# Our picks for second quarter 2009 MIP (most important QG paper)

## Which will prove most valuable for future research? (Select several if you wish.)

20.0%

60.0%

40.0%

20.0%

20.0%

20.0%

20.0%

40.0%
9. ### A geometric perspective on singularity resolution and uniqueness in LQC (Corichi Singh)

20.0%
1. Jun 30, 2009

### marcus

Here are some background independent QG papers which appeared in the 2nd quarter (April-June) of this year, for us to evaluate and try predicting how they will do. The poll is set up to accept multiple choices. Please check off the paper or papers you predict will have the most significant impact on future QG research. If you have one to propose that is not on the list, you can post the arxiv link, title and author(s) on this thread, to be counted as a "write-in".
(vocabulary lookups if desired: relation exponential quantization momentum degrees of freedom black hole )

http://arxiv.org/abs/0905.3168
http://arxiv.org/cits/0905.3168
Black hole entropy and SU(2) Chern-Simons theory
Jonathan Engle, Karim Noui, Alejandro Perez
4 pages, 1 figure
(Submitted on 19 May 2009)
"We show that the isolated horizon boundary condition can be treated in a manifestly SU(2) invariant manner. The symplectic structure of gravity with the isolated horizon boundary condition has an SU(2) Chern-Simons symplectic structure contribution at the horizon with level $$k=a_H/ (4\pi \beta \ell^2_p)$$. Upon quantization, state counting is expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere with marked points (defects). In the large black hole limit quantum horizon degrees of freedom can be modelled by a single intertwiner. The coupling constant of the defects with the Chern Simons theory on the horizon is precisely given by the ratio of the area contribution of the defect to the macroscopic area $$a_H$$, namely $$\lambda= 16\pi^2 \beta \ell^2_p (j(j+1))^{1/2}/a_H$$."

http://arxiv.org/abs/0906.5477
http://arxiv.org/cits/0906.5477
Scaling behaviour of three-dimensional group field theory
Jacques Magnen (CPHT), Karim Noui (LMPT), Vincent Rivasseau (LPT), Matteo Smerlak (CPT)
(Submitted on 30 Jun 2009)
"Group field theory is a generalization of matrix models, with triangulated pseudomanifolds as Feynman diagrams and state sum invariants as Feynman amplitudes. In this paper, we consider Boulatov's three-dimensional model and its Freidel-Louapre positive regularization (hereafter the BFL model) with a 'ultraviolet' cutoff, and study rigorously their scaling behavior in the large cutoff limit. We prove an optimal bound on large order Feynman amplitudes, which shows that the BFL model is perturbatively more divergent than the former. We then upgrade this result to the constructive level, using, in a self-contained way, the modern tools of constructive field theory: we construct the Borel sum of the BFL perturbative series via a convergent 'cactus' expansion, and establish the 'ultraviolet' scaling of its Borel radius. Our method shows how the 'sum over triangulations' in quantum gravity can be tamed rigorously, and paves the way for the renormalization program in group field theory."

http://arxiv.org/abs/0905.3627
http://arxiv.org/cits/0905.3627
Holomorphic Factorization for a Quantum Tetrahedron
Laurent Freidel, Kirill Krasnov, Etera R. Livine
(Submitted on 22 May 2009)
"We provide a holomorphic description of the Hilbert space H(j1,..,jn) of SU(2)-invariant tensors (intertwiners) and establish a holomorphically factorized formula for the decomposition of identity in H(j1,..,jn). Interestingly, the integration kernel that appears in the decomposition formula turns out to be the n-point function of bulk/boundary dualities of string theory. Our results provide a new interpretation for this quantity as being, in the limit of large conformal dimensions, the exponential of the Kahler potential of the symplectic manifold whose quantization gives H(j1,..,jn). For the case n=4, the symplectic manifold in question has the interpretation of the space of 'shapes' of a geometric tetrahedron with fixed face areas, and our results provide a description for the quantum tetrahedron in terms of holomorphic coherent states. We describe how the holomorphic intertwiners are related to the usual real ones by computing their overlap. The semi-classical analysis of these overlap coefficients in the case of large spins allows us to obtain an explicit relation between the real and holomorphic description of the space of shapes of the tetrahedron. Our results are of direct relevance for the subjects of loop quantum gravity and spin foams, but also add an interesting new twist to the story of the bulk/boundary correspondence."

