HAMILTONIAN GENERAL RELATIVITY IN FINITE SPACE AND COSMOLOGICAL POTENTIAL PERTURBATIONS

2006 ◽  
Vol 21 (28n29) ◽  
pp. 5957-5990 ◽  
Author(s):  
B. M. BARBASHOV ◽  
V. N. PERVUSHIN ◽  
A. F. ZAKHAROV ◽  
V. A. ZINCHUK
Keyword(s):  
General Relativity ◽  
Background Radiation ◽  
Hamiltonian Formulation ◽  
Hamiltonian Reduction ◽  
Specific Reference ◽  
Schwarzschild Solution ◽  
Scale Invariant ◽  
Cosmological Perturbation ◽  
Cosmological Perturbation Theory ◽  
Finite Space

The Hamiltonian formulation of general relativity is considered in finite space–time and a specific reference frame given by the diffeo-invariant components of the Fock simplex in terms of the Dirac–ADM variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are constructed by the separation of the cosmological scale factor a(x0) and its identification with the spatial averaging of the metric determinant, so that the dimension of the kinemetric group of diffeomorphisms coincides with the dimension of a set of variables whose velocities are removed by the Gauss-type constraints in accordance with the second Nöther theorem. This coincidence allows us to solve the energy constraint, fulfil Dirac's Hamiltonian reduction, and to describe the potential perturbations in terms of the Lichnerowicz scale-invariant variables distinguished by the absence of the time derivatives of the spatial metric determinant. It was shown that the Hamiltonian version of the cosmological perturbation theory acquires attributes of the theory of superfluid liquid, and it leads to a generalization of the Schwarzschild solution. The astrophysical application of this approach to general relativity is considered under supposition that the Dirac–ADM Hamiltonian frame is identified with that of the Cosmic Microwave Background radiation distinguished by its dipole component in the frame of an Earth observer.

scholarly journals Gauge invariant canonical cosmological perturbation theory with geometrical clocks in extended phase-space — A review and applications

2018 ◽  
Vol 27 (08) ◽  
pp. 1830005 ◽  
Author(s):  
Kristina Giesel ◽  
Adrian Herzog
Keyword(s):  
General Relativity ◽  
Perturbation Theory ◽  
Phase Space ◽  
Hamiltonian Formulation ◽  
Cosmological Perturbations ◽  
Cosmological Perturbation ◽  
Common Procedure ◽  
Gauge Invariant ◽  
Cosmological Perturbation Theory ◽  
Starting Point

The theory of cosmological perturbations is a well-elaborated field and has been successfully applied, e.g. to model the structure formation in our universe and the prediction of the power spectrum of the cosmic microwave background. To deal with the diffeomorphism invariance of general relativity, one generally introduces combinations of the metric and matter perturbations, which are gauge invariant up to the considered order in the perturbations. For linear cosmological perturbations, one works with the so-called Bardeen potentials widely used in this context. However, there exists no common procedure to construct gauge invariant quantities also for higher-order perturbations. Usually, one has to find new gauge invariant quantities independently for each order in perturbation theory. With the relational formalism introduced by Rovelli and further developed by Dittrich and Thiemann, it is in principle possible to calculate manifestly gauge invariant quantities, that is quantities that are gauge invariant up to arbitrary order once one has chosen a set of so-called reference fields, often also called clock fields. This article contains a review of the relational formalism and its application to canonical general relativity following the work of Garcia, Pons, Sundermeyer and Salisbury. As the starting point for our application of this formalism to cosmological perturbation theory, we also review the Hamiltonian formulation of the linearized theory for perturbations around FLRW spacetimes. The main aim of our work will be to identify clock fields in the context of the relational formalism that can be used to reconstruct quantities like the Bardeen potential as well as the Mukhanov–Sasaki variable. This requires a careful analysis of the canonical formulation in the extended ADM-phase-space where lapse and shift are treated as dynamical variables. The actual construction of such observables and further investigations thereof will be carried out in our companion paper.

scholarly journals Enlightening the CSL model landscape in inflation

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Gabriel León ◽  
Gabriel R. Bengochea
Keyword(s):  
Momentum Tensor ◽  
Scale Invariant ◽  
Cosmological Perturbation ◽  
Cosmological Perturbation Theory ◽  
Spacetime Curvature ◽  
Cosmological Context ◽  
Generating Operator ◽  
Spontaneous Localization ◽  
Continuous Spontaneous Localization ◽  
Covariant Version

AbstractWe propose a novel realization for the natural extrapolation of the continuous spontaneous localization (CSL) model, in order to account for the origin of primordial inhomogeneities during inflation. This particular model is based on three main elements: (i) the semiclassical gravity framework, (ii) a collapse-generating operator associated to a relativistic invariant scalar of the energy-momentum tensor, and (iii) an extension of the CSL parameter(s) as a function of the spacetime curvature. Furthermore, employing standard cosmological perturbation theory at linear order, and for a reasonable range within the parameter space of the model, we obtain a nearly scale invariant power spectrum consistent with recent observational CMB data. This opens a vast landscape of different options for the application of the CSL model to the cosmological context, and possibly sheds light on searches for a full covariant version of the CSL theory.

scholarly journals PROBING FOR DYNAMICS OF DARK-ENERGY IN MASS VARYING NEUTRINOS: COSMIC MICROWAVE BACKGROUND RADIATION AND LARGE SCALE STRUCTURE

