Scalar and tensor perturbations in DHOST bounce cosmology

Abstract

We investigate the bounce realization in the framework of DHOST cosmology, focusing on the relation with observables. We perform a detailed analysis of the scalar and tensor perturbations during the Ekpyrotic contraction phase, the bounce phase, and the fast-roll expansion phase, calculating the power spectra, the spectral indices and the tensor-to-scalar ratio. Furthermore, we study the initial conditions, incorporating perturbations generated by Ekpyrotic vacuum fluctuations, by matter vacuum fluctuations, and by thermal fluctuations. The scale invariance of the scalar power spectrum can be acquired introducing a matter contraction phase before the Ekpyrotic phase, or invoking a thermal gas as the source. The DHOST bounce scenario with cosmological perturbations generated by thermal fluctuations proves to be the most efficient one, and the corresponding predictions are in perfect agreement with observational bounds. Especially the tensor-to-scalar ratio is many orders of magnitude within the allowed region, since it is suppressed by the Hubble parameter at the beginning of the bounce phase.

Generating cosmological perturbations at Horndeski bounce

“…Tensor power spectrum is obtained by replacing 2G S → G T /4 (i.e., g S → 1/4) and u S → u T = 1, and multiplying by 2 due two two tensor polarizations. This gives the result for P T quoted in (27).…”

“…One way [22,23,24,25,26,27] of getting around this theorem is to employ beyond Horndeski theories [28,29] Degenerate Higher-Order Scalar-Tensor (DHOST) generalizations [30]. These, however, have their own problems, since adding conventional matter fields often results in superluminality [31].…”

Improved DHOST Genesis

“…This fact is already found in [1,74] as long as the DHOST coupling is non-trivial only during the NEC violation phase. Moreover, observational singnals from scalar perturbation, such as the scalar spectra index and tensorto-scalar ratio, will not be affected by DHOST action in bounce cosmology [75], and in section IV, we will similarly find that the scalar spectra index is independent of the DHOST action.…”

Perturbative unitarity and NEC violation in genesis cosmology

“…see [85][86][87][88] for recent studies. It can be checked that the action (3.4) still belongs to the "beyond Horndeski" (GLPV) theory [74,75], 2 which is free from the Ostrogradsky instabilities.…”

“…The "no-go" theorem proved in [55,56] indicates that pathological instabilities of perturbations appear in either the NEC-violating period or sooner or later in spatial flat nonsingular cosmology constructed by Horndeski theory [57][58][59], see also [60][61][62][63][64][65][66][67][68]. It is then demonstrated explicitly with the EFT method [69][70][71][72][73] that fully stable NEC-violating nonsingular cosmological models can be constructed in "beyond Horndeski" theories [74,75], see [76][77][78][79][80][81][82][83][84][85][86][87][88][89] for later developments. Notably, the physics represented by higher derivative "beyond Horndeski" operators plays an essential role in realizing fully stable NEC-violating nonsingular cosmology.…”