http://arxiv.org/abs/0905.4916
http://arxiv.org/cits/0905.4916
Black holes in full quantum gravity
Kirill Krasnov, Carlo Rovelli
(Submitted on 29 May 2009)
"Quantum black holes have been studied extensively in quantum gravity and string theory, using various semiclassical or background dependent approaches. We explore the possibility of studying black holes in the full non-perturbative quantum theory, without recurring to semiclassical considerations, and in the context of loop quantum gravity. We propose a definition of a quantum black hole as the collection of the quantum degrees of freedom that do not influence observables at infinity. From this definition, it follows that for an observer at infinity a black hole is described by an SU(2) intertwining operator. The dimension of the Hilbert space of such intertwiners grows exponentially with the horizon area. These considerations shed some light on the physical nature of the microstates contributing to the black hole entropy. In particular, it can be seen that the microstates being counted for the entropy have the interpretation of describing different horizon shapes. The space of black hole microstates described here is related to the one arrived at recently by Engle, Noui and Perez, and sometime ago by Smolin, but obtained here directly within the full quantum theory."

http://arxiv.org/abs/0906.3947
http://arxiv.org/cits/0906.3947
Quantum gravity as sum over spacetimes
Jan Ambjorn, Jerzy Jurkiewicz, Renate Loll
67 pages, lectures given at the summer school "New Paths Towards Quantum Gravity", May 12-16 2008. To appear as part of a Springer Lecture Notes publication
(Submitted on 22 Jun 2009)
"A major unsolved problem in theoretical physics is to reconcile the classical theory of general relativity with quantum mechanics. These lectures will deal with an attempt to describe quantum gravity as a path integral over geometries known as 'Causal Dynamical Triangulations' (CDT)."

http://arxiv.org/abs/0905.1665
http://arxiv.org/cits/0905.1665
Fractal Quantum Space-Time
Leonardo Modesto
(Submitted on 11 May 2009)
"In this paper we calculated the spectral dimension of loop quantum gravity (LQG) using the scaling property of the area operator spectrum on spin-network states and using the scaling property of the volume and length operators on Gaussian states. We obtained that the spectral dimension of the spatial section runs from 1.5 to 3, and under particular assumptions from 2 to 3 across a 1.5 phase when the energy of a probe scalar field decreases from high to low energy in a fictitious time T. We calculated also the spectral dimension of space-time using the scaling of the area spectrum operator calculated on spin-foam models. The main result is that the effective dimension is 2 at the Planck scale and 4 at low energy. This result is consistent with two other approaches to non perturbative quantum gravity: 'causal dynamical triangulation' and 'asymptotically safe quantum gravity'. We studied the scaling properties of all the possible curvature invariants and we have shown that the singularity problem seems to be solved in the covariant formulation of quantum gravity in terms of spin-foam models. For a particular form of the scaling (or for a particular area operator spectrum) all the curvature invariants are regular also in the Trans-Planckian regime."

http://arxiv.org/abs/0906.3731
http://arxiv.org/cits/0906.3731
Prospects for constraining quantum gravity dispersion with near term observations
Giovanni Amelino-Camelia, Lee Smolin
(Submitted on 19 Jun 2009)
"We discuss the prospects for bounding and perhaps even measuring quantum gravity effects on the dispersion of light using the highest energy photons produced in gamma ray bursts measured by the Fermi telescope. These prospects are brigher than might have been expected as in the first 10 months of operation Fermi has reported so far eight events with photons over 100 MeV seen by its Large Area Telescope (LAT). We review features of these events which may bear on Planck scale phenomenology and we discuss the possible implications for the alternative scenarios for in-vacua dispersion coming from breaking or deforming of Poincare invariance. Among these are semi-conservative bounds, which rely on some relatively weak assumptions about the sources, on subluminal and superluminal in-vacuo dispersion. We also propose that it may be possible to look for the arrival of still higher energy photons and neutrinos from GRB's with energies in the range 10^14 - 10^17 eV. In some cases the quantum gravity dispersion effect would predict these arrivals to be delayed or advanced by days to months from the GRB, giving a clean separation of astrophysical source and spacetime propagation effects."