2007 ◽  
Vol 22 (25n28) ◽  
pp. 2131-2142 ◽  
Author(s):  
YONG-YEON KEUM
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
Cosmic Microwave Background ◽  
Large Scale ◽  
Background Radiation ◽  
Coupling Parameter ◽  
Cosmic Acceleration ◽  
Microwave Background ◽  
Cosmological Perturbation ◽  
Cosmological Perturbation Theory

We present cosmological perturbation theory in neutrino probe interacting dark-energy models, and calculate cosmic microwave background anisotropies and matter power spectrum. In these models, the evolution of the mass of neutrinos is determined by the quintessence scalar field, which is responsible for the cosmic acceleration today. We consider several types of scalar field potentials and put constraints on the coupling parameter between neutrinos and dark energy. Assuming the flatness of the universe, the constraint we can derive from the current observation is Σ mν < 0.87eV at the 95 % confidence level for the sum over three species of neutrinos.

General Relativity

2019 ◽  
Author(s):  
Steven Carlip
Keyword(s):  
General Relativity ◽  
High Energy Physics ◽  
Hamiltonian Formulation ◽  
Experimental Tests ◽  
High Energy ◽  
Gravitational Energy ◽  
Field Equations ◽  
Physics First ◽  
Condensed Matter Theory ◽  
Introductory Textbooks

This work is a short textbook on general relativity and gravitation, aimed at readers with a broad range of interests in physics, from cosmology to gravitational radiation to high energy physics to condensed matter theory. It is an introductory text, but it has also been written as a jumping-off point for readers who plan to study more specialized topics. As a textbook, it is designed to be usable in a one-quarter course (about 25 hours of instruction), and should be suitable for both graduate students and advanced undergraduates. The pedagogical approach is “physics first”: readers move very quickly to the calculation of observational predictions, and only return to the mathematical foundations after the physics is established. The book is mathematically correct—even nonspecialists need to know some differential geometry to be able to read papers—but informal. In addition to the “standard” topics covered by most introductory textbooks, it contains short introductions to more advanced topics: for instance, why field equations are second order, how to treat gravitational energy, what is required for a Hamiltonian formulation of general relativity. A concluding chapter discusses directions for further study, from mathematical relativity to experimental tests to quantum gravity.

scholarly journals Measurement and Implications of the Cosmic Microwave Background Spectrum

1996 ◽  
Vol 168 ◽  
pp. 17-29
Author(s):  
John C. Mather
Keyword(s):  
Background Radiation ◽  
Far Infrared ◽  
Big Bang ◽  
Scale Invariant ◽  
Background Spectrum ◽  
Nasa Goddard Space ◽  
Wide Range ◽  
Infrared Background ◽  
Microwave Radiometers ◽  
The Big Bang

The Cosmic Background Explorer (COBE) was developed by NASA Goddard Space Flight Center to measure the diffuse infrared and microwave radiation from the early universe. It also measured emission from nearby sources such as the stars, dust, molecules, atoms, ions, and electrons in the Milky Way, and dust and comets in the Solar System. It was launched 18 November 1989 on a Delta rocket, carrying one microwave instrument and two cryogenically cooled infrared instruments. The Far Infrared Absolute Spectrophotometer (FIRAS) mapped the sky at wavelengths from 0.01 to 1 cm, and compared the CMBR to a precise blackbody. The spectrum of the CMBR differs from a blackbody by less than 0.03%. The Differential Microwave Radiometers (DMR) measured the fluctuations in the CMBR originating in the Big Bang, with a total amplitude of 11 parts per million on a 10° scale. These fluctuations are consistent with scale-invariant primordial fluctuations. The Diffuse Infrared Background Experiment (DIRBE) spanned the wavelength range from 1.2 to 240 μm and mapped the sky at a wide range of solar elongation angles to distinguish foreground sources from a possible extragalactic Cosmic Infrared Background Radiation (CIBR). In this paper we summarize the COBE mission and describe the results from the FIRAS instrument. The results from the DMR and DIRBE were described by Smoot and Hauser at this Symposium.

scholarly journals HOLLOWGRAPHY DRIVEN HOLOGRAPHY: BLACK HOLE WITH VANISHING VOLUME INTERIOR

2010 ◽  
Vol 19 (14) ◽  
pp. 2345-2351 ◽  
Author(s):  
AHARON DAVIDSON ◽  
ILYA GURWICH
Keyword(s):  
Phase Transition ◽  
General Relativity ◽  
Black Hole ◽  
Degrees Of Freedom ◽  
Schwarzschild Solution ◽  
Entropy Formula ◽  
Gravitational Theories ◽  
Hollow Interior ◽  
Spatial Volume ◽  
Self Similar

Hawking–Bekenstein entropy formula seems to tell us that no quantum degrees of freedom can reside in the interior of a black hole. We suggest that this is a consequence of the fact that the volume of any interior sphere of finite surface area simply vanishes. Obviously, this is not the case in general relativity. However, we show that such a phenomenon does occur in various gravitational theories which admit a spontaneously induced general relativity. In such theories, due to a phase transition (one-parameter family degenerates) which takes place precisely at the would-have-been horizon, the recovered exterior Schwarzschild solution connects, by means of a self-similar transition profile, with a novel "hollow" interior exhibiting a vanishing spatial volume and a locally varying Newton constant. This constitutes the so-called "hollowgraphy" driven holography.

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