Separable sequences in Bianchi I loop quantum cosmology

Abstract

In this paper, we discuss the properties of one-parameter sequences that arise when solving the Hamiltonian constraint in Bianchi I loop quantum cosmology using a separation of variables method. In particular, we focus on finding an expression for the sequence for all real values of the parameter, and discuss the pre-classicality of this function. We find that the behavior of these preclassical sequences imply time asymmetry on either side of the classical singularity in Bianchi I cosmology.Comment: 5 pages, 3 figures, published versio

Observational issues in loop quantum cosmology

“…Many studies have already been devoted to Bianchi-I LQC [97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117]. In particular, it was shown that the bounce prediction is robust.…”

Wave functions for the Schwarzschild black hole interior

“…We can expand the function B(y) = β 0 + yF (y) in a Taylor series, to read off the values of the sequence β n for any real n, as done in previous work [14]. However, in this case the function is not easily written in a compact form.…”

“…Similar reasoning lets us ignore the difference between the full recursion relation and the "bulk" relation, where m ≥ 2 allows us to simplify the absolute value signs for m. 2 Notice that we are focussing solely on integer values of the parameter k, despite the fact that µ and τ (and hence m, n) can take any real value. It has been shown elsewhere [14] that using the sequence solution for integer values can be extended to all real numbers.…”

Conserved quantities in isotropic loop quantum cosmology

“…A crucial difference between this conserved quantity and the charge (15) obtained from the APS quantization is what happens to the prefactor of Q at the classical singularity. As stated above, for the APS model (13), at this singularity, C + (0) = 0, so Q can take any real value; this allows the charge for wave functions passing through the classical singularity to be non-zero, and thus provide a relation between semi-classical limits of the wave function far away from the v = 0 point. On the other hand, for the earlier quantization (22), we have the difference in volumes V µ+µ0 − V µ−µ0 at µ = 0 is V µ0 − V −µ0 = 0 so that the charge Q = 0 for any wave function passing through the µ = 0 classical singularity.…”