Nonperturbative quantum de Sitter universe

Abstract

The dynamical generation of a four-dimensional classical universe from nothing but fundamental quantum excitations at the Planck scale is a long-standing challenge to theoretical physicists. A candidate theory of quantum gravity which achieves this goal without invoking exotic ingredients or excessive fine-tuning is based on the nonperturbative and background-independent technique of Causal Dynamical Triangulations. We demonstrate in detail how in this approach a macroscopic de Sitter universe, accompanied by small quantum fluctuations, emerges from the full gravitational path integral, and how the effective action determining its dynamics can be reconstructed uniquely from Monte Carlo data. We also provide evidence that it may be possible to penetrate to the sub-Planckian regime, where the Planck length is large compared to the lattice spacing of the underlying regularization of geometry.

The transfer matrix in four-dimensional CDT

“…Using four-simplices (which is the case having our attention in this article) as building blocks one can, for suitable choices of bare coupling constants, observe a four-dimensional (Euclidean) universe [47,48]. For these choices of coupling constants the shape of the universe is consistent with an interpretation as an (Euclidean) de Sitter space, at least as long as one looks at the scale factor [49,50]. This is the region of coupling constants which will have our interest (for other choices of the coupling constants one obtains more degenerate configurations [51][52][53]).…”

Signature change of the metric in CDT quantum gravity?

“…Evidence for such a fixed point has come mainly from functional renormalization group methods [6][7][8][9][10][11] and lattice approaches to quantum gravity [12][13][14][15]. In a lattice formulation of quantum gravity a non-trivial fixed point would appear as a second-order critical point, the approach to which would define a continuum limit [16].…”

Quantum Gravity via Causal Dynamical Triangulations

“…We have managed to reconstruct it in detail from the simulation data for the volumevolume correlator V 3 (t)V 3 (t ′ ) , and have also shown that the quantum fluctuations around the de Sitter "background geometry" are well described by the action (28), yet another non-trivial result [32]. The same data have allowed us to relate the continuum coupling constant G in (27) to the constant k 1 in (28) according to…”

“…where i denotes (integer) lattice time, N 4 the total number of four-simplices and N 3 (i) the number of tetrahedra at time i [31,32], and s 0 is a constant. 10 Can the functional form of the expectation value found in (26) be obtained directly from an action principle?…”

“…The question is whether we can adjust k 1 to go to zero. Since k 1 depends on the bare coupling constants κ 0 and ∆, we have performed a scan of phase C to determine its qualitative behaviour [32]. Moving toward the A-C phase transition, k 1 is indeed decreasing, without going all the way to zero in the range of coupling constants scanned so far.…”