http://arxiv.org/abs/0904.4841
http://arxiv.org/cits/0904.4841
The quantization of unimodular gravity and the cosmological constant problem
Lee Smolin
22 pages
(Submitted on 30 Apr 2009)
"A quantization of unimodular gravity is described, which results in a quantum effective action which is also unimodular, ie a function of a metric with fixed determinant. A consequence is that contributions to the energy momentum tensor of the form of the metric times a spacetime constant, whether classical or quantum, are not sources of curvature in the equations of motion derived from the quantum effective action. This solves the first cosmological constant problem, which is suppressing the enormous contributions to the cosmological constant coming from quantum corrections. We discuss several forms of uniodular gravity and put two of them, including one proposed by Henneaux and Teitelboim, in constrained Hamiltonian form. The path integral is constructed from the latter. Furthermore, the second cosmological constant problem, which is why the measured value is so small, is also addressed by this theory. We argue that a mechanism first proposed by Ng and van Dam for suppressing the cosmological constant by quantum effects obtains at the semiclassical level."

http://arxiv.org/abs/0905.4949
http://arxiv.org/cits/0905.4949
A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
Alejandro Corichi, Parampreet Singh
(Submitted on 29 May 2009)
"We re-examine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties of spacetime and can be defined not only at the classical and effective level, but also at an operator level in the quantum theory. From the spectrum of the corresponding operators and their behavior in the effective loop quantum spacetime, we show that one can severely restrict the ambiguities in regularization of the quantum constraint and rule out unphysical choices. We analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the former case we show that the expansion rate operator has a bounded spectrum only for the so called improved quantization, a result which synergizes with uniqueness of this quantization as proved earlier. For the Bianchi-I spacetime, we show that out of the available choices, the expansion rate and shear operator are bounded for only one regularization of the quantum constraint. It turns out only this choice has a well defined quantum gravity scale."

Incidentally although it is too early for cite counts to mean much (if they ever do!) when I checked cites to date on these papers, the Engle-Noui-Perez paper was leading, followed by Corichi-Singh. Rivasseau will be giving a series of lectures along with Rovelli, Ashtekar and Baez, at the September QG school on the island of Corfu. The Rivasseau paper listed here may be related to what he will teach at the Corfu school.

Last edited: Jul 1, 2009
2. Jul 1, 2009

### Chronos

Tough choices, marcus. I very much like Loll's DT conjecture, so it was difficult to chose. I am disappointed she has not advanced it as much as I had hoped for over the past few years. I also believe Smolin is very close to the truth. We do live in interesting times.

3. Jul 1, 2009

### marcus

That we do! Exciting ones. Glad you found several papers that seemed like good bets to you, making it hard to pick just one.

4. Jul 2, 2009

### MTd2

It took me 3 days to decide...

5. Jul 2, 2009

### marcus

I really like your choices. They are extremely thoughtful. Maybe it helps to take three days to think it over.
For me, Rivasseau is a big deal. It is only 3D and by now I am filtering out almost all papers that are just 3D because that is too much a "toy model". But this is one 3D paper that struck me as the beginning of something new, that could go somewhere. You must have had, or may have had, a similar impression.

6. Jul 3, 2009

### MTd2

Part of the popularity of string theory it is that it induced many breakthroughs in mathematics, so it is nice to praise other models that tries to come up with new things in mathematics.

7. Jul 3, 2009

### marcus

In that respect I think immediately of the Freidel Krasnov Livine paper. They are all three outstanding! Etera Livine has shown up here at PF on rare occasions to correct something or respond to a question.

8. Jul 24, 2009

### marcus

We should start accumulating ideas for third quarter MIP candidates.
I think this by Krasnov is potentially important because it suggests a spinfoam mechanism whereby the running of couplings could arise. Weinberg has put the spotlight on renormalization and possible UV fixedpoint---asymsafe QFT. But that scenario still needs a background independent presentation of spacetime. I don't see how asymsafe QFT could evade the requirement for a background independent quantum geometry, like spinfoam, for the other fields to live on. Also there is this upcoming Perimeter confererence (with Weinberg) on Asmyptotic Safety, an even brighter spotlight.

