale that are accessible to an observer. This number varies with cosmic time…
In quantum logic, i.e., within the structure of the Hilbert lattice imposed on all closed linear subspaces of a Hilbert space, the assignment of truth values to quantum propositions (i.e., experimentally verifiable propositions relating to…
In a fully inhomogeneous, anisotropic cosmological simulation performed by solving Einstein's equations with numerical relativity, we find a local measurement of the effective Hubble parameter differs by less than 1\% compared to the global…
We consider a linear Hamiltonian system consisting of a classical particle and a scalar field describing by the wave or Klein-Gordon equations with variable coefficients. The initial data of the system are supposed to be a random function…
What can be measured by an observer in our universe? We address this question by constructing an algebra of gravitationally-dressed observables accessible to a comoving observer in FLRW spacetimes that are asymptotically de Sitter in the…
Even if the luminosity distance as a function of redshift is obtained accurately using, for example, Type Ia supernovae, the equation of state of the Universe cannot be determined uniquely but depends on one free parameter $\Omega_{k0}…
Recent advances in observational cosmology are changing the way we view the nature of time. In general relativity, the freedom in choosing a time hypersurface has hampered the implementation of the theory. Fortunately, Hamilton-Jacobi…
One of the basic peoblems of quantum cosmology is the problem of time. Various solutions have been proposed for this problem. One approach is to use the Bohmian time. Another Approach is to use the probabilistic time which was recently…
The paper uses geometrical arguments to derive equations with relevance for cosmology; 5-dimensional spacetime is assumed because it has been shown in other works to provide a setting for significant unification of different areas of…