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On the Properties of the Power-Law Cosmological Solutions in Lovelock Gravity

Sergey Pavluchenko

TL;DR

The paper addresses whether high-order Kasner (power-law) cosmologies in Lovelock gravity can possess past and future asymptotes and support transitions that realize dynamical compactification. By deriving generalized Kasner constraints in a two-subspace, flat-Bianchi-I setup and focusing on the highest Lovelock term $L_{2n}$, the authors analyze $n=2$, $n=3$, $n=4$, and general $n$ across varying numbers of extra dimensions $D$, finding that $n=2$ and $n=3$ can yield viable compactification branches for sufficiently large $D$, while $n\ge 4$ generally precludes positive expansion exponents for the 3D subspace. This indicates a potential obstruction to spontaneous compactification in higher-order Lovelock gravity, with implications for the viability of Lovelock-based theories in higher-dimensional, string-inspired contexts; the results motivate further work on more complex compactification schemes beyond the simple two-subspace, flat-case considered here.

Abstract

In this paper we study the properties of Kasner cosmological solutions in Lovelock gravity. Recent progress in the investigation of flat cosmological models in Lovelock gravity unveiled the fact that in quadratic (Gauss--Bonnet) and cubic Lovelock gravities, the higher-order power-law solutions could play the role of both future and past asymptotes, and under some conditions, there could exist a smooth transition between them. So it is natural to question if this feature is unique to Gauss--Bonnet and cubic Lovelock gravities, or if it is a general feature of Lovelock gravity. Our analysis suggests that starting from quartic and in all higher-order Lovelock gravities, the high-order Kasner solution cannot play the role of a past asymptote, not only preventing the abovementioned transition from happening, but also potentially hindering the possibility of reaching viable compactification.

On the Properties of the Power-Law Cosmological Solutions in Lovelock Gravity

TL;DR

The paper addresses whether high-order Kasner (power-law) cosmologies in Lovelock gravity can possess past and future asymptotes and support transitions that realize dynamical compactification. By deriving generalized Kasner constraints in a two-subspace, flat-Bianchi-I setup and focusing on the highest Lovelock term , the authors analyze , , , and general across varying numbers of extra dimensions , finding that and can yield viable compactification branches for sufficiently large , while generally precludes positive expansion exponents for the 3D subspace. This indicates a potential obstruction to spontaneous compactification in higher-order Lovelock gravity, with implications for the viability of Lovelock-based theories in higher-dimensional, string-inspired contexts; the results motivate further work on more complex compactification schemes beyond the simple two-subspace, flat-case considered here.

Abstract

In this paper we study the properties of Kasner cosmological solutions in Lovelock gravity. Recent progress in the investigation of flat cosmological models in Lovelock gravity unveiled the fact that in quadratic (Gauss--Bonnet) and cubic Lovelock gravities, the higher-order power-law solutions could play the role of both future and past asymptotes, and under some conditions, there could exist a smooth transition between them. So it is natural to question if this feature is unique to Gauss--Bonnet and cubic Lovelock gravities, or if it is a general feature of Lovelock gravity. Our analysis suggests that starting from quartic and in all higher-order Lovelock gravities, the high-order Kasner solution cannot play the role of a past asymptote, not only preventing the abovementioned transition from happening, but also potentially hindering the possibility of reaching viable compactification.
Paper Structure (9 sections, 16 equations, 3 figures)

This paper contains 9 sections, 16 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The Model
  3. Particular $n$ Cases
  4. $n=2$ (Gauss--Bonnet)
  5. $n=3$ (Cubic Lovelock)
  6. $n=4$
  7. Conclusions
  8. General $n$ Case
  9. Discussion and Conclusions

Figures (3)

  • Figure S1: Non-trivial Kasner solution for $n=2$ (panels (a,b)), $n=3$ (panels (c,d)), and $n=4$ (panels (e,f)) Lovelock gravities: low-$D$ details on panels (a,c,e) and high-$D$ behavior on panels (b,d,f) (see text for more details).
  • Figure S2: Behavior of three distinct Kasner exponents: $p_1$ on panels (a,b) (scan over $n$ and $D$ on panel (a) and several examples on panel (b)); $p_2$ on panels (c--e) (scan over $n$ and $D$ on panels (c,d) with large-$n$ behavior on (d) and several examples on panel (e)); $p_3$ on panels (f,g) (scan over $n$ and $D$ on panel (f) and several examples on panel (g)) (see text for more details).
  • Figure S3: $K_3 \to K_3$ transition lack in EGB $D=3$ the vacuum case (panel (a)) and its presence in the EGB $D=3$$\Lambda$-term case (panel (b)) (see text for more details).