Coupled scalar per- turbations of Galileon cosmologies in the mechanical approach in the late Universe Jan Novák Coupled scalar perturbations of Galileon cosmologies in the mechanical approach in the late Universe Jan Novák Technical university in Liberec, Czech republic 18.1.2018, Srní 1 / 23
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Coupled scalar perturbations of Galileon cosmologies in ...¡k_ja… · Coupled scalar per-turbations of Galileon cosmologies in the mechanical approach in the late Universe Jan Novák
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One can assume that the dark energy is due to a new field.The other possibility is to modify the law of gravity fromgeneral relativity at large distances.
Mostly inspired by DGP models, people derived the fiveLagrangians that lead to field equations invariant under theGalilean symmetry ∂µφ→ ∂µφ+ bµ in the Minkowski spacetime:
L1 = M3φ, L2 = (∇φ)2, L3 = (φ)(∇φ)2/M3,
L4 = (∇φ)2[2(∇φ)2 − 2φ;µνφµν − R(∇φ)2/2]/M6,
L5 = (∇φ)2[(∇φ)3 − 3(φ)φ;µνφ;µν + 2φ ν
;µ φ ρ;ν φ
µ;ρ
−6φ;µφ;µνφ;ρGνρ]/M9,
The scalar field that respects the Galileon symmetry is theGalileon.
The mechanical approach works well for the ΛCDMmodel, where the peculiar velocities of the inhomogeneities couldbe considered as negligibly small, when we compare it with thespeed of light. Additionally, we consider scales deep inside thecell of uniformity. Then we can drop the peculiar velocities atthe first order of approximation.
α is a small parameter, which measure the deviationfrom the model of minimally coupled scalar field and it has unitsL3 ( L is a length). First we will compute the tensor of energymomentum for this Lagrangian by the following formula:
When we consider the mechanical approach, we candrop the terms containing the peculiar velocities of theinhomogeneities and radiation as these are negligible whencompared with their respective energy density and pressurefluctuations. If we deal with a scalar field, such an approach isnot evident since the quantity treated as the peculiar velocity ofthe scalar field is proportional to the scalar field perturbation ϕ.
As matter sources, we also include dust-like matter (baryonic andCDM) and radiation. The background (average) energy densityof the dust-like matter takes the form εDUST = ρc2/a3, whereρ = const. is the average comoving rest mass density. Forradiation we have the EoS pRAD = 1
The dust like matter component is considered in theform of discrete distributed inhomogeneities. Then we arelooking for solutions of previous equation, which have aNewtonian limit near gravitating masses. Such an asymptoticbehaviour will take place if we impose Ω = Ω(~r).
Maxim Eingorn, J.N., Alexander Zhuk, f(R) gravity: scalarperturbations in the late Universe, EPJ CMariam Bouhmadi-Lopéz, J.N., Coupled scalarperturbations of Galileon cosmologies in the mechanicalapproach in the late Universe, in preparationAlexander Zhuk, Perfect fluids coupled to inhomogeneitiesin the late UniverseAlvina Burgazli, Alexander Zhuk, João Morais, MariamBouhmadi Lopéz, K.Sravan Kumar, Coupled scalar fields inthe late Universe: The mechanical approach and the latetime cosmic accelerationMariam Bouhmadi-Lopéz, K.Sravan Kumar, João Marto,João Morais, Alexander Zhuk, K-essence model from themechanical approach point of view: coupled scalar field andthe late time cosmic acceleration
Sources of pictures: Arizona State University, Backreaction:blogger, Discovery magazine blog, NASA Getty Images, TheUniversity of Chicago, Cosmology: Brian Koberlein, New