Dependence of the spectra of fluctuations in inflationary cosmology on trans-Planckian physics

By Jérôme Martin, Robert Brandenberger. 2003

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We calculate the power spectrum of metric fluctuations in inflationary cosmology starting with initial conditions which are imposed mode by mode when the wavelength equals some critical length $\ell_{_{\rm C}}$ corresponding to a new energy scale $M_{_{\rm C}}$ at which trans-Planckian physics becomes important. In this case, the power spectrum can differ from what is calculated in the usual framework (which amounts to choosing the adiabatic vacuum state). The fractional difference in the results depends on the ratio $\sigma_0$ between the Hubble expansion rate $H_{\rm inf}$ during inflation and the new energy scale $M_{_{\rm C}}$. We show how and why different choices of the initial vacuum state (stemming from different assumptions about trans-Planckian physics) lead to fractional differences which depend on different powers of $\sigma_0$. As we emphasize, the power in general also depends on whether one is calculating the power spectrum of density fluctuations or of gravitational waves.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/9102dd382b8c0b5eb08f63e5b5733157404321b3

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Citations in the corpus

Lorentz violation at high energy: Concepts, phenomena, and astrophysical constraints (2005, background): “Early in the third millennium this line of research led to work on the related question of the possible imprint of trans–Planckian frequencies on the primordial fluctuation spectrum [30].”
Planck2018 results (2018, background): “Periodic or quasi-periodic modulations of the power spectrum which extend over the entire observable range of wavenumbers can occur in a variety of models [cf., e.g., Danielsson (2002); Martin & Brandenberger (2003); Bozza et al. (2003); Chen (2012); Jackson & Shiu (2013)].”
Trans-Planckian issues for inflationary cosmology (2012, background): “Whereas the prescription adopted by [27, 28, 31] leads to oscillations of the abovementioned magnitude, the choice made by [29] and studied in more detail in [32] leads to oscillations with amplitude suppressed by three powers of H/M C .”
Analogue Gravity (2005, background): “We expect that these analogue models provide us with new insights as to how their inherent modified dispersion relations affect cosmological process such as the generation of a primordial spectrum of perturbations (see for example [250, 251, 46, 42, 41, 107, 209, 229, 230, 249, 275, 275, 274, 43, 47”
Introduction to Quantum Fields in Curved Spacetime and the Hawking Effect (2003, background): “(See for example [61] and references therein for discussions of these issues.”
Modern Tests of Lorentz Invariance (2005, background): “A number of authors have addressed the possible signatures of trans-Planckian physics in the CMB, for a sampling see [94, 212, 214, 262, 101, 164, 66, 236] and references therein.”