Trans-Planckian dark energy?

Abstract

It has recently been proposed in Refs. [1,2,3] that the dark energy could be attributed to the cosmological properties of a scalar field with a non-standard dispersion relation that decreases exponentially at wave-numbers larger than Planck scale (k phys > M Pl ). In this scenario, the energy density stored in the modes of trans-Planckian wave-numbers but sub-Hubble frequencies produced by amplification of the vacuum quantum fluctuations would account naturally for the dark energy. The present article examines this model in detail and shows step by step that it does not work. In particular, we show that this model cannot make definite predictions since there is no welldefined vacuum state in the region of wave-numbers considered, hence the initial data cannot be specified unambiguously. We also show that for most choices of initial data this scenario implies the production of a large amount of energy density (of order ∼ M 4 Pl ) for modes with momenta ∼ M Pl , far in excess of the background energy density. We evaluate the amount of fine-tuning in the initial data necessary to avoid this back-reaction problem and find it is of order H/M Pl . We also argue that the equation of state of the trans-Planckian modes is not vacuum-like. Therefore this model does not provide a suitable explanation for the dark energy.

Checking the Alleged “Incompatibility of the Relic Dark Energy Hypothesis” with Physically Admissible Solutions to the Cosmic Ray Problem of Doubly Special Relativity

“…Our calculations imply that a Trans-Planckian dark energy depends upon initial conditions which are too specialized and which do not match up with known astrophysical data obtained as of the 1990s. This is in tandem with Lemoine, Martin, and Uzan [5] who dispute on the Trans Planckian hypothesis on different grounds.…”

“…We find that the answer is yes after modifying an energy equation of E = MC 2 to obtain a highly non linear dispersion relationship. However, this dispersion relationship does NOT solve the cosmic ( ) M k ω matches the Epstein function used by Mercini et al [2] only if we cease trying to fit cosmic ray data [5] which lead to Magueijo [3] proposing their alteration of special relativity in the first place. We follow Mersini et al [2] in their derivation of a Trans Planckian dark energy over total energy ratio.…”

Analogue Gravity

“…Models considered to date focus on variants of the BEC-inspired analogues:

Fedichev and Fischer [195, 194] have investigated WKB estimates of the cosmological particle production rate and (1+1) dimensional cosmologies, both in expanding BECs.

Lidsey [403], and Fedichev and Fischer [196] have focussed on the behaviour of cigar-like condensates in grossly-asymmetric traps.

Barceló et al [46, 47] have focussed on BECs and tried to mimic FLRW behaviour as closely as possible, both via free expansion, and via external control of the scattering length using a Feshbach resonance.

Fischer and Schützhold [206] propose the use of two-component BECs to simulate cosmic inflation.

Weinfurtner [674, 675] has concentrated on the approximate simulation of de Sitter spacetimes.

Weinfurtner, Jain, et al have undertaken both numerical [328] and general theoretical [677, 683] analyses of cosmological particle production in a BEC-based FLRW universe.

In all of these models the general expectations of the relativity community have been borne out — the theory definitely predicts particle production, and the very interesting question is the extent to which the formal predictions are going to be modified when working with real systems experimentally [47]. We expect that these analogue models provide us with new insights as to how their inherent modified-dispersion relations affect cosmological processes such as the generation of a primordial spectrum of perturbations (see, for example, [85, 84, 86, 87, 88, 89, 90, 122, 179, 269, 296, 297, 343, 380, 381, 406, 426, 423, 424, 425, 458, 459, 460, 487, 566, 587, 588, 589, 600] where analogue-like ideas are applied to cosmological inflation).…”

Analogue Gravity

“…We expect that these analogue models provide us with new insights as to how their inherent modified dispersion relations affect cosmological processes such as the generation of a primordial spectrum of perturbations (see for example [42, 41, 43, 44, 45, 46, 47, 70, 107, 158, 177, 178, 207], [229, 230, 244, 252, 249, 250, 251, 274, 275, 296, 349, 361, 362, 363, 371] where analogue-like ideas are applied to cosmological inflation).…”