On Signatures of Short Distance Physics in the Cosmic Microwave Background

TL;DR

The paper investigates whether trans-Planckian (string) physics can leave detectable signatures in the CMB within inflationary cosmology. It argues that significant effects arise from nonadiabatic evolution of the initial local vacuum on sub-Planckian scales, producing excited states at horizon crossing and encoded in Bogoliubov coefficients $B_1(k)$ and $B_2(k)$, rather than solely from suppressed local-vacuum amplitudes $(H_{ m inf}/M)^2$. The authors introduce a time-dependent dispersion framework with $k_{ m eff}^2(k,\eta) = a^2(\eta) \omega_{ m phys}^2[k/a(\eta)]$ and a three-phase evolution that can modify the power spectra ${\cal P}_{\cal R}(k)$ and ${\cal P}_g(k)$ within back-reaction constraints. They argue that, under plausible dispersion relations and viable parameter windows, trans-Planckian physics could yield detectable imprints on CMB anisotropies, challenging the view that such effects are generically unobservable, and they provide a pedagogical treatment of cosmological perturbations to illuminate these potential short-distance signals.

Abstract

Following a self-contained review of the basics of the theory of cosmological perturbations, we discuss why the conclusions reached in the recent paper by Kaloper et al are too pessimistic estimates of the amplitude of possible imprints of trans-Planckian (string) physics on the spectrum of cosmic microwave anisotropies in an inflationary Universe. It is shown that the likely origin of large trans-Planckian effects on late time cosmological fluctuations comes from nonadiabatic evolution of the state of fluctuations while the wavelength is smaller than the Planck (string) scale, resulting in an excited state at the time that the wavelength crosses the Hubble radius during inflation.

Figures (4)

• Figure 1: Space-time sketch of the evolution of a comoving length scale with comoving wavenumber $k$ in an inflationary Universe. The coordinates are physical distance and cosmic time $t$. At very early times, the wavelength is smaller than the Planck scale $\ell _{\rm Pl}$ (Phase I), at intermediate times it is larger than $\ell _{\rm Pl}$ but smaller than the Hubble radius $H^{-1}$ (Phase II), and at late times during inflation it is larger than the Hubble radius (Phase III).
• Figure 2: Various dispersion relations considered in the literature (see Refs. UnruhCJKG, and also Ref. Mersini for another dispersion relation not displayed on the plot). For $k_{\rm phys} \ll k_{_{\rm C}}=k_{_{\rm Pl}}$, all the dispersion relations are linear, $\omega_{\rm phys}\simeq k_{\rm phys}$, which guarantees that the laws of physics on scales below the Planck scale are the standard ones. On the other hand on very small scales, for $k_{\rm phys}\gg k_{_{\rm C}}$, the dispersion relations deviate from the standard one.
• Figure 3: Example of a dispersion relation where the WKB approximation can be violated during phase I.
• Figure 4: Region in the $(k_{_{\rm C}}, H_{\rm inf})$ plan where a correction of order $\epsilon$ is expected with a back-reaction problem. The shaded region indicates the region obtained for $\epsilon =0.01$. For larger $epsilon$ the shaded region should be extended up to the corresponding straight line indicated on the figure.