Reconstruction of general relativistic cosmological solutions in modified gravity theories

Abstract

We study the special class of the exact solutions in cosmological models based on the Generalized Scalar-Tensor Gravity with non-minimal coupling of a scalar field to the Ricci scalar and to the Gauss-Bonnet scalar in 4D Friedmann universe corresponding to similar ones in GR. The parameters of cosmological perturbations in such models correspond to the case of Einstein gravity with a high precision. As the example of proposed approach, we obtain the exact solutions for the power-law and exponential power-law inflation. * ingvor@inbox.ru † chervon.sergey@gmail.com 1 We have to stress that Starobinsky model [1] was related to modified f(R) gravity.

Gauss–Bonnet term corrections in scalar field cosmology

“…In papers [56][57][58][59][60] it was proposed to consider the relationship between standard inflationary models and EGBinflation directly from the equations of cosmological dynam-0123456789(). : V,-vol ics in flat four-dimensional Friedmann-Robertson-Walker (FRW) space-time, which is sufficient for comparing such a models, since this type of geometry is the basis for constructing phenomenologically correct cosmological of models [53,54,61,62].…”

“…: V,-vol ics in flat four-dimensional Friedmann-Robertson-Walker (FRW) space-time, which is sufficient for comparing such a models, since this type of geometry is the basis for constructing phenomenologically correct cosmological of models [53,54,61,62]. Also, this approach was used to analyze cosmological inflationary models based on the other modifications of Einstein gravity [60,63,64]. Thus, the application of the approach based on a connection between Einstein-Gauss-Bonnet gravity and General Relativity in relevant cosmological models makes it possible to evaluate the effects of the non-minimal coupling of a scalar field and the Gauss-Bonnet term.…”

“…The aim of this work is to develop the method of analysis of Gauss-Bonnet term corrections to standard inflationary models which was proposed in [56][57][58][59][60]. The article is organized as follows.…”

Stability analysis of de Sitter solutions in models with the Gauss-Bonnet term

“…The Gauss-Bonnet term is a topological invariant quantity in four dimensions but may have dynamical relevance if coupled to an evolving scalar field. The Gauss-Bonnet term coupled to a scalar field arises naturally in the string theory [1] and uses in string inspired cosmological models [2,3,4,5,6,7], because have interesting cosmological implications both for early Universe [8,9,10,11,12,13,14,15] and for the late time dynamics [16,17,18,19,20,21] 1 .…”

Anomalous behavior of dispersion of longitudinal and transverse collective excitations in water

“…Such behavior may be interpreted as a smooth structural crossover between the structures with different length scales of the potential. Such crossover is responsible for many anomalous properties like density, diffusion and structural anomalies or high value of the heat capacity [51,52]. In the context of this work the smooth structural crossover makes the system effectively softer under isochoric heating which make the frequencies smaller.…”