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 quantised 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

“…Introducing a linearly quantized power spectrum with k0 = 3.225 × 10 −4 Mpc −1 and spacing ∆k = 2.257 × 10 −4 Mpc −1 provides a better fit to the Planck 2018 observations than the concordance baseline, with ∆χ 2 = −8.55. Extending the results of Lasenby et al [1], we show that the requirement for perturbations to remain finite beyond the future conformal boundary in a universe containing dark matter and a cosmological constant results in a linearly quantized primordial power spectrum. It is found that the infrared cutoffs for this future conformal boundary quantized cosmology do not provide cosmic microwave background power spectra compatible with observations, but future theories may predict more observationally consistent quantized spectra.…”

“…There has been much historical discussion of the significance of low-multipole features in the cosmic microwave background power spectrum [2][3][4], with many proposed primordial mechanisms to explain these features with varying degrees of naturalness [5]. In a recent paper, Lasenby et al [1] 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 wavevectors for the primordial power spectrum of curvature perturbations.…”

“…Lasenby et al [1] established in detail how such quantized spectra arise through consistency considerations of a linearized treatment of pertubations, and in particular their behaviour as they approach and then pass through the future conformal boundary (FCB). [1] also derived the evolution of particle gedoesics through the FCB, and discussed how one can interpret the nature of a universe beyond this point.…”

“…Lasenby et al [1] established in detail how such quantized spectra arise through consistency considerations of a linearized treatment of pertubations, and in particular their behaviour as they approach and then pass through the future conformal boundary (FCB). [1] also derived the evolution of particle gedoesics through the FCB, and discussed how one can interpret the nature of a universe beyond this point. In Section III we fit these models to the latest Planck 2018 CMB data [6,7] and find that whilst these models produce qualitatively interesting observational features they do not provide a better fit in comparison with the ΛCDM baseline.…”

Constraining Quantum Initial Conditions before Inflation

“…finding they are sinusoidal with a constant wavelength of 2πkt 3 . The FIC primordial power spectrum therefore has uniformly spaced peaks which suggests a similarity to the quantized primordial power spectra considered in [31,32]. The pseudo-quantized primordial power spectrum of FIC may therefore provide an improved fit to the Planck observations as was found by Bartlett et al [32] for a fully quantized spectra.…”