Anisotropically inflating universes

Barrow, John D.; Hervik, Sigbjørn

doi:10.1103/physrevd.73.023007

Cited by 169 publications

(216 citation statements)

References 42 publications

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“…(21) and (22) -or, equivalently, eqs. (20) and (21) -are the equations of motion for the perturbations. We can also obtain these equations in a different but equivalent form by simply expanding at first order in the perturbations the general equations of motion of the model.…”

Section: Identification Of Ghosts and Their Associated Instabilitymentioning

confidence: 99%

Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature

2009

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We prove that many cosmological models characterized by vectors nonminimally coupled to the curvature (such as the Turner-Widrow mechanism for the production of magnetic fields during inflation, and models of vector inflation or vector curvaton) contain ghosts. The ghosts are associated with the longitudinal vector polarization present in these models, and are found from studying the sign of the eigenvalues of the kinetic matrix for the physical perturbations. Ghosts introduce two main problems: (1) they make the theories ill-defined at the quantum level in the high energy/sub horizon regime (and create serious problems for finding a well behaved UV completion); (2) they create an instability already at the linearized level. This happens because the eigenvalue corresponding to the ghost crosses zero during the cosmological evolution. At this point the linearized equations for the perturbations become singular (we show that this happens for all the models mentioned above). We explicitly solve the equations in the simplest cases of a vector without vev in a FRW geometry, and of a vector with vev plus a cosmological constant, and we show that indeed the solutions of the linearized equations diverge when these equations become singular.

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Section: Identification Of Ghosts and Their Associated Instabilitymentioning

confidence: 99%

Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature

2009

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“…Many results point towards isotropization and genericness of inflation starting from initial anisotropic conditions, however counter-examples have also been found (see for eg. [21,24,25]). Since the anisotropic shear diverges in classical gravity close to the initial singularity, it has been argued that a consistent treatment of anisotropies in the pre-inflationary epoch is incomplete without inputs from quantum gravity [9,14].…”

Section: Introductionmentioning

confidence: 99%

A quantum gravitational inflationary scenario in Bianchi-I spacetime

Gupt¹,

Singh²

2013

Class. Quantum Grav.

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We investigate the φ 2 inflationary model in the Bianchi-I spacetime using the effective spacetime description of loop quantum cosmology to understand the issues of the resolution of initial singularity, isotropization, effect of anisotropies on the amount of inflation, and the phase space attractors in the presence of non-perturbative quantum gravitational modifications. A comparative analysis with the classical theory by including more general initial conditions than the ones previously considered in the latter is also performed. We show that, in general, the classical singularity is replaced by a bounce of the mean scale factor in loop quantum cosmology. Due to the underlying quantum geometric effects, the energy density of the inflaton and the anisotropic shear remain bounded throughout the non-singular evolution. Starting from arbitrary anisotropic initial conditions, a loop quantum universe isotropizes either before or soon after the onset of slow-roll inflation. We find a double attractor behavior in the phase space dynamics of loop quantum cosmology, similar to the one in classical theory, but with some additional subtle features. Quantum modifications to the dynamical equations are such that, unlike the classical theory, the amount of inflation does not monotonically depend on the initial anisotropy in loop quantum cosmology. Our results suggest that a viable non-singular inflationary model can be constructed from highly anisotropic initial conditions in the Planck regime.

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“…Instabilities of de Sitter space in the gravity sector were found in Refs. [23,24,25,26], while stability with respect to black hole nucleation was studied in Refs. [27].…”

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confidence: 99%

Matter instability in modified gravity

2006

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The Dolgov-Kawasaki instability discovered in the matter sector of the modified gravity scenario incorporating a −µ 4 /R correction to Einstein gravity is studied in general f (R) theories. A stability condition is found in the metric version of these theories to help ruling out models that are unviable from the theoretical point of view. For example, the theories f (R) = R + αµ 2(n+1) /R n , where α and n are real constants and n > 0, are ruled out for any negative value of α.PACS numbers: 98.80.-k, 04.90.+e, 04.50.+h Analyses of type Ia supernovae [1] and of the cosmic microwave background, including the 3-year WMAP results [2], confirm that the present expansion of the universe is accelerated. This is currently explained by invoking a form of dark energy comprising 70% of the total cosmic energy density ρ and with exotic properties (it does not cluster at small scales and has negative pressure P de ≃ −ρ de ). Recently, as an alternative to this exotic dark energy, it has been proposed to explain the cosmic acceleration with geometry by modifying Einstein gravity at the largest scales (or at low curvatures) by introducing corrections to the Einstein-Hilbert Lagrangian ("f (R)", or "fourth order", or "modified" gravity). The simplest form for the action of modified gravity iswhere κ ≡ 8πG, R is the Ricci curvature [3], and S (m) is the matter action. One can vary the action with respect to the metric ("metric formalism") or perform a Palatini variation in which the metric and the connection are treated as independent variables [5] ("Palatini formalism")-the resulting field equations, which coincide in general relativity, are different in higher order gravity. Furthermore, if the matter action S (m) also depends on the connection, one obtains a third possibility, metric-affine gravity theories [6]. Quadratic quantum corrections were originally introduced to improve the renormalizability of general relativity [7] and were used to achieve inflation in the early universe [8]. There is also motivation for modified gravity from string/M theory [9].The field equations obtained by varying the action (1) in the metric formalism arewhere a prime denotes differentiation with respect to R, g ab and R ab are the metric and Ricci tensors, and T ab is the stress-energy tensor of ordinary matter. The idea of modified gravity consists in introducing corrections to the Einstein-Hilbert action that are negligible in the early universe and only become effective at late times when the Ricci curvature R decreases (the radiation era with R = 0 deserves a special discussion -see below). The prototype is the theory f (R) = R − µ 4 /R [10, 11, 12] which, however, was found to be unstable [13,14]. Therefore, we parametrize the deviations from Einstein gravity aswhere ǫ is a small parameter with the dimensions of an inverse squared length and ϕ is arranged to be dimensionless (in the previous example with f = R − µ 4 /R it is ǫ = −µ 4 with µ ≃ H 0 ≈ 10 −33 eV, the present value of the Hubble parameter H). In order for the effects of th...

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Anisotropically inflating universes

Cited by 169 publications

References 42 publications

Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature

Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature

A quantum gravitational inflationary scenario in Bianchi-I spacetime

Matter instability in modified gravity

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