Power-Law Inflation in Spacetimes Without Symmetry

Heinzle, Jakob; Rendall, Alan D.

doi:10.1007/s00220-006-0133-y

Cited by 71 publications

(30 citation statements)

References 14 publications

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“…It can also be demonstrated that initially expanding solutions for initial data induced by the Einstein field equations with a positive cosmological constant and coupled to various reasonable matter models exist globally in time [183]. In particular, global results are possible for inflationary scalar field cosmological models with an exponential self potential in which the rate of expansion increases polynomially with cosmological time [184,185]. We note that inflationary behaviour also occurs for scalar field models with a power law self potential, but this arises at intermediate times and not to the asymptotic future.…”

Section: Stability Of De Sitter Spacetimementioning

confidence: 99%

Mathematical general relativity

Coley

2019

Gen Relativ Gravit

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We present a number of open problems within general relativity. After a brief introduction to some technical mathematical issues and the famous singularity theorems, we discuss the cosmic censorship hypothesis and the Penrose inequality, the uniqueness of black hole solutions and the stability of Kerr spacetime and the final state conjecture, critical phenomena and the Einstein-Yang-Mills equations, and a number of other problems in classical general relativity. We then broaden the scope and discuss some mathematical problems motivated by quantum gravity, including AdS/CFT correspondence and problems in higher dimensions and, in particular, the instability of anti-de Sitter spacetime, and in cosmology, including the cosmological constant problem and dark energy, the stability of de Sitter spacetime and cosmological singularities and spikes. Finally, we briefly discuss some problems in numerical relativity and relativistic astrophysics.

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Section: Stability Of De Sitter Spacetimementioning

confidence: 99%

Mathematical general relativity

Coley

2019

Gen Relativ Gravit

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“…Models with a scalar field with an exponential potential are also inflationary because the rate of (volume) expansion is increasing with time, and global results are possible [240,241]. Inflationary behaviour also arises in the presence of a scalar field with a power law potential, but occurs at intermediate times rather than at late times.…”

Section: Stability Of De Sitter Spacetimementioning

confidence: 99%

Open problems in mathematical physics

Coley

2017

Phys. Scr.

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We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recent article proposing 42 fundamental questions (in physics) which must be answered on the road to full enlightenment [1]. But paraphrasing a famous quote by the British football manager Bill Shankly, in response to the question of whether mathematics can answer the Ultimate Question of Life, the Universe, and Everything, mathematics is, of course, much more important than that.

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“…Models with a scalar field with an exponential potential are also inflationary because the rate of (volume) expansion is increasing with time, and global results are possible [240,241]. Inflationary behavior also arises in the presence of a scalar field with a power law potential, but occurs at intermediate times rather than at late times.…”

Section: Stability Of De Sitter Spacetimementioning

confidence: 99%