Perturbations and the future conformal boundary

Abstract

The concordance model of cosmology predicts a universe which finishes in a finite amount of conformal time at a future conformal boundary. We show that for particular cases we study, the background variables and perturbations may be analytically continued beyond this boundary and that the "end of the universe" is not necessarily the end of their physical development. Remarkably, these theoretical considerations of the end of the universe might have observable consequences today: perturbation modes consistent with these boundary conditions have a quantized power spectrum which may be relevant to features seen in the large scale cosmic microwave background. Mathematically these cosmological models may either be interpreted as a palindromic universe mirrored in time, a reflecting boundary condition, or a double cover, but are identical with respect to their observational predictions and stand in contrast to the predictions of conformal cyclic cosmologies.

Improved cosmological fits with quantized primordial power spectra

“…Lasenby et al [5] also showed that for a universe with only matter, the equations are analytically continuable if the energy density is viewed as ρ m ∼ a −3 ¼ s 3 . However, as s and a are negative on the other side of the future conformal boundary, this results in radically different behavior in contrast to the symmetry associated with the radiation-only case.…”

“…In Ref. [5] it was shown that for a universe with only radiation and a cosmological constant, the equations governing the background and perturbations are analytically continuable through the future conformal boundary. Making the requirement that the perturbative expansion remains finite throughout the domain results in there being only a discrete set of wave vectors that are allowed.…”

“…As in Ref. [5], we start by approximating these components as perfect fluids and later consider the impact of higher-order multipoles in the Boltzmann hierarchy. However, unlike in Ref.…”

“…There has been much historical discussion of the significance of low-multipole features in the cosmic microwave background power spectrum [1][2][3], with many proposed primordial mechanisms to explain these features with varying degrees of naturalness [4]. In a recent paper, Lasenby et al [5] proposed a novel mechanism for setting initial conditions on cosmological perturbations derived from considerations of the future conformal boundary in radiation dominated universes. The key prediction of this theory is a quantization of wave vectors for the primordial power spectrum of curvature perturbations.…”

“…Lasenby et al [5] established in detail how such quantized spectra arise through consistency considerations of a linearized treatment of perturbations, and in particular their behavior as they approach and then pass through the future conformal boundary (FCB). They also derived the evolution of particle geodesics through the FCB, and discussed how one can interpret the nature of a universe beyond this point, and "two-sheeted universes" have been discussed by [6].…”