Ostrogradsky's construction of a Hamiltonian formalism for nondegenerate higher derivative Lagrangians is reviewed. The resulting instability imposes by far the most powerful restriction on fundamental, interacting, continuum Lagrangian field theories. A discussion given problems raised attempts to evade this restriction.

We report on a revision of our previous computation the renormalized expectation value stress-energy tensor massless, minimally coupled scalar with quartic self-interaction locally de Sitter background. This model is important because it demonstrates that quantum effects can lead to violations weak energy condition cosmological scales---on average, not just in fluctuations---although effect this particular far too small be observed. The consists modifying propagator so dimensional...

We explore nonlocally modified models of gravity, inspired by quantum loop corrections, as a mechanism for explaining current cosmic acceleration. These theories enjoy two major advantages: they allow delayed response to events, here the transition from radiation matter dominance, and avoid usual level fine-tuning; instead, emulating Dirac's dictum, required large numbers come time scales involved. Their solar system effects are safely negligible, may even prove useful black hole information problem.

On August 17, 2017 the LIGO interferometers detected gravitational wave (GW) signal (GW170817) from coalescence of binary neutron stars. This was also simultaneously seen throughout electromagnetic (EM) spectrum radio waves to gamma-rays. We point out that this simultaneous detection GW and EM signals rules a class modified gravity theories, termed ``dark matter emulators,'' which dispense with need for dark by making ordinary couple different metric GW. discuss other kinds theories are...

We derive a simple form for the propagator of massless, minimally coupled scalar in locally de Sitter geometry arbitrary spacetime dimension. then employ it to compute fully renormalized stress tensor at one- and two-loop orders ϕ4 theory which is released Bunch–Davies vacuum t = 0 co-moving coordinates. In this system, uncertainty principle elevates above minimum its potential, resulting phase super-acceleration. With non-derivative self-interaction scalar's breaking invariance becomes...

We show that the nonlocal gravity models, proposed to explain current cosmic acceleration without dark energy, pass two essential tests: first, they can be defined so as not alter the, observationally correct, general relativity predictions for gravitationally bound systems. Second, are stable, ghost-free, with no additional excitations beyond those of relativity. In this differ from their, ghostful, localized versions. The systems' initial value constraints same in relativity, and our...

We work in the locally de Sitter background of an inflating universe and consider a massless, minimally coupled scalar with quartic self-interaction. use dimensional regularization to compute fully renormalized self-mass-squared at one two loop order for state which is released Bunch-Davies vacuum t=0. Although field strength coupling constant renormalizations are identical those lfat space, geometry induces non-zero mass renormalization. The finite part also shows sort growing that competes...

We recently derived exact solutions for the scalar, vector, and tensor mode functions of a single, minimally coupled scalar plus gravity in an arbitrary homogeneous isotropic background. These are applied to obtain improved estimates primordial power spectra anisotropies cosmic microwave

We generalize Starobinski\ifmmode \breve{\imath}\else \u{\i}\fi{}'s stochastic technique to the theory of a massless, minimally coupled scalar interacting with massless fermion in locally de Sitter geometry. The is an ``active'' field that can engender infrared logarithms. passive cannot cause logarithms but which carry them, and also induce new interactions between active fields. procedure for dealing fields integrate them out, then stochastically simplify resulting effective action...

We consider vacuum polarization from massless scalar electrodynamics in de Sitter inflation. The theory exhibits a 3+1 dimensional analog of the Schwinger mechanism which photon mass is dynamically generated. generic for light fields that couple minimally to gravity. nonvanishing during inflation may result magnetic on cosmological scales.

A procedure is given for generalizing local, gauge-invariant field theories to nonlocal ones which are finite, Poincar\'e invariant, and perturbatively unitary. These endowed with gauge symmetries ensure current conservation decoupling in the same way that their local analogs do parent theories. An elegant of viewing resulting on-shell symmetry transformations as ``quantum representations'' group representation matrices become field-dependent, operators. By varying scale nonlocality one can...

I give a pedagogical explanation of what it is about quantization that makes general relativity go from being nearly perfect classical theory to very problematic quantum one. also explain why some gravity unavoidable, field theories have divergences, the divergences are worse than those other forces, physicists think this means and they might do with consistent if had Finally, discuss gravitational data recently become available cosmology.

We consider the cosmology of modified gravity models in which Newton's constant is distorted by a function inverse d'Alembertian acting on Ricci scalar. derive technique for choosing distortion so as to fit an arbitrary expansion history. This applied numerically case ΛCDM cosmology, and result agrees well with simple hyperbolic tangent.