Stable exponential cosmological solutions with three different Hubble-like parameters in EGB model with a $\Lambda$-term

Abstract

We consider a $D$-dimensional Einstein-Gauss-Bonnet model with a cosmological term $\Lambda$ and two non-zero constants: ${\alpha }_1$ and ${\alpha }_2$. We restrict the metrics to be diagonal ones and study a class of solutions with exponential time dependence of three scale factors, governed by three non-coinciding Hubble-like parameters: $H\ne 0$, $h_1$ and $h_2$, obeying $mH+k_1{h}_1+k_2{h}_2\ne 0$ and corresponding to factor spaces of dimensions $m>1$, $k_1>1$ and $k_2>1$, respectively ($D=1+m+k_1+k_2$). We analyse two cases: i) $m<k_1<k_2$ and ii) $1<k_1=k_2=k$, $k\ne m$. We show that in both cases the solutions exist if $\alpha ={\alpha }_2/{\alpha }_1>0$ and $\alpha \Lambda >0$ satisfies certain restrictions, e.g. upper and lower bounds. In case ii) explicit relations for exact solutions are found. In both cases the subclasses of stable and non-stable solutions are singled out. For $m>3$ the case i) contains a subclass of solutions describing an exponential expansion of $3$-dimensional subspace with Hubble parameter $H>0$ and zero variation of the effective gravitational constant $G$. The case $H=0$ is also considered.

arXiv comment38 pages, 6 figures, LaTex, Section 7 and Figure 6 are added

References in corpus (26)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• Accelerating Cosmologies in the Einstein-Gauss-Bonnet Theory with Dilaton
• One-loop effective action for non-local modified Gauss-Bonnet gravity in de Sitter space
• Stationary vs. singular points in an accelerating FRW cosmology derived from six-dimensional Einstein-Gauss-Bonnet gravity
• Observational constraints on Gauss-Bonnet cosmology
• Cosmic acceleration with a negative cosmological constant in higher dimensions
• On cosmological-type solutions in multi-dimensional model with Gauss-Bonnet term
• General features of Bianchi-I cosmological models in Lovelock gravity
• Exact exponential solutions in Einstein-Gauss-Bonnet flat anisotropic cosmology
• The nature of singularity in multidimensional anisotropic Gauss-Bonnet cosmology with a perfect fluid
• A note on differences between (4+1)- and (5+1)-dimensional anisotropic cosmology in the presence of the Gauss-Bonnet term
• On stability of exponential cosmological solutions with non-static volume factor in the Einstein-Gauss-Bonnet model
• Stability analysis of the exponential solutions in Lovelock cosmologies
• On anisotropic Gauss-Bonnet cosmologies in (n+1) dimensions, governed by an n-dimensional Finslerian 4-metric
• Non-constant volume exponential solutions in higher-dimensional Lovelock cosmologies
• Friedmann dynamics recovered from compactified Einstein-Gauss-Bonnet cosmology
• Cosmological dynamics of spatially flat Einstein-Gauss-Bonnet models in various dimensions: Low-dimensional $\Lambda$-term case
• Cosmological dynamics of spatially flat Einstein-Gauss-Bonnet models in various dimensions: High-dimensional $\Lambda$-term case
• Stable exponential cosmological solutions with zero variation of $G$ and three different Hubble-like parameters in the Einstein-Gauss-Bonnet model with a $\Lambda$-term
• Stable exponential cosmological solutions with two factor spaces in the Einstein-Gauss-Bonnet model with a $\Lambda$-term
• Unifying Inflation with Early and Late-time Dark Energy in $F(R)$ Gravity
• Examples of stable exponential cosmological solutions with three factor spaces in EGB model with a $\Lambda$-term

Cited by in corpus (3)

• Cosmological Models in Lovelock Gravity: An Overview of Recent Progress
• On the Properties of the Power-Law Cosmological Solutions in Lovelock Gravity
• Examples of exact exponential cosmological solutions with three isotropic subspaces in the Einstein-Gauss-Bonnet gravity