So this is a timely motivation for research to look how to fit renormalization together with spinfoam and GFT (group field theory---a formalism used for spinfoam calculations).

http://arxiv.org/abs/0907.4064
Gravity as BF theory plus potential
Kirill Krasnov
7 pages, published in Proceedings of the Second Workshop on Quantum Gravity and Noncommutative Geometry (Lisbon, Portugal)
(Submitted on 23 Jul 2009)

"Spin foam models of quantum gravity are based on Plebanski's formulation of general relativity as a constrained BF theory. We give an alternative formulation of gravity as BF theory plus a certain potential term for the B-field. When the potential is taken to be infinitely steep one recovers general relativity. For a generic potential the theory still describes gravity in that it propagates just two graviton polarizations. The arising class of theories is of the type amenable to spin foam quantization methods, and, we argue, may allow one to come to terms with renormalization in the spin foam context."

The next paper elaborates on stuff given in John Barrett's invited talk at the Planck Scale conference at Wroclaw. One reason it may be valuable for future research is simply that, as we know, having a graphic calculus to facilitate calculating amplitudes can be a help.

http://arxiv.org/abs/0907.2440
Lorentzian spin foam amplitudes: graphical calculus and asymptotics
John W. Barrett, Richard J. Dowdall, Winston J. Fairbairn, Frank Hellmann, Roberto Pereira
30 pages
(Submitted on 14 Jul 2009)
"The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graphical calculus for the unitary representations of the Lorentz group. The asymptotics of this amplitude are studied in the limit when the representation parameters are large, for various cases of boundary data. It is shown that for boundary data corresponding to a Lorentzian simplex, the asymptotic formula has two terms, with phase plus or minus the Lorentzian signature Regge action for the 4-simplex geometry, multiplied by an Immirzi parameter. Other cases of boundary data are also considered, including a surprising contribution from Euclidean signature metrics."

To watch the video of Barrett's talk, go here:
http://www.ift.uni.wroc.pl/~planckscale/movie/index2.html
and scroll down to the sixth title. Or an alternative source is at Reni Durka's site.
http://www.ift.uni.wroc.pl/~rdurka/planckscale/index-video.php [Broken]
The Durka source is good quality, you can get whichever lecture you want directly in one click:
http://www.ift.uni.wroc.pl/~rdurka/planckscale/index-video.php?plik=http://panoramix.ift.uni.wroc.pl/~planckscale/video/Day2/2-6.flv&tytul=2.6%20Barrett [Broken]
And in addition the format is a bit larger.

Last edited by a moderator: May 4, 2017
9. Jul 27, 2009

### marcus

Continuing to list ideas for third quarter MIP candidates. This by Bahr and Dittrich:
http://arxiv.org/abs/0907.4323
Improved and Perfect Actions in Discrete Gravity
Benjamin Bahr, Bianca Dittrich
28 pages, 2 figures
(Submitted on 24 Jul 2009)
"We consider the notion of improved and perfect actions within Regge calculus. These actions are constructed in such a way that they - although being defined on a triangulation - reproduce the continuum dynamics exactly, and therefore capture the gauge symmetries of General Relativity. We construct the perfect action in three dimensions with cosmological constant, and in four dimensions for one simplex. We conclude with a discussion about Regge Calculus with curved simplices, which arises naturally in this context."

Here's some stuff about Benjamin Bahr (Thiemann PhD 2008.)
http://www.pet.cam.ac.uk/fellows/bab26/ [Broken]
Dittrich we know. Thiemann PhD, Perimeter postdoc, Loll postdoc, now at Potsdam AEI.
They are trying to make 4D Regge calculus work right (also with positive Lambda) and then develop 4D quantum Regge calculus. And they have gotten the (I think brilliant) idea to use simplices of constant curvature, simplices that are not flat.

Here are the two ideas we already have, for 3rd quarter nominees:

http://arxiv.org/abs/0907.4064
Gravity as BF theory plus potential
Kirill Krasnov
7 pages, published in Proceedings of the Second Workshop on Quantum Gravity and Noncommutative Geometry (Lisbon, Portugal)
(Submitted on 23 Jul 2009)

The Krasnov paper, you recall, had this in its abstract: "... may allow one to come to terms with renormalization in the spin foam context."

http://arxiv.org/abs/0907.2440
Lorentzian spin foam amplitudes: graphical calculus and asymptotics
John W. Barrett, Richard J. Dowdall, Winston J. Fairbairn, Frank Hellmann, Roberto Pereira
30 pages
(Submitted on 14 Jul 2009)

To watch the video of a related talk by Barrett talk, go here:
http://www.ift.uni.wroc.pl/~rdurka/planckscale/index-video.php?plik=http://panoramix.ift.uni.wroc.pl/~planckscale/video/Day2/2-6.flv&tytul=2.6%20Barrett [Broken]

