In the unstable branch of quadratic gravity, singularity-free bouncing cosmologies exist but their second-order action variation has negative eigenvalues, indicating instability and a possible transition to a Big Bang.
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Stability of cosmological singularity-free solutions in quadratic gravity
In the unstable branch of quadratic gravity, singularity-free bouncing cosmologies exist but their second-order action variation has negative eigenvalues, indicating instability and a possible transition to a Big Bang.