Compactly supported linearised observables in single-field inflation

Fröb, Markus B.; Higuchi, Atsushi; Hack, Thomas-Paul

doi:10.1088/1475-7516/2017/07/043

Cited by 23 publications

(55 citation statements)

References 62 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We then gave an explicit and covariant transformation of the CDK tensors into the set (24), the FHH tensors, together with the reverse transformation (25). The FHH tensors are chosen such that their linearisations reproduce the FHH observables (21), thus closing the problem of identifying a Stewart-Walker type geometric interpretation for these observables (partially left open in [4]). At the same time the linearisation of these transformations automatically gives explicit relations (26) and (27) between the CDK and FHH observables, thus showing explicitly the completeness of the CDK observables, which was proven in [4] for the FHH ones but left open in [6].…”

Section: Discussionmentioning

confidence: 99%

“…For constant curvature spacetimes (like de Sitter or anti-de Sitter), the components of the linearised Riemann tensor also do the job, provided its tensor indices are appropriately raised or lowered before linearisation [36,37]. Unfortunately, no simple generalisation of these results exists for an arbitrary spacetime, which explains the necessity of the works [4,6] and their present conclusion to produce the answer for spatially flat inflationary cosmologies. Any other spacetime, or family of spacetimes, like in the Bianchi homogeneous anisotropic cosmology classification, needs to be analysed separately.…”

Section: How Do Gauge Invariant Variables Help With Quantization?mentioning

confidence: 98%

“…We have not yet defined a tensor C µν whose linearisation coincides with the formula for C (1) µν . Such a tensor will actually be defined in the next section, solving the problem (left open in [4]) of finding a geometric interpretation for all of the components of C (1) µν . It is again convenient to choose a slightly different tensor, takinĝ…”

Section: Linearised Fhh Tensorsmentioning

confidence: 99%

“…where E (1) = g µν E (1) µν , and F (1) is the linearisation of the Klein-Gordon equation (16b). Since the formula for C (1) µν of [4] was anyway only given for on-shell fields (those annihilated by E (1) µν [h, ψ] and F (1) [h, ψ]), these additional terms can be simply seen as our preferred choice of an off-shell representative.…”

Section: Linearised Fhh Tensorsmentioning

confidence: 99%

“…Thus, in one direction we propagate the proof of completeness, and in the other direction we propagate a geometric interpretation. In Sections 2 and 3, we respectively review the relevant results from [6] and [4], reproducing the explicit formulas that we will need. In Section 4, the two sets of observables are related by explicit transformations.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Approaches to linear local gauge-invariant observables in inflationary cosmologies

Fröb¹,

Hack²,

Khavkine³

2018

Class. Quantum Grav.

Self Cite

View full text Add to dashboard Cite

We review and relate two recent complementary constructions of linear local gauge-invariant observables for cosmological perturbations in generic spatially flat single-field inflationary cosmologies. After briefly discussing their physical significance, we give explicit, covariant and mutually invertible transformations between the two sets of observables, thus resolving any doubts about their equivalence. In this way, we get a geometric interpretation and show the completeness of both sets of observables, while previously each of these properties was available only for one of them.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: How Do Gauge Invariant Variables Help With Quantization?mentioning

confidence: 98%

Section: Linearised Fhh Tensorsmentioning

confidence: 99%

Section: Linearised Fhh Tensorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Approaches to linear local gauge-invariant observables in inflationary cosmologies

Fröb¹,

Hack²,

Khavkine³

2018

Class. Quantum Grav.

Self Cite

View full text Add to dashboard Cite

show abstract

Background Independence in Gauge Theories

Tehrani

Zahn

2020

Ann. Henri Poincaré

View full text Add to dashboard Cite

Classical field theory is insensitive to the split of the field into a background configuration and a dynamical perturbation. In gauge theories, the situation is complicated by the fact that a covariant (w.r.t. the background field) gauge fixing breaks this split independence of the action. Nevertheless, background independence is preserved on the observables, as defined via the BRST formalism, since the violation term is BRST exact. In quantized gauge theories, however, BRST exactness of the violation term is not sufficient to guarantee background independence, due to potential anomalies. We define background-independent observables in a geometrical formulation as flat sections of the observable algebra bundle over the manifold of background configurations, with respect to a flat connection which implements background variations. A theory is then called background independent if such a flat (Fedosov) connection exists. We analyze the obstructions to preserve background independence at the quantum level for pure Yang-Mills theory and for perturbative gravity. We find that in the former case, all potential obstructions can be removed by finite renormalization. In the latter case, as a consequence of power-counting non-renormalizability, there are infinitely many non-trivial potential obstructions to background independence. We leave open the question whether these obstructions actually occur. Contents The Free Algebra Wφ Time-Ordered Products The Interacting Algebra W int φ 2.2. Background Independence of Renormalized Scalar Field Theory 3. Pure Yang-Mills Theory 3.1. Classical Gauge Theory 3.1.1. The Basic Setting Background and Dynamical Gauge Transformations Localization of the Interaction and Split Independence 3.1.2. BV-BRST Formalism and Background Covariant Gauge Fixing Local Gauge Covariance Classical BV-BRST Cohomology The BRST Charge 3.1.3. Background-Independent Local Functionals 3.2. Perturbative Quantum Yang-Mills Theory on a BackgroundĀ 3.2.1. Ward Identities 3.2.2. Quantum BRST Charge and the Algebra of Physical Observables 3.2.3. Perturbative Agreement and the Background Dependence of the Anomaly 3.3. Background Independence 3.3.1. Well-Definedness of the Connection on the Quantum BRST Cohomology 3.3.2. Flatness of the Connection on the Quantum BRST Cohomology 3.3.3. Absence of Obstructions to Background Independence 3.3.4. Summary of Assumptions 3.3.5. Renormalized Background-Independent Interacting Fields 4. Perturbative Quantum Gravity 4.1. Background Independence as Triviality of the Relative Cauchy Evolution A Lemmata on the Anomaly References

show abstract

Cosmological de Sitter Solutions of the Semiclassical Einstein Equation

Gottschalk

Rothe

Siemssen

2023

Ann. Henri Poincaré

View full text Add to dashboard Cite

Exponentially expanding space–times play a central role in contemporary cosmology, most importantly in the theory of inflation and in the dark energy driven expansion in the late universe. In this work, we give a complete list of de Sitter solutions of the semiclassical Einstein equation (SCE), where classical gravity is coupled to the expected value of a renormalized stress–energy tensor of a free quantum field in the Bunch–Davies state. To achieve this, we explicitly determine the stress–energy tensor associated with the Bunch–Davies state using the recently proposed “moment approach” on the cosmological coordinate patch of de Sitter space. From the energy component of the SCE, we thus obtain an analytic consistency equation for the model’s parameters which has to be fulfilled by solutions to the SCE. Using this equation, we then investigate the number of solutions and the structure of the solution set in dependency on the coupling parameter of the quantum field to the scalar curvature and renormalization constants using analytic arguments in combination with numerical evidence. We also identify parameter sets where multiple expansion rates separated by several orders of magnitude are possible. Potentially for such parameter settings, a fast (semi-stable) expansion in the early universe could be compatible with a late-time “Dark Energy-like” behavior of the universe.

show abstract

Compactly supported linearised observables in single-field inflation

Cited by 23 publications

References 62 publications

Approaches to linear local gauge-invariant observables in inflationary cosmologies

Approaches to linear local gauge-invariant observables in inflationary cosmologies

Background Independence in Gauge Theories

Cosmological de Sitter Solutions of the Semiclassical Einstein Equation

Contact Info

Product

Resources

About