Oscillatory Universes in Loop Quantum Cosmology

marcus

this just out:


http://arxiv.org/gr-qc/0406042

Oscillatory Universes in Loop Quantum Cosmology and Initial Conditions for Inflation
James E. Lidsey, David J. Mulryne, N. J. Nunes, Reza Tavakol
6 pages, 4 figures

LQC continues attracting new researchers: these people are newcomers in the field this year AFAIK. They are at the University of London. looks like a the start of a group there

"Our aim here is to study oscillatory universes within the context of Loop Quantum Cosmology (LQC) which is the application of Loop Quantum Gravity(LQG) to anhomogeneous minisuperspace environment. LQG is at present the main background independent and non– perturbative candidate for a quantum theory of gravity (see for example[4, 5]). This approach provides a (discrete) description of high–energy dynamics in the form of a difference equation. An important consequence of this discretization is the removal of the initial singularity [6]. As the universe expands and its volume increases, it enters an intermediate semi–classical phase in which the evolution equations take a continuous form but include modifications due to non–perturbative quantization effects [7]..."

Abstract:
"Positively-curved, oscillatory universes are studied within the context of Loop Quantum Cosmology subject to a consistent semi-classical treatment. The semi-classical effects are reformulated in terms of an effective phantom fluid with a variable equation of state. In cosmologies sourced by a massless scalar field, these effects lead to a universe that undergoes ever-repeating cycles of expansion and contraction. The presence of a self-interaction potential for the field breaks the symmetry of the cycles and can enable the oscillations to establish the initial conditions for successful slow-roll inflation, even when the field is initially at the minimum of its potential. The displacement of the field from its minimum is enhanced for lower and more natural values of the parameter that sets the effective quantum gravity scale. For sufficiently small values of this parameter, the universe can enter a stage of eternal self-reproduction."

meteor

The text mentions the modified Friedmann equation. Is this the same as the effective Friedmann Equation of other papers?

marcus

which other papers, meteor?

in this paper what they call the modified F. eq. is equation (1) on page 1.
It is fairly simple so I could transcribe it in LaTex if necessary.
We just need to compare it with the effective F. eq. in those other papers.

meteor

I refer to
gr-qc/0312110
astro-ph/0311015
astro-ph/0309478

well I have looked at the Effective Friedmann equations in those papers, and is not the same that this equation,though the equation that appears in gr-qc/0312110 is very similar

In fact, the effective Friedmann Equation is different in each of the 3 papers, so there's a chance that this Modified Friedmann equation is really the Effective Friedmann equation

marcus

meteor I am glad you answered this question so I will just relax
but will have a look at
http://arxiv.org/gr-qc/0312110
because i have forgotten what paper that is

I am excited by the semiclassical range of the scale-factor a that they talk about on page 1
"The semi–classical phaseof LQC arises when the scale factor lies in the range a_i <a<a_*, where a_i


(and then some formulas)


j is a quantization parameter which must take half integer values. Below the scale a_i, the discrete nature of spacetime is important, whereas the standard classical cosmology is recovered above a_*."

In the large scale limit they recover the classical Friedmann
and in the small scale they have a LQC quantized version of the friedmann which becomes a difference equation

and in this semiclassical range they have a bridge
a differential equation that approximates at small scale the difference equation and at large scale the standard cosmology model---the ordinary Friedmann equation.

And the size of this semiclassical range, this transition between a very quantum universe and a familiar expanding universe, the size of the transition range depends on this parameter j

lots to think about here