scholarly journals Conformal equivalence between certain geometries in dimension $\mathbf 6$ and $\mathbf 7$

2008 ◽  
Vol 15 (4) ◽  
pp. 631-640 ◽  
Author(s):  
Richard Cleyton ◽  
Stefan Ivanov
Keyword(s):  
Conformal Equivalence

The interaction between dark energy and dark matter and its connection to the modified gravity

2015 ◽  
Vol 30 (28n29) ◽  
pp. 1545012
Author(s):  
Jian-Hua He ◽  
Bin Wang
Keyword(s):  
Analytic Form ◽  
Rate Function ◽  
Einstein Frame ◽  
Linear Perturbation ◽  
Jordan Frame ◽  
Expansion Of The Universe ◽  
Text Model ◽  
Conformal Equivalence ◽  
The Universe ◽  
Dilation Rate

We review the conformal equivalence in describing the background expansion of the universe by [Formula: see text] gravity both in the Jordan frame and the Einstein frame. In the Jordan frame, we present the general analytic expression for [Formula: see text] models that have the same expansion history as the [Formula: see text]CDM model. This analytic form can provide further insights on how cosmology can be used to test the [Formula: see text] gravity at the largest scales. Moreover we present a systematic and self-consistent way to construct the viable [Formula: see text] model in Jordan frame using the mass dilation rate function from the Einstein frame through the conformal transformation. In addition, we extend our study to the linear perturbation theories and we further exhibit the equivalence of the [Formula: see text] gravity presented in the Jordan frame and Einstein frame in the perturbed space–time. We argue that this equivalence has solid physics root.

Geometric phase of cosmological scalar and tensor perturbations in f(R) gravity

2018 ◽  
Vol 33 (14) ◽  
pp. 1850077
Author(s):  
Hamideh Balajany ◽  
Mohammad Mehrafarin
Keyword(s):  
Scalar Field ◽  
Harmonic Oscillator ◽  
Geometric Phase ◽  
Berry Phase ◽  
Time Dependent ◽  
Einstein Theory ◽  
Tensor Perturbations ◽  
Cosmological Scalar ◽  
Conformal Equivalence

By using the conformal equivalence of f(R) gravity in vacuum and the usual Einstein theory with scalar-field matter, we derive the Hamiltonian of the linear cosmological scalar and tensor perturbations in f(R) gravity in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes as a Lewis–Riesenfeld phase.

scholarly journals Remarks on the Elliptic Case of the Mapping Theorem for Simply-Connected Riemann Surfaces

1955 ◽  
Vol 9 ◽  
pp. 17-20 ◽  
Author(s):  
Maurice Heins
Keyword(s):  
Riemann Surface ◽  
Meromorphic Function ◽  
Riemann Surfaces ◽  
Simple Pole ◽  
Conformal Map ◽  
Elliptic Case ◽  
Extended Plane ◽  
Simply Connected ◽  
Conformal Equivalence

It is well-known that the conformal equivalence of a compact simply-connected Riemann surface to the extended plane is readily established once it is shown that given a local uniformizer t(p) which carries a given point p0 of the surface into 0, there exists a function u harmonic on the surface save at p0 which admits near p0 a representation of the form(α complex 0; h harmonic at p0). For the monodromy theorem then implies the existence of a meromorphic function on the surface whose real part is u. Such a meromorphic function has a simple pole at p0 and elsewhere is analytic. It defines a univalent conformal map of the surface onto the extended plane.

Conformal equivalence of triangle meshes

2008 ◽  
Author(s):  
Boris Springborn ◽  
Peter Schröder ◽  
Ulrich Pinkall
Keyword(s):  
Triangle Meshes ◽  
Conformal Equivalence

QUANTUM CORRECTIONS HELP EINSTEIN GRAVITY EXIT GRACIOUSLY

1991 ◽  
Vol 06 (10) ◽  
pp. 861-867 ◽  
Author(s):  
J. PÉREZ-MERCADER
Keyword(s):  
Initial Period ◽  
Einstein Gravity ◽  
Bubble Nucleation ◽  
Time Dependent ◽  
Quantum Corrections ◽  
Exponential Potential ◽  
Exit Problem ◽  
Conformal Equivalence ◽  
The Universe ◽  
Natural Way

We exploit the conformal equivalence between the 1-loop corrected Einstein gravity coupled to a scalar field, and linear Einstein gravity with an exponential potential, to show how the Graceful Exit Problem is solved in the context of this theory in a natural and simple way. What emerges is a scenario with a chaotic initial period followed by an era of old inflation. The resulting bubble nucleation rate is time-dependent in such a way that the second inflationary period, helped by the chaotic period, brings the Universe out of its inflationary era in a self-regulated and natural way.

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