To watch a recent talk by Dittrich go here:
http://www.ift.uni.wroc.pl/~rdurka/planckscale/index-video.php?plik=http://panoramix.ift.uni.wroc.pl/~planckscale/video/Day4/4-4.flv&tytul=4.4%20Dittrich [Broken]

These are Planck Scale conference videos posted by Remi Durka:
http://www.ift.uni.wroc.pl/~rdurka/planckscale/index-video.php [Broken]

Last edited by a moderator: May 4, 2017
10. Jul 28, 2009

### marcus

Definitely have to include Bianchi's paper in the poll! I started a thread on it in case anyone has comment. New development of Loop kinematics, standard quantization method, spin networks Bianchi-style turn out to be especially compatible with spinfoam dynamics.

"From this point of view, they are closer to the use that is made of spin networks as boundary states within the context of spin foams..." (page 11)

Here's the abstract:
http://arxiv.org/abs/0907.4388
Loop Quantum Gravity a la Aharonov-Bohm
Eugenio Bianchi
19 pages, 1 figure
(Submitted on 24 Jul 2009)
"The state space of Loop Quantum Gravity admits a decomposition into orthogonal subspaces associated to diffeomorphism equivalence classes of graphs. In this paper I discuss the possibility of obtaining this state space from the quantization of a topological field theory with many degrees of freedom. The starting point is a theory of locally-flat connections on a manifold which is non simply-connected because of the presence of a network of defects. The quantization procedure relies on standard field theoretical methods. The functional integral defining the scalar product is shown to reduce to a finite dimensional integral over moduli space. A non-trivial measure given by the Faddeev-Popov determinant is derived. The resulting state space is surprisingly close to the one of ordinary Loop Quantum Gravity. Spin networks arise again and provide the tool for describing gauge- and diffeomorphism-invariant functionals of the connection. The role played by defects and loops in this approach is analogous to the one played by solenoids and Wilson loops in the Aharonov-Bohm effect."

11. Jul 28, 2009

### Rebel

Yeah, I like the new papers you put, mainly, Krasnov's and Barret's ones... also, I just comment that the papers by A. Perez, Corichi and likely the one of Rovelli and krasnov are related with the workshop of Valencia; there was a talk about SU(2) Chern-Simons related with LQG by one of he spanish young guys..

12. Sep 14, 2009

### marcus

In a couple of weeks from now, around 1 October, it will be time to put up the third quarter MIP poll. Here's an attempt at sifting down to a short list of significant nonstring QG papers, to have as candidate for Most Important Paper

(for now, to keep it short, just the arxiv code and principal author)

http://arxiv.org/abs/0909.1861 Markopoulou
http://arxiv.org/abs/0909.0939 Lewandowski
http://arxiv.org/abs/0908.4476 Christensen
http://arxiv.org/abs/0908.3388 Smolin
http://arxiv.org/abs/0908.1964 Weinberg
http://arxiv.org/abs/0907.4323 Dittrich
http://arxiv.org/abs/0907.4325 Dittrich
http://arxiv.org/abs/0907.4238 Woodard
http://arxiv.org/abs/0907.4064 Krasnov
http://arxiv.org/abs/0907.2617 Reuter
http://arxiv.org/abs/0907.2440 Barrett

Last edited: Sep 14, 2009
13. Sep 14, 2009

### marcus

Arxiv tag, principal author, and list of cites to date
(really too soon for any significant number of cites to have occurred, useful later though.)

http://arxiv.org/abs/0909.1861 Markopoulou
http://arxiv.org/cits/0909.1861

http://arxiv.org/abs/0909.0939 Lewandowski
http://arxiv.org/cits/0909.0939

http://arxiv.org/abs/0908.4476 Christensen
http://arxiv.org/cits/0908.4476

http://arxiv.org/abs/0908.3388 Smolin
http://arxiv.org/cits/0908.3388

http://arxiv.org/abs/0908.1964 Weinberg
http://arxiv.org/cits/0908.1964

http://arxiv.org/abs/0907.4323 Dittrich
http://arxiv.org/cits/0907.4323

http://arxiv.org/abs/0907.4325 Dittrich
http://arxiv.org/cits/0907.4325

http://arxiv.org/abs/0907.4238 Woodard
http://arxiv.org/cits/0907.4238

http://arxiv.org/abs/0907.4064 Krasnov
http://arxiv.org/cits/0907.4064

http://arxiv.org/abs/0907.2617 Reuter
http://arxiv.org/cits/0907.2617

http://arxiv.org/abs/0907.2440 Barrett
http://arxiv.org/cits/0907.2440

Dittrich actually leads at the moment with 3 cites and 2 cites for her two papers, but way too early to say anything meaningful.

