2,779 research outputs found
Entropy measures as geometrical tools in the study of cosmology
Classical chaos is often characterized as exponential divergence of nearby
trajectories. In many interesting cases these trajectories can be identified
with geodesic curves. We define here the entropy by with
being the distance between two nearby geodesics. We derive an
equation for the entropy which by transformation to a Ricatti-type equation
becomes similar to the Jacobi equation. We further show that the geodesic
equation for a null geodesic in a double warped space time leads to the same
entropy equation. By applying a Robertson-Walker metric for a flat
three-dimensional Euclidian space expanding as a function of time, we again
reach the entropy equation stressing the connection between the chosen entropy
measure and time. We finally turn to the Raychaudhuri equation for expansion,
which also is a Ricatti equation similar to the transformed entropy equation.
Those Ricatti-type equations have solutions of the same form as the Jacobi
equation. The Raychaudhuri equation can be transformed to a harmonic oscillator
equation, and it has been shown that the geodesic deviation equation of Jacobi
is essentially equivalent to that of a harmonic oscillator. The Raychaudhuri
equations are strong geometrical tools in the study of General Relativity and
Cosmology. We suggest a refined entropy measure applicable in Cosmology and
defined by the average deviation of the geodesics in a congruence.Comment: Final Versio
Information Gains from Cosmological Probes
In light of the growing number of cosmological observations, it is important
to develop versatile tools to quantify the constraining power and consistency
of cosmological probes. Originally motivated from information theory, we use
the relative entropy to compute the information gained by Bayesian updates in
units of bits. This measure quantifies both the improvement in precision and
the 'surprise', i.e. the tension arising from shifts in central values. Our
starting point is a WMAP9 prior which we update with observations of the
distance ladder, supernovae (SNe), baryon acoustic oscillations (BAO), and weak
lensing as well as the 2015 Planck release. We consider the parameters of the
flat CDM concordance model and some of its extensions which include
curvature and Dark Energy equation of state parameter . We find that,
relative to WMAP9 and within these model spaces, the probes that have provided
the greatest gains are Planck (10 bits), followed by BAO surveys (5.1 bits) and
SNe experiments (3.1 bits). The other cosmological probes, including weak
lensing (1.7 bits) and {} measures (1.7 bits), have contributed
information but at a lower level. Furthermore, we do not find any significant
surprise when updating the constraints of WMAP9 with any of the other
experiments, meaning that they are consistent with WMAP9. However, when we
choose Planck15 as the prior, we find that, accounting for the full
multi-dimensionality of the parameter space, the weak lensing measurements of
CFHTLenS produce a large surprise of 4.4 bits which is statistically
significant at the 8 level. We discuss how the relative entropy
provides a versatile and robust framework to compare cosmological probes in the
context of current and future surveys.Comment: 26 pages, 5 figure
How many quanta are there in a quantum spacetime?
Following earlier insights by Livine and Terno, we develop a technique for
describing quantum states of the gravitational field in terms of coarse grained
spin networks. We show that the number of nodes and links and the values of the
spin depend on the observables chosen for the description of the state. Hence
the question in the title of this paper is ill posed, unless further
information about what is been measured is given.Comment: 16 pages, 9 figure
Gravity and the Quantum
The goal of this article is to present a broad perspective on quantum gravity
for \emph{non-experts}. After a historical introduction, key physical problems
of quantum gravity are illustrated. While there are a number of interesting and
insightful approaches to address these issues, over the past two decades
sustained progress has primarily occurred in two programs: string theory and
loop quantum gravity. The first program is described in Horowitz's contribution
while my article will focus on the second. The emphasis is on underlying ideas,
conceptual issues and overall status of the program rather than mathematical
details and associated technical subtleties.Comment: A general review of quantum gravity addresed non-experts. To appear
in the special issue `Space-time Hundred Years Later' of NJP; J.Pullin and R.
Price (editors). Typos and an attribution corrected; a clarification added in
section 2.
Background Independent Quantum Gravity: A Status Report
The goal of this article is to present an introduction to loop quantum
gravity -a background independent, non-perturbative approach to the problem of
unification of general relativity and quantum physics, based on a quantum
theory of geometry. Our presentation is pedagogical. Thus, in addition to
providing a bird's eye view of the present status of the subject, the article
should also serve as a vehicle to enter the field and explore it in detail. To
aid non-experts, very little is assumed beyond elements of general relativity,
gauge theories and quantum field theory. While the article is essentially
self-contained, the emphasis is on communicating the underlying ideas and the
significance of results rather than on presenting systematic derivations and
detailed proofs. (These can be found in the listed references.) The subject can
be approached in different ways. We have chosen one which is deeply rooted in
well established physics and also has sufficient mathematical precision to
ensure that there are no hidden infinities. In order to keep the article to a
reasonable size, and to avoid overwhelming non-experts, we have had to leave
out several interesting topics, results and viewpoints; this is meant to be an
introduction to the subject rather than an exhaustive review of it.Comment: 125 pages, 5 figures (eps format), the final version published in CQ
The Physics of Timelessness
The nature of time is yet to be fully grasped and finally agreed upon among physicists, philosophers, psychologists and scholars from various disciplines. Present paper takes clue from the known assumptions of time as - movement, change, becoming - and the nature of time will be thoroughly discussed.
The real and unreal existences of time will be pointed out and presented. The complex number notation of nature of time will be put forward. Natural scientific systems and various cosmic processes will be identified as constructing physical form of time and the physical existence of time will be designed.
The finite and infinite forms of physical time and classical, quantum and cosmic times will be delineated and their mathematical constructions and loci will be narrated.
Thus the physics behind time-construction, time creation and time-measurement will be given.
Based on these developments the physics of Timelessness will be developed and presented
Loop Quantum Gravity
The problem of finding the quantum theory of the gravitational field, and
thus understanding what is quantum spacetime, is still open. One of the most
active of the current approaches is loop quantum gravity. Loop quantum gravity
is a mathematically well-defined, non-perturbative and background independent
quantization of general relativity, with its conventional matter couplings. The
research in loop quantum gravity forms today a vast area, ranging from
mathematical foundations to physical applications. Among the most significative
results obtained are: (i) The computation of the physical spectra of
geometrical quantities such as area and volume; which yields quantitative
predictions on Planck-scale physics. (ii) A derivation of the
Bekenstein-Hawking black hole entropy formula. (iii) An intriguing physical
picture of the microstructure of quantum physical space, characterized by a
polymer-like Planck scale discreteness. This discreteness emerges naturally
from the quantum theory and provides a mathematically well-defined realization
of Wheeler's intuition of a spacetime ``foam''. Long standing open problems
within the approach (lack of a scalar product, overcompleteness of the loop
basis, implementation of reality conditions) have been fully solved. The weak
part of the approach is the treatment of the dynamics: at present there exist
several proposals, which are intensely debated. Here, I provide a general
overview of ideas, techniques, results and open problems of this candidate
theory of quantum gravity, and a guide to the relevant literature.Comment: Review paper written for the electronic journal `Living Reviews'. 34
page
- …