Anisotropically Inflating Universes

TL;DR

The paper investigates gravity theories with quadratic curvature invariants in the presence of a positive cosmological constant $\\Lambda>0$ and shows that the cosmic no-hair theorem does not necessarily hold in these theories. By deriving the generalized field equations from the action that includes $R$, $R^{2}$ and $R_{\\mu\\nu}R^{\\mu\\nu}$, it analyzes the flat de Sitter solution and finds that its stability depends on the sign of $(3\\alpha+\\beta)$. It then constructs two exact vacuum anisotropic cosmologies of Bianchi types II and VI_h that inflate anisotropically and do not approach de Sitter, with inflation driven by the Ricci curvature invariants and the higher-order terms; these solutions require $\\beta\\neq0$ and are non-perturbative, lacking a general-relativistic counterpart. The work further shows that the effective stress-energy from the higher-order terms violates standard energy conditions, providing a mechanism to evade the no-hair theorems and raising questions about early-universe inflation and gravitational thermodynamics in higher-order gravity.

Abstract

We show that in theories of gravity that add quadratic curvature invariants to the Einstein-Hilbert action there exist expanding vacuum cosmologies with positive cosmological constant which do not approach the de Sitter universe. Exact solutions are found which inflate anisotropically. This behaviour is driven by the Ricci curvature invariant and has no counterpart in the general relativistic limit. These examples show that the cosmic no-hair theorem does not hold in these higher-order extensions of general relativity and raises new questions about the ubiquity of inflation in the very early universe and the thermodynamics of gravitational fields.