Dynamical analysis of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>R</mml:mi><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mo>□</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mfrac><mml:mi>R</mml:mi></mml:mrow></mml:math>cosmology: Impact of initial conditions and constraints from supernovae

We present an improved version of our original cosmological model to explain the current phase of cosmological acceleration without resorting to a cosmological constant or any other mass scale. Like the original, this phenomenological approach is based on an effective quantum gravitational action, but now depends on the original nonlocal dimensionless scalar X = −1 R only through Y = −1 g µν X ,µ X ,ν . Both X and Y are quiescent during the radiation-dominated (R = 0) era, both only grow logarithmically during matter dominance, and neither affects the propagation of gravitational radiation. However, while X has the same sign for gravitationally bound systems as for cosmology, we show that the sign of Y differs for the two cases: it is positive for cosmology and negative for strongly gravitationally bound systems. We can therefore enforce the ΛCDM expansion history by making a suitable choice of the nonlocal distortion function f (Y ) for Y > 0, while ensuring that there is no change in the heavily constrained solar system phenomenology simply by making f vanish for Y < 0 without discontinuity. The required f (Y > 0) is determined numerically to have a strikingly simple exponential form.

Section: The Cosmological Sectormentioning

confidence: 99%

Nonlocal cosmology II. Cosmic acceleration without fine tuning or dark energy

Deser

Woodard

2019

“…Actually, the initial conditions depend on the thermal history of the Universe as shown in [18], which points out that the nonzero initial conditions should not be ignored. In this paper, we do not focus on the situation with the nonzero initial conditions.…”

Section: Numerical Analysismentioning

confidence: 99%

“…Unfortunately, the Wetterich model can not produce a viable cosmological evolution [12]. Subsequently, other forms of nonlocal modified term were put forward consecutively, such as "m 2 −1 R" [15], "R −2 R" [16][17][18], "R µν −1 R µν " [19,20], "G −1 G" [21] where G is the Gauss-Bonnet invariant (G ≡ R 2 − 4R µν R µν + R µνρσ R µνρσ ). Although these different forms of nonlocal term may produce a viable solution of the accelerated expansion of current universe to some extent, they have lost the structural simplicity.…”

Section: Introductionmentioning

confidence: 99%

Structure formation in the new Deser-Woodard nonlocal gravity model

Ding

Deng

2019

We consider the structure formation in the nonlocal gravity model proposed recently by Deser and Woodard (DW-2019 model), which can not only reproduce the ΛCDM cosmology without fine-tuning puzzle but also may provide a screening mechanism for free. By using the direct numerical method of the reconstructing technique, the nonlocal distortion153(Y −16.97) which has a small deviation with the fitted function proposed by Deser and Woodard. Based on the numerical results, we plotted the curve of the growth rate f σ 8 (z) under DW-2019 model, which shows this model is notruled out by the f σ 8 data from the Redshift-space distortions measurements. Since the source of the nonlocal scalar Y is defined as the quadratic term about the nonlocal scalar −1 R, the first-order perturbation of Y disappears. And this causes that the evolution of f σ 8 has an unnatural plummet at z 0.39, which implies that a potential phase transition appears. Finally, the qualitative analysis of the possible screening mechanism is discussed, and DW-2019 model will not be ruled out by Lunar Laser Ranging. *

“…Trying to work out a similar model at the level of the quantum effective action, rather than of the equations of motion, led to the RR model (2.46) [21], which, at least at the level of cosmology, shared all good properties of the RT model. Its cosmological solutions were studied in detail in [21][22][23] (see also [238] for a different branch of solutions). A natural generalization of the RR model is given by the quantum effective action…”

Section: Discussionmentioning

confidence: 99%

Gravity in the infrared and effective nonlocal models

Belgacem

Dirian

Finke

et al. 2020

We provide a systematic and updated discussion of a research line carried out by our group over the last few years, in which gravity is modified at cosmological distances by the introduction of nonlocal terms, assumed to emerge at an effective level from the infrared behavior of the quantum theory. The requirement of producing a viable cosmology turns out to be very stringent and basically selects a unique model, in which the nonlocal term describes an effective mass for the conformal mode. We discuss how such a specific structure could emerge from a fundamental local theory of gravity, and we perform a detailed comparison of this model with the most recent cosmological datasets, confirming that it fits current data at the same level as ΛCDM.Most notably, the model has striking predictions in the sector of tensor perturbations, leading to a very large effect in the propagation of gravitational wave (GWs) over cosmological distances. At the redshifts relevant for the next generation of GW detectors such as Einstein Telescope, Cosmic Explorer and LISA, this leads to deviations from GR that could be as large as 80%, and could be verified with the detection of just a single coalescing binary with electromagnetic counterpart. This would also have potentially important consequences for the search of the counterpart since, for a given luminosity distance to the source, as inferred through the GW signal, the actual source redshift could be significantly different from that predicted by ΛCDM. At the redshifts relevant for advanced LIGO/Virgo/Kagra the effect is smaller, but still potentially observable over a few years of runs at target sensitivity. arXiv:2001.07619v1 [astro-ph.CO] 21 Jan 2020 4 Conclusions 66 A Difficulties of alternative nonlocal models 68 -1 -2 The Lichnerowicz operator is defined by E µν,ρσ ≡ 1 2, where 2 = η µν ∂µ∂ν is the flat-space d'Alembertian. We use the signature ηµν = (−, +, +, +) and MTW [14] sign conventions. 3 We assume here 3 + 1 spacetime dimensions. See [13] for the corresponding equations in d + 1 spacetime dimensions, with d generic.