Avoiding dark energy with 1/r modifications of gravity

By Richard P. Woodard. 2006

638 citations recorded by the source corpus.

Scalar quintessence seems epicyclic because one can choose the potential to reproduce any cosmology (I review the construction) and because the properties of this scalar seem to raise more questions than they answer. This is why there has been so much recent interest in modified gravity. I review the powerful theorem of Ostrogradski which demonstrates that the only potentially stable, local modification of general relativity is to make the Lagrangian an arbitrary function of the Ricci scalar. Such a theory can certainly reproduce the current phase of cosmic acceleration without Dark Energy. However, this explanation again seems epicyclic in that one can construct a function of the Ricci scalar to support any cosmology (I give the technique). Models of this form are also liable to problems in the way they couple to matter, both in terms of matter’s impact upon them and in terms of the long range gravitational force they predict. Because of these problems my own preference for avoiding Dark Energy is to bypass Ostrogradski’s theorem by considering the fully nonlocal effective action built up by quantum gravitational processes during the epoch of primordial inflation.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/90324baccf4c41ebd96dc9a1c6f92a95d5adfa92

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Citations in the corpus

Born–Infeld inspired modifications of gravity (2017, background): “The reason is clear from the well-known fact that an arbitrary action containing a non-linear function of the Ricci tensor will give rise to higher order gravitational field equations and, thus, it will be prone to the Ostrogradski instability [366].”
Boundary Terms, Variational Principles and Higher Derivative Modified Gravity (2008, methodology): “They are invoked to explain cosmic acceleration without the need for dark energy [6, 7, 8, 9, 10], and as quantum corrections to Einstein gravity [13, 14].”
Modified Gravity and Cosmology (2011, background): “The Ostrogradski instability does not, therefore, apply to f(R) theories of gravity [1281].”
Beyond the Cosmological Standard Model (2014, positive): “Here we review Ostrogradsky’s theorem, following [252].”
Testing modified gravity at cosmological distances with LISA standard sirens (2019, background): “However, although sufficient, this requirement is not necessary in order to avoid dangerous Ostrogradsky instabilities [80, 81].”
Dust of dark energy (2010, neutral): “[26] R.”
Primordial Non-Gaussianities from Inflation Models (2010, background): “Different treatment of such terms and discussions on their effects can be found in [78–80].”