Markopoulou's Time essay is really interesting IMHO and won a prize in the FQXi contest.
Lewandowski we discussed, the paper adapts spinfoam so it's more completely compatible with canonical Loop.
Christensen because people are just getting started using computers to calculate with spinfoam.
Smolin's paper sets up for a collaboration with Lisi on E8.
Weinberg tells the Asymptotic Safety story and motivates the approach. See pages 17-20.
Woodard is a senior theoretical physicist who was invited to write an authoritative 100-page survey of the current quantum gravity picture.
Krasnov's paper we already discussed. Launches a new action which could lead to a new spinfoam.
Reuter strugges with the issue of background metric in the AsymSafe context.
Barrett invents some Feynman-like diagrams and makes a valuable contribution to understanding the new model spinfoam.

Last edited: Sep 14, 2009
14. Sep 16, 2009

### MTd2

New one for Q3:

http://arxiv.org/abs/0909.2821

Stability of the Einstein static universe in Hořava-Lifgarbagez gravity

Puxun Wu, Hongwei Yu
(Submitted on 15 Sep 2009)
We study the stability of Einstein static universe in the Ho\v{r}ava-Lifgarbagez (HL) gravity with the detailed-balance condition, where the Friedmann equation gets corrected by a $1/{a^4}$ term. We find that, if the cosmological constant $\Lambda$ is negative, there exists a stable Einstein static state. The universe can stay at this stable state eternally and thus the big bang singularity can be avoided. However, in this case, it is difficult for the universe to break this stable state and then enter an inflationary era. For a positive $\Lambda$, the system has both an unstable state and a stable one. The former corresponds to an exponentially expanding phase. The universe can stay at this stable state past-eternally. Once the equation of state $w$ reaches infinity: $w\to\infty$ or $w\to-\infty$, this stable critical point coincides with the unstable one. Thus the stable state is broken and then the universe enters an inflationary era. Therefore, the big bang singularity can be avoided and a subsequent inflation can occur.

I don't know if anyone remembers, but there is a paper on LQG from Q2 about mini black holes, in which there is a small mass in which the black hole is in stable equilibrium, and another mass which is in unstable equilibrium with the CMB. Sounds like a somewhat similar situation here, with 2 unstable equilibrium, except that they are broken.

I have a prediction. LQG will never yield general relativity, unless it emerges with dark matter, just like Horava gravity cannot give up its scalar fields at classical approximation, because they are dark matter.

That doesn't mean GR is wrong. Maybe it is time to rethink how we incorporate EM into GR. For example:

http://arxiv.org/abs/0909.2581

Cosmology and Astrophysics without Dark Energy and Dark Matter

Shlomo Barak, Elia M Leibowitz
(Submitted on 14 Sep 2009)
We show that there is no need for the hypothetical Dark Energy (DE) and Dark Matter (DM) to explain phenomena attributed to them. In contrast to the consensus of the last decade, we show that the time derivative of the cosmological scale factor, is a constant. We derive H(z), the Hubble parameter, as a function of the redshift, z. Based on H(z), we derive a curve of the Distance Modulus versus log(z). This curve fits data from supernovae observations, without any free parameters. This fit is as good as that obtained by current cosmology, which needs the free parameters Omega_M and Omega_Lambda. We obtain these results by using the hitherto un-noticed fact that the global gravitational energy density in our Hubble Sphere (HS) is equal to the Cosmological Microwave Background (CMB) energy density. We derive the dynamic and kinematic relations that govern the motions of celestial bodies in and around galaxies. This derivation does not require any gravitating matter beyond the observed baryonic matter. The theoretical Rotation Curves (RC), resulting from these relations, fit observed RCs. We obtain these results by examining the interplay between the local gravitational energy density, around a galaxy, and the CMB energy density. This interplay causes the inhomogeneous and anisotropic space expansion around a galaxy.