Holographic signatures of resolved cosmological singularities

Abstract

The classical gravity approximation is often employed in AdS/CFT to study the dual field theory, as it allows for many computations. A drawback is however the generic presence of singularities in classical gravity, which limits the applicability of AdS/CFT to regimes where the singularities are avoided by bulk probes, or some other form of regularisation is applicable. At the same time, quantum gravity is expected to resolve those singularities and thus to extend the range of applicability of AdS/CFT also in classically singular regimes. This paper provides a proof of principle that such computations are already possible. We use a quantum corrected Kasner-AdS metric inspired by results from loop quantum gravity to compute the 2-point correlator in the geodesic approximation for a negative Kasner exponent. The correlator derived in the classical gravity approximation has previously been shown to contain a pole at finite distance as a signature of the singularity. Using the quantum corrected metric, we show explicitly how the pole is resolved and that a new subdominant long-distance contribution to the correlator emerges, caused by geodesics passing arbitrarily close to the resolved classical singularity. We stress that these results rely on several choices in the quantum corrected metric which allow for an analytic computation and may not hold in general. An alternative choice is presented where the correlator may remain singular even though the bulk singularity is resolved.

Holographic signatures of resolved cosmological singularities II: numerical investigations

“…Let us recall from Sec. 2 that both in the classical case [22,23] and the quantum corrected case considered in [21], the relation was 6…”

“…However, the affine parametrisation turns out to be more convenient for computing the renormalised geodesic length. The explicit solution z(s) parametrised with respect to the geodesic length s reads as [21]…”

“…In order to investigate the intermediate distance behaviour of the two-point correlater, we plot z(t ⇤ ) vs. x(t 0 ) for the case a ext = 1, p = 1/4, for the two values = 1 corresponding to the quantum theory and = 0 corresponding to the classical theory in figure 1 for and t 0 = 100 and figure 2 for t 0 = 4. t ⇤ = t 0 corresponds to the point (0, 0), from which on t ⇤ decreases until it reaches 0. Figure 2: Plots of z(t * ) vs. l = x(t0) for p = −1/4 and aext = 1 taken from [21]. The red line represents the classical case with λ = 0, while the blue line represents the quantum corrected case with λ = 1 respectively for t * = t0 = 100 at (0,0) (a), and t * = t0 = 4 at (0,0) (b).…”

“…Both of these features, Kasner transitions and a z-dependent scale for the onset of quantum effects, were neglected in (2.6) to allow for an analytic computation in [21]. In principle, both of them can have important qualitative effects on the results for the two-point correlator:…”

“…(2.7). Therefore, unlike in [23,21], Eqs. (3.3) do not decouple and as such they do not appear to be analytically solvable anymore.…”